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15 September 2024, Volume 33 Issue 9 Previous issue    Next issue

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TOPICAL REVIEW — Stephen J. Pennycook: A research life in atomic-resolution STEM and EELS

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Probing nickelate superconductors at atomic scale: A STEM review Yihan Lei(雷一涵), Yanghe Wang(王扬河), Jiahao Song(宋家豪), Jinxin Ge(葛锦昕), Dirui Wu(伍迪睿), Yingli Zhang(张英利), and Changjian Li(黎长建) Chin. Phys. B, 2024, 33 (9):  096801.  DOI: 10.1088/1674-1056/ad6a0d Abstract ( 106 )   HTML ( 1 )   PDF (1466KB) ( 186 )   The discovery of nickelate superconductors, including doped infinite-layer (IL) nickelates $R$NiO$_{2}$ ($R= {\rm La}$, Pr, Nd), layered square-planar nickelate Nd$_{6}$Ni$_{5}$O$_{12}$, and the Ruddlesden-Popper (RP) phase La$_{3}$Ni$_{2}$O$_{7}$, has spurred immense interest in fundamental research and potential applications. Scanning transmission electron microscopy (STEM) has proven crucial for understanding structure-property correlations in these diverse nickelate superconducting systems. In this review, we summarize the key findings from various modes of STEM, elucidating the mechanism of different nickelate superconductors. We also discuss future perspectives on emerging STEM techniques for unraveling the pairing mechanism in the “nickel age” of superconductivity.

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Electronic structure engineering of transition metal dichalcogenides for boosting hydrogen energy conversion electrocatalysts Bing Hao(郝兵), Jingjing Guo(郭晶晶), Peizhi Liu(刘培植), and Junjie Guo(郭俊杰) Chin. Phys. B, 2024, 33 (9):  096802.  DOI: 10.1088/1674-1056/ad625b Abstract ( 80 )   HTML ( 0 )   PDF (6646KB) ( 51 )   Electrocatalytic water splitting for hydrogen production is an appealing strategy to reduce carbon emissions and generate renewable fuels. This promising process, however, is limited by its sluggish reaction kinetics and high-cost catalysts. The two-dimensional (2D) transition metal dichalcogenides (TMDCs) have presented great potential as electrocatalytic materials due to their tunable bandgaps, abundant defective active sites, and good chemical stability. Consequently, phase engineering, defect engineering and interface engineering have been adopted to manipulate the electronic structure of TMDCs for boosting their exceptional catalytic performance. Particularly, it is essential to clarify the local structure of catalytically active sites of TMDCs and their structural evolution in catalytic reactions using atomic resolution electron microscopy and the booming in situ technologies, which is beneficial for exploring the underlying reaction mechanism. In this review, the growth regulation, characterization, particularly atomic configurations of active sites in TMDCs are summarized. The significant role of electron microscopy in the understanding of the growth mechanism, the controlled synthesis and functional optimization of 2D TMDCs are discussed. This review will shed light on the design and synthesis of novel electrocatalysts with high performance, as well as prompt the application of advanced electron microscopy in the research of materials science.

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Revealing the microstructures of metal halide perovskite thin films via advanced transmission electron microscopy Yeming Xian(冼业铭), Xiaoming Wang(王晓明), and Yanfa Yan(鄢炎发) Chin. Phys. B, 2024, 33 (9):  096803.  DOI: 10.1088/1674-1056/ad6259 Abstract ( 73 )   HTML ( 1 )   PDF (3980KB) ( 158 )   Metal halide perovskites (MHPs) are excellent semiconductors that have led to breakthroughs in applications in thin-film solar cells, detectors, and light-emitting diodes due to their remarkable optoelectronic properties and defect tolerance. However, the performance and stability of MHP-based devices are significantly influenced by their microstructures including the formation of defects, composition fluctuations, structural inhomogeneity, etc. Transmission electron microscopy (TEM) is a powerful tool for direct observation of microstructure at the atomic-scale resolution and has been used to correlate the microstructure and performance of MHP-based devices. In this review, we highlight the application of TEM techniques in revealing the microstructures of MHP thin films at the atomic scale. The results provide critical understanding of the performance of MHP devices and guide the design of strategies for improving the performance and stability of MHP devices.

SPECIAL TOPIC — Stephen J. Pennycook: A research life in atomic-resolution STEM and EELS

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Visualizing extended defects at the atomic level in a Bi2Sr2CaCu2O8+δ superconducting wire Kejun Hu(胡柯钧), Shuai Wang(王帅), Boyu Li(李泊玉), Ying Liu(刘影), Binghui Ge(葛炳辉), and Dongsheng Song(宋东升) Chin. Phys. B, 2024, 33 (9):  096101.  DOI: 10.1088/1674-1056/ad6ccd Abstract ( 75 )   HTML ( 1 )   PDF (2448KB) ( 133 )   The microstructure significantly influences the superconducting properties. Herein, the defect structures and atomic arrangements in high-temperature Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ (Bi-2212) superconducting wire are directly characterized via state-of-the-art scanning transmission electron microscopy. Interstitial oxygen atoms are observed in both the charge reservoir layers and grain boundaries in the doped superconductor. Inclusion phases with varied numbers of CuO$_{2}$ layers are found, and twist interfaces with different angles are identified. This study provides insights into the structures of Bi-2212 wire and lays the groundwork for guiding the design of microstructures and optimizing the production methods to enhance superconducting performance.

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Atomically self-healing of structural defects in monolayer WSe2 Kangshu Li(李康舒), Junxian Li(李俊贤), Xiaocang Han(韩小藏), Wu Zhou(周武), and Xiaoxu Zhao(赵晓续) Chin. Phys. B, 2024, 33 (9):  096804.  DOI: 10.1088/1674-1056/ad641f Abstract ( 67 )   HTML ( 0 )   PDF (1554KB) ( 46 )   Minimizing disorder and defects is crucial for realizing the full potential of two-dimensional transition metal dichalcogenides (TMDs) materials and improving device performance to desired properties. However, the methods in defect control currently face challenges with overly large operational areas and a lack of precision in targeting specific defects. Therefore, we propose a new method for the precise and universal defect healing of TMD materials, integrating real-time imaging with scanning transmission electron microscopy (STEM). This method employs electron beam irradiation to stimulate the diffusion migration of surface-adsorbed adatoms on TMD materials grown by low-temperature molecular beam epitaxy (MBE), and heal defects within the diffusion range. This approach covers defect repairs ranging from zero-dimensional vacancy defects to two-dimensional grain orientation alignment, demonstrating its universality in terms of the types of samples and defects. These findings offer insights into the use of atomic-level focused electron beams at appropriate voltages in STEM for defect healing, providing valuable experience for achieving atomic-level precise fabrication of TMD materials.

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Multiphase cooperation for multilevel strain accommodation in a single-crystalline BiFeO3 thin film Wooseon Choi, Bumsu Park, Jaejin Hwang, Gyeongtak Han, Sang-Hyeok Yang, Hyeon Jun Lee, Sung Su Lee, Ji Young Jo, Albina Y. Borisevich, Hu Young Jeong, Sang Ho Oh, Jaekwang Lee, and Young-Min Kim Chin. Phys. B, 2024, 33 (9):  096805.  DOI: 10.1088/1674-1056/ad62e0 Abstract ( 71 )   HTML ( 0 )   PDF (2024KB) ( 38 )   The functionalities and diverse metastable phases of multiferroic BiFeO$_{3}$ (BFO) thin films depend on the misfit strain. Although mixed phase-induced strain relaxation in multiphase BFO thin films is well known, it is unclear whether a single-crystalline BFO thin film can accommodate misfit strain without the involvement of its polymorphs. Thus, understanding the strain relaxation behavior is key to elucidating the lattice strain-property relationship. In this study, a correlative strain analysis based on dark-field inline electron holography (DIH) and quantitative scanning transmission electron microscopy (STEM) was performed to reveal the structural mechanism for strain accommodation of a single-crystalline BFO thin film. The nanoscale DIH strain analysis results indicated a random combination of multiple strain states that acted as a primary strain relief, forming irregularly strained nanodomains. The STEM-based bond length measurement of the corresponding strained nanodomains revealed a unique strain accommodation behavior achieved by a statistical combination of multiple modes of distorted structures on the unit-cell scale. The globally integrated strain for each nanodomain was estimated to be close to $-1.5%$, irrespective of the nanoscale strain states, which was consistent with the fully strained BFO film on the SrTiO$_{3}$ substrate. Density functional theory calculations suggested that strain accommodation by the combination of metastable phases was energetically favored compared to single-phase-mediated relaxation. This discovery allows a comprehensive understanding of strain accommodation behavior in ferroelectric oxide films, such as BFO, with various low-symmetry polymorphs.

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Multidimensional images and aberrations in STEM Eric R. Hoglund and Andrew R. Lupini Chin. Phys. B, 2024, 33 (9):  096807.  DOI: 10.1088/1674-1056/ad73b2 Abstract ( 65 )   HTML ( 0 )   PDF (2083KB) ( 41 )   Recent advances in scanning transmission electron microscopy (STEM) have led to increased development of multi-dimensional STEM imaging modalities and novel image reconstruction methods. This interest arises because the main electron lens in a modern transmission electron microscope usually has a diffraction-space information limit that is significantly better than the real-space resolution of the same lens. This state-of-affairs is sometimes shared by other scattering methods in modern physics and contributes to a broader excitement surrounding multidimensional techniques that scan a probe while recording diffraction-space images, such as ptychography and scanning nano-beam diffraction. However, the contrasting resolution in the two spaces raises the question as to what is limiting their effective performance. Here, we examine this paradox by considering the effects of aberrations in both image and diffraction planes, and likewise separate the contributions of pre- and post-sample aberrations. This consideration provides insight into aberration-measurement techniques and might also indicate improvements for super-resolution techniques.

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A large language model-powered literature review for high-angle annular dark field imaging Wenhao Yuan(袁文浩), Cheng Peng(彭程), and Qian He(何迁) Chin. Phys. B, 2024, 33 (9):  098703.  DOI: 10.1088/1674-1056/ad625c Abstract ( 92 )   HTML ( 0 )   PDF (1248KB) ( 116 )   High-angle annular dark field (HAADF) imaging in scanning transmission electron microscopy (STEM) has become an indispensable tool in materials science due to its ability to offer sub-Å resolution and provide chemical information through Z-contrast. This study leverages large language models (LLMs) to conduct a comprehensive bibliometric analysis of a large amount of HAADF-related literature (more than 41000 papers). By using LLMs, specifically ChatGPT, we were able to extract detailed information on applications, sample preparation methods, instruments used, and study conclusions. The findings highlight the capability of LLMs to provide a new perspective into HAADF imaging, underscoring its increasingly important role in materials science. Moreover, the rich information extracted from these publications can be harnessed to develop AI models that enhance the automation and intelligence of electron microscopes.

TOPICAL REVIEW — Quantum computing and quantum sensing

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Approximate constructions of counterdiabatic driving with NMR quantum systems Hui Zhou(周辉), Xiaoli Dai(代晓莉), Jianpei Geng(耿建培), Yunlan Ji(季云兰), and Xinhua Peng(彭新华) Chin. Phys. B, 2024, 33 (9):  090301.  DOI: 10.1088/1674-1056/ad58b2 Abstract ( 120 )   HTML ( 0 )   PDF (1473KB) ( 58 )   Counterdiabatic driving (CD) offers a fast and robust route to manipulate quantum systems, which has widespread applications in quantum technologies. However, for higher-dimensional complex systems, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form, impeding its experimental realization. Recently, many approximate methods have been proposed for designing CD passages in many-body systems. In this topical review, we focus on the CD formalism and briefly introduce several experimental constructions and applications of approximate CD driving in spin-chain models with nuclear magnetic resonance (NMR) systems.

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Compact magneto-optical traps using planar optics Zhi Tan(谭智), Bo Lu(鹿博), Chengyin Han(韩成银), and Chaohong Lee(李朝红) Chin. Phys. B, 2024, 33 (9):  093701.  DOI: 10.1088/1674-1056/ad607a Abstract ( 161 )   HTML ( 2 )   PDF (4682KB) ( 155 )   Magneto-optical traps (MOTs) composed of magnetic fields and light fields have been widely utilized to cool and confine microscopic particles. Practical technology applications require miniaturized MOTs. The advancement of planar optics has promoted the development of compact MOTs. In this article, we review the development of compact MOTs based on planar optics. First, we introduce the standard MOTs. We then introduce the grating MOTs with micron structures, which have been used to build cold atomic clocks, cold atomic interferometers, and ultra-cold sources. Further, we introduce the integrated MOTs based on nano-scale metasurfaces. These new compact MOTs greatly reduce volume and power consumption, and provide new opportunities for fundamental research and practical applications.

SPECIAL TOPIC — Quantum computing and quantum sensing

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A quantum-enhanced magnetometer using a single high-spin nucleus in silicon Tao Xin(辛涛), Ke Zhang(张科), and Jun Li(李俊) Chin. Phys. B, 2024, 33 (9):  090302.  DOI: 10.1088/1674-1056/ad5a75 Abstract ( 76 )   HTML ( 0 )   PDF (947KB) ( 100 )   Quantum enhanced metrology has the potential to go beyond the standard quantum limit and eventually to the ultimate Heisenberg bound. In particular, quantum probes prepared in nonclassical coherent states have recently been recognized as a useful resource for metrology. Hence, there has been considerable interest in constructing magnetic quantum sensors that combine high resolution and high sensitivity. Here, we explore a nanoscale magnetometer with quantum-enhanced sensitivity, based on $^{123}$Sb ($I=7/2$) nuclear spin doped in silicon, that takes advantage of techniques of spin-squeezing and coherent control. With the optimal squeezed initial state, the magnetic field sensitivity may be expected to approach 6 aT$\cdot $Hz$^{-1/2}\cdot$cm$^{-3/2}$ and 603 nT$\cdot $Hz$^{-1/2}$ at the single-spin level. This magnetic sensor may provide a novel sensitive and high-resolution route to microscopic mapping of magnetic fields as well as other applications.

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Correction of microwave pulse reflection by digital filters in superconducting quantum circuits Liang-Liang Guo(郭亮亮), Peng Duan(段鹏), Lei Du(杜磊), Hai-Feng Zhang(张海峰), Hao-Ran Tao(陶浩然), Yong Chen(陈勇), Xiao-Yan Yang(杨小燕), Chi Zhang(张驰), Zhi-Long Jia(贾志龙), Wei-Cheng Kong(孔伟成), Zhao-Yun Chen(陈昭昀), and Guo-Ping Guo(郭国平) Chin. Phys. B, 2024, 33 (9):  090303.  DOI: 10.1088/1674-1056/ad5d98 Abstract ( 110 )   HTML ( 0 )   PDF (877KB) ( 111 )   Reducing the control error is vital for high-fidelity digital and analog quantum operations. In superconducting circuits, one disagreeable error arises from the reflection of microwave signals due to impedance mismatch in the control chain. Here, we demonstrate a reflection cancelation method when considering that there are two reflection nodes on the control line. We propose to generate the pre-distortion pulse by passing the envelopes of the microwave signal through digital filters, which enables real-time reflection correction when integrated into the field-programmable gate array (FPGA). We achieve a reduction of single-qubit gate infidelity from 0.67% to 0.11% after eliminating microwave reflection. Real-time correction of microwave reflection paves the way for precise control and manipulation of the qubit state and would ultimately enhance the performance of algorithms and simulations executed on quantum processors.

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Delayed-measurement one-way quantum computing on cloud quantum computer Zhi-Peng Yang(杨智鹏), Yu-Ran Zhang(张煜然), Fu-Li Li(李福利), and Heng Fan(范桁) Chin. Phys. B, 2024, 33 (9):  090304.  DOI: 10.1088/1674-1056/ad6253 Abstract ( 84 )   HTML ( 0 )   PDF (1059KB) ( 99 )   One-way quantum computation focuses on initially generating an entangled cluster state followed by a sequence of measurements with classical communication of their individual outcomes. Recently, a delayed-measurement approach has been applied to replace classical communication of individual measurement outcomes. In this work, by considering the delayed-measurement approach, we demonstrate a modified one-way CNOT gate using the on-cloud superconducting quantum computing platform: Quafu. The modified protocol for one-way quantum computing requires only three qubits rather than the four used in the standard protocol. Since this modified cluster state decreases the number of physical qubits required to implement one-way computation, both the scalability and complexity of the computing process are improved. Compared to previous work, this modified one-way CNOT gate is superior to the standard one in both fidelity and resource requirements. We have also numerically compared the behavior of standard and modified methods in large-scale one-way quantum computing. Our results suggest that in a noisy intermediate-scale quantum (NISQ) era, the modified method shows a significant advantage for one-way quantum computation.

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In-situ deposited anti-aging TiN capping layer for Nb superconducting quantum circuits Hao-Ran Tao(陶浩然), Lei Du(杜磊), Liang-Liang Guo(郭亮亮), Yong Chen(陈勇), Hai-Feng Zhang(张海峰), Xiao-Yan Yang(杨小燕), Guo-Liang Xu(徐国良), Chi Zhang(张 驰), Zhi-Long Jia(贾志龙), Peng Duan(段鹏), and Guo-Ping Guo(郭国平) Chin. Phys. B, 2024, 33 (9):  090310.  DOI: 10.1088/1674-1056/ad6a3c Abstract ( 66 )   HTML ( 0 )   PDF (823KB) ( 40 )   The performance of Nb superconducting quantum devices is predominantly limited by dielectric loss at the metal-air interface, where Nb$_2$O$_5$ is considered the main loss source. Here, we suppress the formation of native oxides by in-situ deposition of a TiN capping layer on the Nb film. With TiN capping layers, no Nb$_2$O$_5$ forms on the surface of the Nb film. The quality factor $Q_{\rm i}$ of the Nb resonator increases from $5.6\times10^{5}$ to $7.9\times10^{5}$ at low input power and from $6.8\times10^{6}$ to $1.1\times10^{7}$ at high input power. Furthermore, the TiN capping layer also shows good aging resistance in Nb resonator devices, with no significant performance fluctuations after one month of aging. These findings highlight the effectiveness of TiN capping layers in enhancing the performance and longevity of Nb superconducting quantum devices.

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Coupling and characterization of a Si/SiGe triple quantum dot array with a microwave resonator Shun-Li Jiang(江顺利), Tian-Yi Jiang(蒋天翼), Yong-Qiang Xu(徐永强), Rui Wu(吴睿), Tian-Yue Hao(郝天岳), Shu-Kun Ye(叶澍坤), Ran-Ran Cai(蔡冉冉), Bao-Chuan Wang(王保传), Hai-Ou Li(李海欧), Gang Cao(曹刚), and Guo-Ping Guo(郭国平) Chin. Phys. B, 2024, 33 (9):  090311.  DOI: 10.1088/1674-1056/ad711d Abstract ( 73 )   HTML ( 3 )   PDF (5749KB) ( 44 )   Scaling up spin qubits in silicon-based quantum dots is one of the pivotal challenges in achieving large-scale semiconductor quantum computation. To satisfy the connectivity requirements and reduce the lithographic complexity, utilizing the qubit array structure and the circuit quantum electrodynamics (cQED) architecture together is expected to be a feasible scaling scheme. A triple-quantum dot (TQD) coupled with a superconducting resonator is regarded as a basic cell to demonstrate this extension scheme. In this article, we investigate a system consisting of a silicon TQD and a high-impedance TiN coplanar waveguide (CPW) resonator. The TQD can couple to the resonator via the right double-quantum dot (RDQD), which reaches the strong coupling regime with a charge-photon coupling strength of ${g_0}/({2\pi})=175$ ${\rm MHz}$. Moreover, we illustrate the high tunability of the TQD through the characterization of stability diagrams, quadruple points (QPs), and the quantum cellular automata (QCA) process. Our results contribute to fostering the exploration of silicon-based qubit integration.

DATA PAPER

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Single crystal growth and characterization of 166-type magnetic kagome metals Huangyu Wu(吴黄宇), Jinjin Liu(刘锦锦), Yongkai Li(李永恺), Peng Zhu(朱鹏), Liu Yang(杨柳), Fuhong Chen(陈富红), Deng Hu(胡灯), and Zhiwei Wang(王秩伟) Chin. Phys. B, 2024, 33 (9):  098101.  DOI: 10.1088/1674-1056/ad553b Abstract ( 115 )   HTML ( 1 )   PDF (895KB) ( 137 )   Kagome magnets were predicted to be a good platform to investigate correlated topology band structure, Chern quantum phase, and geometrical frustration due to their unique lattice geometry. Here we reported single crystal growth of 166-type kagome magnetic materials, including HfMn$_{6}$Sn$_{6}$, ZrMn$_{6}$Sn$_{6}$, GdMn$_{6}$Sn$_{6}$ and GdV$_{6}$Sn$_{6}$, by using the flux method with Sn as the flux. Among them, HfMn$_{6}$Sn$_{6}$ and ZrMn$_{6}$Sn$_{6}$ single crystals were grown for the first time. X-ray diffraction measurements reveal that all four samples crystallize in HfFe$_{6}$Ge$_{6}$-type hexagonal structure with space group P6/mmm. All samples show metallic behavior from temperature dependence of resistivity measurements, and the dominant carrier is hole, except for GdV$_{6}$Sn$_{6}$ which is electron dominated. All samples have magnetic order with different transition temperatures, HfMn$_{6}$Sn$_{6}$, ZrMn$_{6}$Sn$_{6}$ and GdV$_{6}$Sn$_{6}$ are antiferromagnetic with $T_{\rm N}$ of 541 K, 466 K and 4 K respectively, while GdMn$_{6}$Sn$_{6}$ is ferrimagnetic with the critical temperature of about 470 K. This study will enrich the research platform of magnetic kagome materials and help explore the novel quantum phenomena in these interesting materials. The dataset of specific crystal structure parameters for HfMn$_{6}$Sn$_{6}$ are available in Science Data Bank, with the link https://doi.org/10.57760/sciencedb.j00113.00120.

INSTRUMENTATION AND MEASUREMENT

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Frequency-modulated continuous-wave multiplexed gas sensing based on optical frequency comb calibration Linhua Jia(贾琳华), Xinghua Qu(曲兴华), and Fumin Zhang (张福民) Chin. Phys. B, 2024, 33 (9):  094201.  DOI: 10.1088/1674-1056/ad5980 Abstract ( 88 )   HTML ( 0 )   PDF (3675KB) ( 36 )   Laser absorption spectroscopy has proven to be an effective approach for gas sensing, which plays an important role in the fields of military, industry, medicine and basic research. This paper presents a multiplexed gas sensing system based on optical frequency comb (OFC) calibrated frequency-modulated continuous-wave (FMCW) tuning nonlinearity. The system can be used for multi-parameter synchronous measurement of gas absorption spectrum and multiplexed optical path. Multi-channel parallel detection is realized by combining wavelength division multiplexing (WDM) and frequency division multiplexing (FDM) techniques. By introducing nonlinear optical crystals, broadband spectrum detection is simultaneously achieved over a bandwidth of hundreds of nanometers. An OFC with ultra-high frequency stability is used as the frequency calibration source, which guarantees the measurement accuracy. The test samples involve H$^{13}$C$^{14}$N, C$_{2}$H$_{2}$ and Rb vapor cells of varying densities and 5 parallel measurement experiments are designed. The results show that the measurement accuracies of spectral absorption line and the optical path are 150 MHz and 20 μm, respectively. The scheme offers the advantages of multiplexed, multi-parameter, wide spectrum and high resolution detection, which can realize the identification of multi-gas components and the high-precision inversion of absorption lines under different environments. The proposed sensor demonstrates great potential in the field of high-resolution absorption spectrum measurement for gas sensing applications.

REVIEW

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Diamond-based electron emission: Structure, properties and mechanisms Liang-Xue Gu(顾梁雪), Kai Yang(杨凯), Yan Teng(滕妍), Wei-Kang Zhao(赵伟康), Geng-You Zhao(赵耕右), Kang-Kang Fan(凡康康), Bo Feng(冯博), Rong Zhang(张荣), You-Dou Zheng(郑有炓), Jian-Dong Ye(叶建东), Shun-Ming Zhu(朱顺明), Kun Tang(汤琨), and Shu-Lin Gu(顾书林) Chin. Phys. B, 2024, 33 (9):  098102.  DOI: 10.1088/1674-1056/ad5aec Abstract ( 110 )   HTML ( 0 )   PDF (3942KB) ( 102 )   Diamond has an ultrawide bandgap with excellent physical properties, such as high critical electric field, excellent thermal conductivity, high carrier mobility, etc. Diamond with a hydrogen-terminated (H-terminated) surface has a negative elaffinity (NEA) and can easily produce surface electrons from valence or trapped electrons via optical absorption, thermal heating energy or carrier transport in a PN junction. The NEA of the H-terminated surface enables surface electrons to emit with high efficiency into the vacuum without encountering additional barriers and promotes further development and application of diamond-based emitting devices. This article reviews the electron emission properties of H-terminated diamond surfaces exhibiting NEA characteristics. The electron emission is induced by different physical mechanisms. Recent advancements in electron-emitting devices based on diamond are also summarized. Finally, the current challenges and future development opportunities are discussed to further develop the relevant applications of diamond-based electron-emitting devices.

RAPID COMMUNICATION

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Imaging a force field via an optically levitated nanoparticle array Hot! Bihu Lv(吕碧沪), Jiandong Zhang(张建东), and Chuang Li(李闯) Chin. Phys. B, 2024, 33 (9):  090702.  DOI: 10.1088/1674-1056/ad6b86 Abstract ( 118 )   HTML ( 1 )   PDF (655KB) ( 97 )   Levitated optomechanical systems represent an excellent candidate platform for force and acceleration sensing. We propose a force-sensing protocol utilizing an optically levitated nanoparticle array. In our scheme, $N$ nanoparticles are trapped in an optical cavity using holographic optical tweezers. An external laser drives the cavity, exciting $N$ cavity modes interacting simultaneously with the $N$ nanoparticles. The optomechanical interaction encodes the information of the force acting on each nanoparticle onto the intracavity photons, which can be detected directly at the output ports of the cavity. Consequently, our protocol enables real-time imaging of a force field.

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Simultaneous control of ferromagnetism and ferroelasticity by oxygen octahedral backbone stretching Hot! Genhao Liang(梁根豪), Hui Cao(曹慧), Long Cheng(成龙), Junkun Zha(查君坤), Mingrui Bao(保明睿), Fei Ye(叶飞), Hua Zhou(周华), Aidi Zhao(赵爱迪), and Xiaofang Zhai(翟晓芳) Chin. Phys. B, 2024, 33 (9):  097101.  DOI: 10.1088/1674-1056/ad553c Abstract ( 146 )   HTML ( 0 )   PDF (2571KB) ( 68 )   Coexistence of ferromagnetism and ferroelasticity in a single material is an intriguing phenomenon, but has been rarely found. Here we studied both the ferromagnetism and ferroelasticity in a group of LaCoO$_{3}$ films with systematically tuned atomic structures. We found that all films exhibit ferroelastic domains with four-fold symmetry and the larger domain size (higher elasticity) is always accompanied by stronger ferromagnetism. We performed synchrotron x-ray diffraction studies to investigate the backbone structure of the CoO$_{6}$ octahedra, and found that both the ferromagnetism and the elasticity are simultaneously enhanced when the in-plane Co-O-Co bond angles are straightened. Therefore the study demonstrates the inextricable correlation between the ferromagnetism and ferroelasticity mediated through the octahedral backbone structure, which may open up new possibilities to develop multifunctional materials.

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Alternating spin splitting of electronic and magnon bands in two-dimensional altermagnetic materials Hot! Qian Wang(王乾), Da-Wei Wu(邬大为), Guang-Hua Guo(郭光华), Meng-Qiu Long(龙孟秋), and Yun-Peng Wang(王云鹏) Chin. Phys. B, 2024, 33 (9):  097507.  DOI: 10.1088/1674-1056/ad6425 Abstract ( 179 )   HTML ( 7 )   PDF (1362KB) ( 207 )   Unconventional antiferromagnetism dubbed as altermagnetism was first discovered in rutile structured magnets, which is featured by spin splitting even without the spin-orbital coupling effect. This interesting phenomenon has been discovered in more altermagnetic materials. In this work, we explore two-dimensional altermagnetic materials by studying two series of two-dimensional magnets, including $M\mathrm{F_4}$ with $M$ covering all 3d and 4d transition metal elements, as well as $T\mathrm{S_2}$ with $T = {\rm V}$, Cr, Mn, Fe. Through the magnetic symmetry operation of RuF$_4$ and MnS$_2$, it is verified that breaking the time inversion is a necessary condition for spin splitting. Based on symmetry analysis and first-principles calculations, we find that the electronic bands and magnon dispersion experience alternating spin splitting along the same path. This work paves the way for exploring altermagnetism in two-dimensional materials.

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Dzyaloshinskii-Moriya interaction and field-free sub-10 nm topological magnetism in Fe/bismuth oxychalcogenides heterostructures Hot! Yaoyuan Wang(王垚元), Long You(游龙), Kai Chang(常凯), and Hongxin Yang(杨洪新) Chin. Phys. B, 2024, 33 (9):  097508.  DOI: 10.1088/1674-1056/ad6a0e Abstract ( 118 )   HTML ( 1 )   PDF (2033KB) ( 128 )   Topological magnetism with strong robustness, nanoscale dimensions and ultralow driving current density ($\sim 10^{6}$ A/m$^{2}$) is promising for applications in information sensing, storage, and processing, and thus sparking widespread research interest. Exploring candidate material systems with nanoscale size and easily tunable properties is a key for realizing practical topological magnetism-based spintronic devices. Here, we propose a class of ultrathin heterostructures, Fe/Bi$_{2}$O$_{2}X$ ($X ={\rm S}$, Se, Te) by deposing metal Fe on quasi-two-dimensional (2D) bismuth oxychalcogenides Bi$_{2}$O$_{2}X$ ($X ={\rm S}$, Se, Te) with excellent ferroelectric/ferroelastic properties. Large Dzyaloshinskii-Moriya interaction (DMI) and topological magnetism can be realized. Our atomistic spin dynamics simulations demonstrate that field-free vortex-antivortex loops and sub-10 nm skyrmions exist in Fe/Bi$_{2}$O$_{2}$S and Fe/Bi$_{2}$O$_{2}$Se interfaces, respectively. These results provide a possible strategy to tailor topological magnetism in ultrathin magnets/2D materials interfaces, which is extremely vital for spintronics applications.

GENERAL

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Riemann-Hilbert problem for the defocusing Lakshmanan-Porsezian-Daniel equation with fully asymmetric nonzero boundary conditions Jianying Ji(纪建英) and Xiyang Xie(解西阳) Chin. Phys. B, 2024, 33 (9):  090201.  DOI: 10.1088/1674-1056/ad5af2 Abstract ( 88 )   HTML ( 0 )   PDF (621KB) ( 114 )   The Riemann-Hilbert approach is demonstrated to investigate the defocusing Lakshmanan-Porsezian-Daniel equation under fully asymmetric nonzero boundary conditions. In contrast to the symmetry case, this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces. For the direct problem, we analyze the Jost solution of lax pairs and some properties of scattering matrix, including two kinds of symmetries. The inverse problem at branch points can be presented, corresponding to the associated Riemann-Hilbert. Moreover, we investigate the time evolution problem and estimate the value of solving the solutions by Jost function. For the inverse problem, we construct it as a Riemann-Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan-Porsezian-Daniel equation. The solutions of the Riemann-Hilbert problem can be constructed by estimating the solutions. Finally, we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski-Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces. These results are valuable for understanding physical phenomena and developing further applications of optical problems.

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Different topological phase transitions in the Su-Schrieffer-Heeger model under different disorder structures Yan Gu(古燕) and Zhanpeng Lu(陆展鹏) Chin. Phys. B, 2024, 33 (9):  090202.  DOI: 10.1088/1674-1056/ad59fb Abstract ( 95 )   HTML ( 0 )   PDF (728KB) ( 102 )   We investigate the topological phase transition in the Su-Schrieffer-Heeger model with the long-range hopping and quasi-periodic modulation. By numerically calculating the real-space winding number, we obtain topological phase diagrams for different disordered structures. These diagrams suggest that topological phase transitions are different by selecting the specific disordered structure. When quasi-periodic modulation is applied to intracell hopping, the resulting disorder induces topological Anderson insulator (TAI) phase with high winding number ($W=2$), but the topological states are destroyed as the disorder increases. Conversely, when intercell hoppings are modulated quasi-periodically, both TAI phase and the process of destruction and restoration of topological zero modes can be induced by disorder. These topological states remain robust even under strong disorder conditions. Our work demonstrates that disorder effects do not always disrupt topological states; rather, with a judicious selection of disordered structures, topological properties can be preserved.

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Dynamic properties of rumor propagation model induced by Lévy noise on social networks Ying Jing(景颖), Youguo Wang(王友国), Qiqing Zhai(翟其清), and Xianli Sun(孙先莉) Chin. Phys. B, 2024, 33 (9):  090203.  DOI: 10.1088/1674-1056/ad58c5 Abstract ( 88 )   HTML ( 0 )   PDF (1688KB) ( 28 )   Social networks are inevitably subject to disruptions from the physical world, such as sudden internet outages that sever local connections and impede information flow. While Gaussian white noise, commonly used to simulate stochastic disruptions, only fluctuates within a narrow range around its mean and fails to capture large-scale variations, Lévy noise can effectively compensate for this limitation. Therefore, a susceptible-infected-removed rumor propagation model with Lévy noise is constructed on homogeneous and heterogeneous networks, respectively. Then, the existence of a global positive solution and the asymptotic path-wise of the solution are derived on heterogeneous networks, and the sufficient conditions of rumor extinction and persistence are investigated. Subsequently, theoretical results are verified through numerical calculations and the sensitivity analysis related to the threshold is conducted on the model parameters. Through simulation experiments on Watts-Strogatz (WS) and Barabási-Albert networks, it is found that the addition of noise can inhibit the spread of rumors, resulting in a stochastic resonance phenomenon, and the optimal noise intensity is obtained on the WS network. The validity of the model is verified on three real datasets by particle swarm optimization algorithm.

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Effect of distribution of fines on evolution of cooperation in spatial public goods game Xing-Ping Sun(孙兴平), Yan-Zheng Bi(毕研政), Hong-Wei Kang(康洪炜), Yong Shen(沈勇), and Qing-Yi Chen(陈清毅) Chin. Phys. B, 2024, 33 (9):  090204.  DOI: 10.1088/1674-1056/ad5aee Abstract ( 71 )   HTML ( 0 )   PDF (2240KB) ( 79 )   In the realm of public goods game, punishment, as a potent tool, stands out for fostering cooperation. While it effectively addresses the first-order free-rider problem, the associated costs can be substantial. Punishers incur expenses in imposing sanctions, while defectors face fines. Unfortunately, these monetary elements seemingly vanish into thin air, representing a loss to the system itself. However, by virtue of the redistribution of fines to cooperators and punishers, not only can we mitigate this loss, but the rewards for these cooperative individuals can be enhanced. Based upon this premise, this paper introduces a fine distribution mechanism to the traditional pool punishment model. Under identical parameter settings, by conducting a comparative experiment with the conventional punishment model, the paper aims to investigate the impact of fine distribution on the evolution of cooperation in spatial public goods game. The experimental results clearly demonstrate that, in instances where the punishment cost is prohibitively high, the cooperative strategies of the traditional pool punishment model may completely collapse. However, the model enriched with fine distribution manages to sustain a considerable number of cooperative strategies, thus highlighting its effectiveness in promoting and preserving cooperation, even in the face of substantial punishment cost.

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Evolutionary dynamics of tax-based strong altruistic reward and punishment in a public goods game Zhi-Hao Yang(杨智昊) and Yan-Long Yang(杨彦龙) Chin. Phys. B, 2024, 33 (9):  090205.  DOI: 10.1088/1674-1056/ad5274 Abstract ( 70 )   HTML ( 0 )   PDF (512KB) ( 13 )   In public goods games, punishments and rewards have been shown to be effective mechanisms for maintaining individual cooperation. However, punishments and rewards are costly to incentivize cooperation. Therefore, the generation of costly penalties and rewards has been a complex problem in promoting the development of cooperation. In real society, specialized institutions exist to punish evil people or reward good people by collecting taxes. We propose a strong altruistic punishment or reward strategy in the public goods game through this phenomenon. Through theoretical analysis and numerical calculation, we can get that tax-based strong altruistic punishment (reward) has more evolutionary advantages than traditional strong altruistic punishment (reward) in maintaining cooperation and tax-based strong altruistic reward leads to a higher level of cooperation than tax-based strong altruistic punishment.

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Non-monotonic behavior of jam probability and stretched exponential distribution in pedestrian counterflow Ze-Hao Chen(陈泽昊), Zhi-Xi Wu(吴枝喜), and Jian-Yue Guan(关剑月) Chin. Phys. B, 2024, 33 (9):  090206.  DOI: 10.1088/1674-1056/ad57ab Abstract ( 279 )   HTML ( 0 )   PDF (611KB) ( 23 )   We adopt a floor field cellular automata model to study the statistical properties of bidirectional pedestrian flow moving in a straight corridor. We introduce a game-theoretic framework to deal with the conflict of multiple pedestrians trying to move to the same target location. By means of computer simulations, we show that the complementary cumulative distribution of the time interval between two consecutive pedestrians leaving the corridor can be fitted by a stretched exponential distribution, and surprisingly, the statistical properties of the two types of pedestrian flows are affected differently by the flow ratio, i.e., the ratio of the pedestrians walking toward different directions. We also find that the jam probability exhibits a non-monotonic behavior with the flow ratio, where the worst performance arises at an intermediate flow ratio of around 0.2. Our simulation results are consistent with some empirical observations, which suggest that the peculiar characteristics of the pedestrians may attributed to the anticipation mechanism of collision avoidance.

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Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrödinger equation with sextic operator under non-zero boundary conditions Hot! Luyao Zhang(张路瑶) and Xiyang Xie(解西阳) Chin. Phys. B, 2024, 33 (9):  090207.  DOI: 10.1088/1674-1056/ad6258 Abstract ( 214 )   HTML ( 5 )   PDF (1315KB) ( 274 )   We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrödinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses on the dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions under non-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole or double-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and the spatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons, we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions. In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle” crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one and two dark solitons.

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New approach to measuring topological phase transitions utilizing Floquet technology Hot! Xue-Ying Yang(杨雪滢), Wei Wu(吴伟), and Ping-Xing Chen(陈平形) Chin. Phys. B, 2024, 33 (9):  090305.  DOI: 10.1088/1674-1056/ad5d94 Abstract ( 113 )   HTML ( 4 )   PDF (19382KB) ( 98 )   The Floquet technique provides a novel anomalous topological phase for non-equilibrium phase transitions. Based on the high symmetry of the quantum anomalous Hall model, the findings suggest a one-to-one correspondence between the average spin texture and the Floquet quasi-energy spectrum. A new approach is proposed to directly measure the quasi-energy spectrum, replacing previous measurements of the average spin texture. Finally, we proposed a reliable experimental scheme based on ion trap platforms. This scheme markedly reduces the measurement workload, improves the measurement fidelity, and is applicable to multiple platforms such as cold atoms and nuclear magnetic resonance.

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Preparation of entangled W states based on the cavity QED system Ke Li(李可) and Jun-Long Zhao(赵军龙) Chin. Phys. B, 2024, 33 (9):  090306.  DOI: 10.1088/1674-1056/ad50bf Abstract ( 65 )   HTML ( 2 )   PDF (603KB) ( 17 )   We present a qubit-loss-free (QLF) fusion scheme for generating large-scale atom W states in cavity quantum electrodynamics (QED) system. Compared to the most current fusion schemes which are conditioned on the case where one particle can be extracted from each initial W state to the fusion process, our scheme will access one or two particles from each W state. Based on the atom-cavity-field detuned interaction, three $|W\rangle_{n+m+t}$ states can be generated from the $|W\rangle_n$, $|W\rangle_m$, and $|W\rangle_t$ states with the help of two auxiliary atoms, and three $|W\rangle_{n+m+t+q}$ states can be generated from $|W\rangle_n$, $|W\rangle_m$, $|W\rangle_t$, and a $|W\rangle_q$ state with the help of three auxiliary atoms. Comparing the numerical simulations of the resource cost of fusing three small-size W states based on the previous schemes, our fusion scheme seems to be more efficient. This QLF fusion scheme can be generalized to the case of fusing $k$ different or identical particle W states. Furthermore, with no qubit loss, it greatly reduces the number of fusion steps and prepares W states with larger particle numbers.

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Variational data encoding and correlations in quantum-enhanced machine learning Ming-Hao Wang(王明浩) and Hua Lü(吕桦) Chin. Phys. B, 2024, 33 (9):  090307.  DOI: 10.1088/1674-1056/ad5c3b Abstract ( 76 )   HTML ( 0 )   PDF (1256KB) ( 78 )   Leveraging the extraordinary phenomena of quantum superposition and quantum correlation, quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers. This paper tackles two pivotal challenges in the realm of quantum computing: firstly, the development of an effective encoding protocol for translating classical data into quantum states, a critical step for any quantum computation. Different encoding strategies can significantly influence quantum computer performance. Secondly, we address the need to counteract the inevitable noise that can hinder quantum acceleration. Our primary contribution is the introduction of a novel variational data encoding method, grounded in quantum regression algorithm models. By adapting the learning concept from machine learning, we render data encoding a learnable process. This allowed us to study the role of quantum correlation in data encoding. Through numerical simulations of various regression tasks, we demonstrate the efficacy of our variational data encoding, particularly post-learning from instructional data. Moreover, we delve into the role of quantum correlation in enhancing task performance, especially in noisy environments. Our findings underscore the critical role of quantum correlation in not only bolstering performance but also in mitigating noise interference, thus advancing the frontier of quantum computing.

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Generation of macroscopic entanglement in ensemble systems based on silicon vacancy centers Jian-Zhuang Wu(武建壮), Ying Xi(奚滢), Bo-Ya Li(李博雅), Lian-E Lu(芦连娥), and Yong-Hong Ma(马永红) Chin. Phys. B, 2024, 33 (9):  090308.  DOI: 10.1088/1674-1056/ad5d93 Abstract ( 64 )   HTML ( 0 )   PDF (704KB) ( 11 )   Entanglement in macroscopic systems, as a fundamental quantum resource, has been utilized to propel the advancement of quantum technology and probe the boundary between the quantum and classical realms. This study focuses on a unique hybrid quantum system comprising of an ensemble of silicon vacancy (SiV) centers coupled to phononic waveguides in diamond via strain interactions. By employing two sets of time-dependent, non-overlapping driving fields, we investigate the generation process and dynamic properties of macroscopic quantum entanglement, providing fresh insights into the behavior of such hybrid quantum systems. Furthermore, it paves the way for new possibilities in utilizing quantum entanglement as an information carrier in quantum information processing and quantum communication.

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Phase diagram and quench dynamics of a periodically driven Haldane model Minxuan Ren(任民烜), Han Yang(杨焓), and Mingyuan Sun(孙明远) Chin. Phys. B, 2024, 33 (9):  090309.  DOI: 10.1088/1674-1056/ad4eb3 Abstract ( 84 )   HTML ( 1 )   PDF (4961KB) ( 28 )   We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function. By using the Floquet theory, we obtain the topological phase diagram of the system. We also find that anomalous Floquet topological phases exist in the system. Focusing on examining the quench dynamics among topological phases, we analyze the site distribution of the $0$-mode and $\pi$-mode edge states in long-period evolution after a quench. The results demonstrate that, under certain conditions, the site distribution of the $0$-mode can be confined at the edge even in long-period evolution. Additionally, both the $0$-mode and $\pi$-mode can recover and become confined at the edge in long-period evolution when the post-quench parameters $\left( T,\frac{M_2}{M_1} \right) $ in the phase diagram cross away from the phase boundary $\frac{M_2}{M_1}=\frac{6\sqrt{3} t_2}{M_1}-1$. Furthermore, we conclude that whether the edge state is confined at the edge in the long-period evolution after a quench depends on the similarity of the edge states before and after the quench. Our findings reveal some new characteristics of quench dynamics in a periodically driven system.

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Noise-induced phase transition in the Vicsek model through eigen microstate methodology Yongnan Jia(贾永楠), Jiali Han(韩佳丽), and Qing Li(李擎) Chin. Phys. B, 2024, 33 (9):  090501.  DOI: 10.1088/1674-1056/ad5aed Abstract ( 66 )   HTML ( 0 )   PDF (1043KB) ( 15 )   This paper presents a comprehensive framework for analyzing phase transitions in collective models such as the Vicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of social animals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noise remains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and non-equilibrium states, the eigen microstate method is employed here for a quantitative examination of the phase transitions in the Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phase transitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for these phase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions with escalation of population density.

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Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions Minfang Zhao(赵敏芳), Lingting Kong(孔令婷), Miao Liu(刘淼), and Shaoyong Lai(赖绍永) Chin. Phys. B, 2024, 33 (9):  090502.  DOI: 10.1088/1674-1056/ad5d92 Abstract ( 57 )   HTML ( 0 )   PDF (579KB) ( 72 )   The distribution of continuous service time in call centers is investigated. A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time, respectively. Using the statistical mechanical and asymptotic limit methods, Fokker-Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision kernels. The steady-state solutions of the Fokker-Planck equation are obtained in exact form. Numerical experiments are provided to support our results under different parameters.

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A real-time performance improvement method for composite time scale Fangmin Wang(王芳敏), Wenlin Li(李汶林), Hongfei Dai(戴鸿飞), Chunyi Li(李春怡), Jianhua Zhou(周建华), Shenhui Xue(薛申辉), and Bo Wang(王波) Chin. Phys. B, 2024, 33 (9):  090601.  DOI: 10.1088/1674-1056/ad6131 Abstract ( 91 )   HTML ( 1 )   PDF (3702KB) ( 82 )   The composite time scale (CTS) provides a stable, accurate, and reliable time scale for modern society. The improvement of CTS's real-time performance will improve its stability, which strengths related applications' performance. Aiming at this goal, a method achieved by determining the optimal calculation interval and accelerating adjustment stage is proposed in this paper. The determinants of the CTS's calculation interval (characteristics of the clock ensemble, the measurement noise, the time and frequency synchronization system's noise and the auxiliary output generator noise floor) are studied and the optimal calculation interval is obtained. We also investigate the effect of ensemble algorithm's initial parameters on the CTS's adjustment stage. A strategy to get the reasonable initial parameters of ensemble algorithm is designed. The results show that the adjustment stage can be finished rapidly or even can be shorten to zero with reasonable initial parameters. On this basis, we experimentally generate a distributed CTS with a calculation interval of 500 s and its stability outperforms those of the member clocks when the averaging time is longer than $\sim 1700 $ s. The experimental result proves that the CTS's real-time performance is significantly improved.

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Determination of liquid viscosity based on dual-frequency-band particle tracking Lihua Yan(闫丽华), Boyin Xue(薛博引), Yuanji Li(李渊骥), Jinxia Feng(冯晋霞), Xingkang Wu(武兴康), and Kuanshou Zhang(张宽收) Chin. Phys. B, 2024, 33 (9):  090701.  DOI: 10.1088/1674-1056/ad597e Abstract ( 72 )   HTML ( 0 )   PDF (1561KB) ( 20 )   An optical-tweezers-based dual-frequency-band particle tracking system was designed and fabricated for liquid viscosity detection. On the basis of the liquid viscosity dependent model of the particle's restricted Brownian motion with the Faxén correction taken into account, the liquid viscosity and optical trap stiffness were determined by fitting the theoretical prediction with the measured power spectral densities of the particle's displacement and velocity that were derived from the dual-frequency-band particle tracking data. When the SiO$_{2}$ beads were employed as probe particles in the measurements of different kinds of liquids, the measurement results exhibit a good agreement with the reported results, as well as a detection uncertainty better than 4.6%. This kind of noninvasive economical technique can be applied in diverse environments for both in situ and ex situ viscosity detection of liquids.

ATOMIC AND MOLECULAR PHYSICS

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Interference of harmonics emitted by different tunneling momentum channels in laser fields Ling-Yu Zhang(张玲玉), Zhuo-Xuan Xie(谢卓璇), Can Wang(王灿), Xin-Lei Ge(葛鑫磊), and Jing Guo(郭静) Chin. Phys. B, 2024, 33 (9):  093201.  DOI: 10.1088/1674-1056/ad5d95 Abstract ( 88 )   HTML ( 0 )   PDF (2722KB) ( 22 )   By numerically solving the semiconductor Bloch equation (SBEs), we theoretically study the high-harmonic generation of ZnO crystals driven by one-color and two-color intense laser pulses. The results show the enhancement of harmonics and the cut-off remains the same in the two-color field, which can be explained by the recollision trajectories and electron excitation from multi-channels. Based on the quantum path analysis, we investigate contribution of different ranges of the crystal momentum $k$ of ZnO to the harmonic yield, and find that in two-color laser fields, the intensity of the harmonic yield of different ranges from the crystal momentum makes a big difference and the harmonic intensity is depressed from all $k$ channels, which is related to the interferences between harmonics from symmetric $k$ channels.

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Time-energy distribution of photoelectron from atomic states with different magnetic quantum numbers in elliptically polarized laser fields Jingyang Xu(徐菁阳), Li Guo(郭丽), Xin Qi(齐昕), Ronghua Lu(陆荣华), Min Zhang(张敏), Jingtao Zhang(张敬涛), and Jing Chen(陈京) Chin. Phys. B, 2024, 33 (9):  093301.  DOI: 10.1088/1674-1056/ad58b3 Abstract ( 92 )   HTML ( 0 )   PDF (13073KB) ( 47 )   A Wigner-distribution-like (WDL) function based on the strong-field approximation (SFA) theory is used to investigate the ionization time of the photoelectron emitted from the initial states with different magnetic quantum number $m$ in elliptically polarized electric fields. The saddle-point method is adopted for comparisons. For different $m$ states, a discrepancy exists in the WDL distributions of the photoelectrons emitted in a direction close to the major axis of the laser field ellipse. Based on the saddle-point analysis, this discrepancy can be ascribed to the interference between electrons ionized from two tunneling instants. Our results show that the relationships between the tunneling instants and kinetic energy of photoelectrons are the same for different $m$ initial states when the Coulomb potential is not considered. Our work sheds some light on the ionization-time information of electrons from different magnetic quantum states.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

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Entropy variances of pure coherent states in the diffusion channel Wei-Feng Wu(吴卫锋), Yong Fang(方勇), and Peng Fu(付鹏) Chin. Phys. B, 2024, 33 (9):  094202.  DOI: 10.1088/1674-1056/ad5d97 Abstract ( 55 )   HTML ( 0 )   PDF (455KB) ( 15 )   Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, we solve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation of its analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in the diffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions in the diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes of the initial coherent states.

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Response analysis of NMRG system considering Rb-Xe coupling Yi Zhang(张燚), Qiyuan Jiang(江奇渊), Bingfeng Sun(孙兵锋), Jiahu Wei(魏加湖), Lin Yang(杨麟), Yongyuan Li(李永远), Zhiguo Wang(汪之国), Kaiyong Yang(杨开勇), and Hui Luo(罗晖) Chin. Phys. B, 2024, 33 (9):  094203.  DOI: 10.1088/1674-1056/ad6130 Abstract ( 63 )   HTML ( 0 )   PDF (891KB) ( 126 )   The dynamic range of the nuclear magnetic resonance gyroscope can be effectively improved through the closed-loop control scheme, which is crucial to its application in inertial measurement. This paper presents the analytical transfer function of Xe closed-loop system in the nuclear magnetic resonance gyroscope considering Rb-Xe coupling effect. It not only considers the dynamic characteristics of the system more comprehensively, but also adds the influence of the practical filters in the gyro signal processing system, which can obtain the accurate response characteristics of signal frequency and amplitude at the same time. The numerical results are compared with an experimentally verified simulation program, which indicate great agreement. The research results of this paper are of great significance to the practical application and development of the nuclear magnetic resonance gyroscope.

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High-quality ghost imaging based on undersampled natural-order Hadamard source Kang Liu(刘炕), Cheng Zhou(周成), Jipeng Huang(黄继鹏), Hongwu Qin(秦宏伍), Xuan Liu(刘轩), Xinwei Li(李鑫伟), and Lijun Song(宋立军) Chin. Phys. B, 2024, 33 (9):  094204.  DOI: 10.1088/1674-1056/ad62e1 Abstract ( 62 )   HTML ( 0 )   PDF (1076KB) ( 15 )   Improving the speed of ghost imaging is one of the main ways to leverage its advantages in sensitivity and imperfect spectral regions for practical applications. Because of the proportional relationship between image resolution and measurement time, when the image pixels are large, the measurement time increases, making it difficult to achieve real-time imaging. Therefore, a high-quality ghost imaging method based on undersampled natural-order Hadamard is proposed. This method uses the characteristics of the Hadamard matrix under undersampling conditions where image information can be fully obtained but overlaps, as well as deep learning to extract aliasing information from the overlapping results to obtain the true original image information. We conducted numerical simulations and experimental tests on binary and grayscale objects under undersampling conditions to demonstrate the effectiveness and scalability of this method. This method can significantly reduce the number of measurements required to obtain high-quality image information and advance application promotion.

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Orbital angular momentum conversion of acoustic vortex beams via planar lattice coupling Qingbang Han(韩庆邦), Zhipeng Liu(刘志鹏), Cheng Yin(殷澄), Simeng Wu(吴思梦), Yinlong Luo(罗寅龙), Zixin Yang(杨子鑫), Xiuyang Pang(庞修洋), Yiqiu Wang(王溢秋), Xuefen Kan(阚雪芬), Yuqiu Zhang(张雨秋), Qiang Yu(俞强), and Jian Wu(吴坚) Chin. Phys. B, 2024, 33 (9):  094301.  DOI: 10.1088/1674-1056/ad57ad Abstract ( 71 )   HTML ( 0 )   PDF (3110KB) ( 82 )   Orbital angular momentum (OAM) conversion is critical in understanding interactions between a structural sound field and a planar lattice. Herein, we explore the evolution of a monochromatic acoustic vortex beam (AVB) that is scattered by a phononic crystal (PnC) or a correlated random lattice. The phenomenon is ascribed to the enhanced orbit-orbit angular momentum coupling induced by the band structure. By modifying the coupling condition, accurate and continuous micro-manipulation of AVBs can be achieved, including the transverse/lateral gravity shift, the dynamics of the phase singularities, and the spatial distribution of acoustic pressure, etc. This research provides insight to the inhomogeneous coupling of AVBs with both propagating Bloch waves and localized Anderson modes, and may facilitate development of novel OAM-based acoustic devices for active sound field manipulation.

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Acoustic radiation force on a cylindrical composite particle with an elastic thin shell and an internal eccentric liquid column in a plane ultrasonic wave field Rui-Qi Pan(潘瑞琪), Zhi-Wei Du(杜芷玮), Cheng-Hui Wang(王成会), Jing Hu(胡静), and Run-Yang Mo(莫润阳) Chin. Phys. B, 2024, 33 (9):  094302.  DOI: 10.1088/1674-1056/ad5d66 Abstract ( 63 )   HTML ( 5 )   PDF (1472KB) ( 15 )   A model with three-layer structure is introduced to explore the acoustic radiation force (ARF) on composite particles with an elastic thin shell. Combing acoustic scattering of cylinder and the thin-shell theorem, the ARF expression was derived, and the longitudinal and transverse components of the force and axial torque for an eccentric liquid-filled composite particle was obtained. It was found that many factors, such as medium properties, acoustic parameters, eccentricity, and radius ratio of the inner liquid column, affect the acoustic scattering field of the particle, which in turn changes the forces and torque. The acoustic response varies with the particle structures, so the resonance peaks of the force function and torque shift with the eccentricity and radii ratio of particle. The acoustic response of the particle is enhanced and exhibits higher force values due to the presence of the elastic thin shell and the coupling effect with the eccentricity of the internal liquid column. The decrease of the inner liquid density may suppress the high-order resonance peaks, and internal fluid column has less effects on the change in force on composite particle at $ka>3$, while limited differences exist at $ka<3$. The axial torque on particles due to geometric asymmetry is closely related to $ka$ and the eccentricity. The distribution of positive and negative force and torque along the axis $ka$ exhibits that composite particle can be manipulated or separated by ultrasound. Our theoretical analysis can provide support for the acoustic manipulation, sorting, and targeting of inhomogeneous particles.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

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Exploration of microscopic physical processes of Z-pinch by a modified electrostatic direct implicit particle-in-cell algorithm Kaixuan Li(李开轩), Cheng Ning(宁成), Ye Dong(董烨), and Chuang Xue(薛创) Chin. Phys. B, 2024, 33 (9):  095201.  DOI: 10.1088/1674-1056/ad553a Abstract ( 61 )   HTML ( 0 )   PDF (2616KB) ( 68 )   For investigating efficiently the stagnation kinetic-process of Z-pinch, we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is used. In our algorithm, the electric field in $z$-direction is solved by a parallel electrode-plate model, the azimuthal magnetic field is obtained by Ampere's law, and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic field. In simulation results of 2 MA deuterium plasma shell Z-pinch, the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation, and the plasma current also closely aligns with the external current. The phase space diagrams and radial-velocity probability distributions of ions and electrons are obtained. The main kinetic characteristic of electron motion is thermal equilibrium and oscillation, which should be oscillated around the ions, while that of ion motion is implosion inwards. In the region of stagnation radius, the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing, while of electrons is basically the equilibrium state. When the initial ion density and current peak are not high enough, the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.

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Influence of ion species on extraction characteristics of mixed ion beams Ao Xu(徐翱), Pingping Gan(甘娉娉), Xiang Wan(万翔), and Yuanjie Shi(石元杰) Chin. Phys. B, 2024, 33 (9):  095202.  DOI: 10.1088/1674-1056/ad5c3d Abstract ( 46 )   HTML ( 0 )   PDF (1459KB) ( 13 )   The spatial distributions of different kinds of ions are usually not completely the same in the process of extracting. In order to study the reason for the different characteristics of ion extraction, a simplified simulation model of Cu$^{+}$ and Cr$^{+}$ ions extraction process was established by 2D3V (two-dimensional in space and three-dimensional in velocity space) particle-in-cell (PIC) method. The effects of different extraction voltages from 0 V to 500 V on the density distribution of Cu$^{+}$ and Cr$^{+}$ ions and the change of plasma emission surface were analyzed. On the basis of this model, the ion density distribution characteristics of Cu$^{+}$ ions mixed with Li$^{+}$, Mg$^{+}$, K$^{+}$, Fe$^{+}$, Y$^{+}$, Ag$^{+}$, Xe$^{+}$, Au$^{+}$, and Pb$^{+}$ ions respectively under 200-V extraction voltage are further simulated, and it is revealed that the atomic mass of the ions is the key reason for different ion density distributions when different kinds of ions are mixed and extracted, which provides support for further understanding of ion extraction characteristics.

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Discharge mode and particle transport in radio frequency capacitively coupled Ar/O2 plasma discharges Zhuo-Yao Gao(高卓瑶), Wan Dong(董婉), Chong-Biao Tian(田崇彪), Xing-Zhao Jiang(蒋星照), Zhong-Ling Dai(戴忠玲), and Yuan-Hong Song(宋远红) Chin. Phys. B, 2024, 33 (9):  095203.  DOI: 10.1088/1674-1056/ad5d65 Abstract ( 73 )   HTML ( 0 )   PDF (2641KB) ( 49 )   Simulations are conducted on capacitively coupled Ar/O$_{2}$ mixed gas discharges employing a one-dimensional fluid coupled with an electron Monte Carlo (MC) model. The research explores the impact of different O$_{2}$ ratio and pressures on the discharge characteristics of Ar/O$_{2}$ plasma. At a fixed Ar/O$_{2}$ gas ratio, with the increasing pressure, higher ion densities, as well as a slight increase in electron density in the bulk region can be observed. The discharge remains dominated by the drift-ambipolar (DA) mode, and the flux of O($^{3}$P) at the electrode increases with the increasing pressure due to higher background gas density, while the fluxes of O($^{1}$D) and Ar$^{\ast }$ decrease due to the pronounced loss rate. With the increasing proportion of O$_{2}$, a change in the dominant discharge mode from $\alpha $ mode to DA mode can be detected, and the O$_{2}$-associated charged particle densities are significantly increased. However, Ar$^{+}$ density shows a trend of increasing and then decreasing, while for neutral fluxes at the electrode, Ar$^{\ast }$ flux decreases, and O($^{3}$P) flux increases with the reduced Ar gas proportion, while trends in O($^{1}$D) flux show slight differences. The evolution of the densities of the charged particle and the neutral fluxes under different discharge parameters are discussed in detail using the ionization characteristics as well as the transport properties. Hopefully, more comprehensive understanding of Ar/O$_{2}$ discharge characteristics in this work will provide a valuable reference for the industry.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

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Strip method to construct a two-dimensional quasilattice with eight-fold symmetry Weishen Huang(黄伟深) and Xiujun Fu(傅秀军) Chin. Phys. B, 2024, 33 (9):  096102.  DOI: 10.1088/1674-1056/ad51f2 Abstract ( 79 )   HTML ( 0 )   PDF (3545KB) ( 29 )   Based on the substitution rule and symmetry, we propose a method to generate an octagonal quasilattice consisting of square and rhombus tiles. Local configurations and Ammann lines are used to guide the growth of the tiles in a quasiperiodic order. The structure obtained is a perfect eight-fold symmetric quasilattice, which is confirmed by the radial distribution function and the diffraction pattern.

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Dendritic tip selection during solidification of alloys: Insights from phase-field simulations Qingjie Zhang(张清杰), Hui Xing(邢辉), Lingjie Wang(王灵杰), and Wei Zhai(翟薇) Chin. Phys. B, 2024, 33 (9):  096103.  DOI: 10.1088/1674-1056/ad57ac Abstract ( 75 )   HTML ( 0 )   PDF (910KB) ( 27 )   The effect of undercooling $\Delta T$ and the interface energy anisotropy parameter $\varepsilon_{4} $ on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys. It was found that the tip radius $\rho $ increases and the tip shape amplitude coefficient $A_{4} $ decreases with the increase of the fitting range for all cases. The dendrite tip shape selection parameter $\sigma^{\ast }$ decreases and then stabilizes with the increase of the fitting range, and $\sigma^{\ast }$ increases with the increase of $\varepsilon_{4} $. The relationship between $\sigma^{\ast }$ and $\varepsilon_{4}$ follows a power-law function $\sigma^{\ast }\propto \varepsilon_{4}^{\alpha } $, and $\alpha $ is independent of $\Delta T$ but dependent on the fitting range. Numerical results demonstrate that the predicted $\sigma^{\ast }$ is consistent with the curve of microscopic solvability theory (MST) for $\varepsilon_{4} <0.02$, and $\sigma ^{\ast }$ obtained from our phase-field simulations is sensitive to the undercooling when $\varepsilon_{4} $ is fixed.

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Theoretical insights into the structures and fundamental properties of pnictogen nitrides Jingjing Wang(王晶晶), Panlong Kong(孔攀龙), Dingmei Zhang(张定梅), Defang Gao(高德芳), Zaifu Jiang(蒋再富), and Wei Dai(戴伟) Chin. Phys. B, 2024, 33 (9):  096201.  DOI: 10.1088/1674-1056/ad6a07 Abstract ( 65 )   HTML ( 0 )   PDF (1788KB) ( 10 )   Recent experimental advancements reported a chemical reaction between antimony and nitrogen under high temperature and high pressure, yielding crystalline antimony nitride (Sb$_{3}$N$_{5}$) with an orthorhombic structure. Motivated by this statement, we calculate the stability, elastic properties, electronic properties and energy density of the $Cmc2_{1}$ structure for pnictogen nitrides $X_{3}$N$_{5}$ ($X=$ P, As, Sb, and Bi) using first-principles calculations combined with particle swarm optimization algorithms. Calculations of formation enthalpies, elastic constants and phonon spectra show that P$_{3}$N$_{5}$, As$_{3}$N$_{5}$ and Sb$_{3}$N$_{5}$ are thermodynamically, mechanically and kinetically stable at 35 GPa, whereas Bi$_{3}$N$_{5}$ is mechanically and kinetically stable but thermodynamically unstable. The computed electronic density of states shows strong covalent bonding between the N atoms and the phosphorus group atoms in the four compounds, confirmed by the calculated electronic localization function. We also calculate the energy densities for Sb$_{3}$N$_{5}$ and find it to be a potentially high-energy-density material.

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Two-dimensional Cr2Cl3S3 Janus magnetic semiconductor with large magnetic exchange interaction and high-TC Lei Fu(伏磊), Shasha Li(李沙沙), Xiangyan Bo(薄祥䶮), Sai Ma(马赛), Feng Li(李峰), and Yong Pu(普勇) Chin. Phys. B, 2024, 33 (9):  096301.  DOI: 10.1088/1674-1056/ad5538 Abstract ( 77 )   HTML ( 0 )   PDF (1605KB) ( 99 )   The two-dimensional (2D) Janus monolayers are promising in spintronic device application due to their enhanced magnetic couplings and Curie temperatures. Van der Waals CrCl$_{3}$ monolayer has been experimentally proved to have an in-plane magnetic easy axis and a low Curie temperature of 17 K, which will limit its application in spintronic devices. In this work, we propose a new Janus monolayer Cr$_{2}$Cl$_{3}$S$_{3}$ based on the first principles calculations. The phonon dispersion and elastic constants confirm that Janus monolayer Cr$_{2}$Cl$_{3}$S$_{3}$ is dynamically and mechanically stable. Our Monte Carlo simulation results based on magnetic exchange constants reveal that Janus monolayer Cr$_{2}$Cl$_{3}$S$_{3}$ is an intrinsic ferromagnetic semiconductor with $T_{\rm C}$ of 180 K, which is much higher than that of CrCl$_{3}$ due to the enhanced ferromagnetic coupling caused by S substitution. Moreover, the magnetic easy axis of Janus Cr$_{2}$Cl$_{3}$S$_{3}$ can be tuned to the perpendicular direction with a large magnetic anisotropy energy (MAE) of 142 μeV/Cr. Furthermore, the effect of biaxial strain on the magnetic property of Janus monolayer Cr$_{2}$Cl$_{3}$S$_{3}$ is evaluated. It is found that the Curie temperature is more robust under tensile strain. This work indicates that the Janus monolayer Cr$_{2}$Cl$_{3}$S$_{3}$ presents increased Curie temperature and out-of-plane magnetic easy axis, suggesting greater application potential in 2D spintronic devices.

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Strain-tuned electronic and valley-related properties in Janus monolayers of SWSiX2 (X = N, P, As) Yunxi Qi(戚云西), Jun Zhao(赵俊), and Hui Zeng(曾晖) Chin. Phys. B, 2024, 33 (9):  096302.  DOI: 10.1088/1674-1056/ad6077 Abstract ( 65 )   HTML ( 0 )   PDF (1585KB) ( 33 )   Exploring novel two-dimensional (2D) valleytronic materials has an essential impact on the design of spintronic and valleytronic devices. Our first principles calculation results reveal that the Janus SWSi$X_{2}$ ($X = {\rm N}$, P, As) monolayer has excellent dynamical and thermal stability. Owing to strong spin-orbit coupling (SOC), the SWSi$X_{2}$ monolayer exhibits a valence band spin splitting of up to 0.49 eV, making it promising 2D semiconductor for valleytronic applications. The opposite Berry curvatures and optical selection rules lead to the coexistence of valley and spin Hall effects in the SWSi$X_{2}$ monolayer. Moreover, the optical transition energies can be remarkably modulated by the in-plane strains. Large tensile (compressive) in-plane strains can achieve spin flipping in the SWSiN$_{2}$ monolayer, and induce both SWSiP$_{2}$ and SWSiAs$_{2}$ monolayers transit from semiconductor to metal. Our research provides new 2D semiconductor candidates for designing high-performance valleytronic devices.

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Theoretical insights into thermal transport and structural stability mechanisms of triaxial compressed methane hydrate Dong-Sheng Chen(陈东升), Ting-Ting Miao(缪婷婷), Cheng Chang(常程), Xu-Yang Guo(郭旭洋), Meng-Yan Guan(关梦言), and Zhong-Li Ji(姬忠礼) Chin. Phys. B, 2024, 33 (9):  096501.  DOI: 10.1088/1674-1056/ad57ae Abstract ( 88 )   HTML ( 2 )   PDF (3247KB) ( 31 )   The heat transfer and stability of methane hydrate in reservoirs have a direct impact on the drilling and production efficiency of hydrate resources, especially in complex stress environments caused by formation subsidence. In this study, we investigated the thermal transport and structural stability of methane hydrate under triaxial compression using molecular dynamics simulations. The results suggest that the thermal conductivity of methane hydrate increases with increasing compression strain. Two phonon transport mechanisms were identified as factors enhancing thermal conductivity. At low compressive strains, a low-frequency phonon transport channel was established due to the overlap of phonon vibration peaks between methane and water molecules. At high compressive strains, the filling of larger phonon bandgaps facilitated the opening of more phonon transport channels. Additionally, we found that a strain of $-0.04$ is a watershed point, where methane hydrate transitions from stable to unstable. Furthermore, a strain of $-0.06$ marks the threshold at which the diffusion capacities of methane and water molecules are at their peaks. At a higher strain of $-0.08$, the increased volume compression reduces the available space, limiting the diffusion ability of water and methane molecules within the hydrate. The synergistic effect of the strong diffusion ability and high probability of collision between atoms increases the thermal conductivity of hydrates during the unstable period compared to the stable period. Our findings offer valuable theoretical insights into the thermal conductivity and stability of methane hydrates in reservoir stress environments.

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Effects of air damping on quality factors of different probes in tapping mode atomic force microscopy Yu Zeng(曾瑜), Guo-Lin Liu(刘国林), Jin-Hao Liu(刘锦灏), and Zheng Wei(魏征) Chin. Phys. B, 2024, 33 (9):  096806.  DOI: 10.1088/1674-1056/ad5539 Abstract ( 70 )   HTML ( 1 )   PDF (2690KB) ( 30 )   The AFM probe in tapping mode is a continuous process of energy dissipation, from moving away from to intermittent contact with the sample surfaces. At present, studies regarding the energy dissipation mechanism of this continuous process have only been reported sporadically, and there are no systematic explanations or experimental verifications of the energy dissipation mechanism in each stage of the continuous process. The quality factors can be used to characterize the energy dissipation in TM-AFM systems. In this study, the vibration model of the microcantilever beam was established, coupling the vibration and damping effects of the microcantilever beam. The quality factor of the vibrating microcantilever beam under damping was derived, and the air viscous damping when the probe is away from the sample and the air squeeze film damping when the probe is close to the sample were calculated. In addition, the mechanism of the damping effects of different shapes of probes at different tip-sample distances was analyzed. The accuracy of the theoretical simplified model was verified using both experimental and simulation methods. A clearer understanding of the kinetic characteristics and damping mechanism of the TM-AFM was achieved by examining the air damping dissipation mechanism of AFM probes in the tapping mode, which was very important for improving both the quality factor and the imaging quality of the TM-AFM system. This study's research findings also provided theoretical references and experimental methods for the future study of the energy dissipation mechanism of micro-nano-electromechanical systems.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

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Bose-Einstein distribution temperature features of quasiparticles around magnetopolaron in Gaussian quantum wells of alkali halogen ions Xin Zhang(张鑫), Sarengaowa(萨仁高娃), Shuang Han(韩爽), Ran An(安然), Xin-Xue Zhang(张新雪), Xin-Ying Ji(纪新颖), Hong-Xu Jiang(江红旭), Xin-Jun Ma(马新军), Pei-Fang Li(李培芳), and Yong Sun(孙勇) Chin. Phys. B, 2024, 33 (9):  097102.  DOI: 10.1088/1674-1056/ad5c3c Abstract ( 47 )   HTML ( 0 )   PDF (1432KB) ( 9 )   We have applied strong coupling unitary transformation method combined with Bose-Einstein statistical law to investigate magnetopolaron energy level temperature effects in halogen ion crystal quantum wells. The obtained results showed that under magnetic field effect, magnetopolaron quasiparticle was formed through the interaction of electrons and surrounding phonons. At the same time, magnetopolaron was influenced by phonon temperature statistical law and important energy level shifts down and binding energy increases. This revealed that lattice temperature and magnetic field could easily affect magnetopolaron and the above results could play key roles in exploring thermoelectric conversion and conductivity of crystal materials.

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Half-metallic ferromagnetic Weyl fermions related to dynamic correlations in the zinc-blende compound VAs Xianyong Ding(丁献勇), Haoran Wei(魏皓然), Ruixiang Zhu(朱瑞翔), Xiaoliang Xiao(肖晓亮), Xiaozhi Wu(吴小志), and Rui Wang(王锐) Chin. Phys. B, 2024, 33 (9):  097103.  DOI: 10.1088/1674-1056/ad5f86 Abstract ( 86 )   HTML ( 0 )   PDF (4783KB) ( 35 )   The realization of 100% polarized topological Weyl fermions in half-metallic ferromagnets is of particular importance for fundamental research and spintronic applications. Here, we theoretically investigate the electronic and topological properties of the zinc-blende compound VAs, which was deemed as a half-metallic ferromagnet related to dynamic correlations. Based on the combination of density functional theory and dynamical mean field theory, we uncover that the half-metallic ferromagnet VAs exhibits attractive Weyl semimetallic behaviors which are very close to the Fermi level in the ${\rm DFT} + U$ regime with effect $U$ values ranging from 1.5 eV to 2.5 eV. Meanwhile, we also investigate the magnetization-dependent topological properties; the results show that the change of magnetization directions only slightly affects the positions of Weyl points, which is attributed to the weak spin-orbital coupling effects. The topological surface states of VAs projected on semi-infinite (001) and (111) surfaces are investigated. The Fermi arcs of all Weyl points are clearly visible on the projected Fermi surfaces. Our findings suggest that VAs is a fully spin-polarized Weyl semimetal with many-body correlated effects in the effective $U$ values range from 1.5 eV to 2.5 eV.

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Current-perpendicular-to-plane transport properties of 2D ferromagnetic material CrTe2 Jin Wang(王瑾), Yu Liu(刘宇), Taikun Wang(王太坤), Yongkang Xu(徐永康), Shuanghai Wang(王双海), Kun He(何坤), Yafeng Deng(邓亚峰), Pengfei Yan(闫鹏飞), and Liang He(何亮) Chin. Phys. B, 2024, 33 (9):  097201.  DOI: 10.1088/1674-1056/ad5af1 Abstract ( 88 )   HTML ( 0 )   PDF (1786KB) ( 94 )   Heterostructures of van der Waals (vdW) ferromagnetic materials have become a focal point in research of low-dimensional spintronic devices. The current direction in spin valves is commonly perpendicular to the plane (CPP). However, the transport properties of the CPP mode remain largely unexplored. In this work, current-in-plane (CIP) mode and CPP mode for CrTe$_{2}$ thin films are carefully studied. The temperature-dependent longitudinal resistance transitions from metallic (CIP) to semiconductor behavior (CPP), with the electrical resistivity of CPP increased by five orders of magnitude. More importantly, the transport properties of the CPP can be categorized into a single-gap tunneling-through model with the activation energy ($E_{\rm a}$) of $\sim$ 1.34 meV/gap at 300-150 K, the variable range hopping model with a linear negative magnetoresistance at 150-20 K, and weak localization region with a nonlinear magnetic resistance below 20 K. This study explores the vertical transport in CrTe$_{2}$ materials for the first time, contributing to understand its unique properties and to pave the way for its potential in spin valve devices.

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In-phase and out-of-phase spin pumping effects in Py/Ru/Py synthetic antiferromagnetic structures Zhaocong Huang(黄兆聪), Xuejian Tang(唐学健), Qian Chen(陈倩), Wei Jiang(蒋伟), Qingjie Guo(郭庆杰), Milad Jalali, Jun Du(杜军), and Ya Zhai(翟亚) Chin. Phys. B, 2024, 33 (9):  097202.  DOI: 10.1088/1674-1056/ad553d Abstract ( 70 )   HTML ( 0 )   PDF (1037KB) ( 40 )   The spin pumping effect in magnetic heterostructures and multilayers is a highly effective method for the generation and transmission of spin currents. In the increasingly prominent synthetic antiferromagnetic structures, the two ferromagnetic layers demonstrate in-phase and out-of-phase states, corresponding to acoustic and optical precession modes. Within this context, our study explores the spin pumping effect in Py/Ru/Py synthetic antiferromagnetic structures across different modes. The heightened magnetic damping resulting from the spin pumping effect in the in-phase state initially decreases with increasing Py thickness before stabilizing. Conversely, in the out-of-phase state, the amplified damping exceeds that of the in-phase state, suggesting a greater spin relaxation within this configuration, which demonstrates sensitivity to alterations in static exchange interactions. These findings contribute to advancing the application of synthetic antiferromagnetic structures in magnonic devices.

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Non-perturbative dynamics of flat-band systems with correlated disorder Qi Li(李骐), Junfeng Liu(刘军丰), Ke Liu(刘克), Zi-Xiang Hu(胡自翔), and Zhou Li(李舟) Chin. Phys. B, 2024, 33 (9):  097203.  DOI: 10.1088/1674-1056/ad5534 Abstract ( 85 )   HTML ( 0 )   PDF (1458KB) ( 34 )   We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder. To achieve this, we introduce a method to generate random on-site energies with prescribed correlations. We verify this method with a one-dimensional (1D) cross-stitch model, and find good agreement with analytical results obtained from the disorder-dressed evolution equations. This allows us to reproduce previous findings, that disorder can mobilize 1D flat-band states which would otherwise remain localized. As explained by the corresponding disorder-dressed evolution equations, such mobilization requires an asymmetric disorder-induced coupling to dispersive bands, a condition that is generically not fulfilled when the flat-band is resonant with the dispersive bands at a Dirac point-like crossing. We exemplify this with the 1D Lieb lattice. While analytical expressions are not available for the two-dimensional (2D) system due to its complexity, we extend the numerical method to the 2D $\alpha$-$T_3$ model, and find that the initial flat-band wave packet preserves its localization when $\alpha = 0$, regardless of disorder and intersections. However, when $\alpha\neq 0$, the wave packet shifts in real space. We interpret this as a Berry phase controlled, disorder-induced wave-packet mobilization. In addition, we present density functional theory calculations of candidate materials, specifically ${\rm Hg}_{1-x}{\rm Cd}_x{\rm Te}$. The flat-band emerges near the $\varGamma$ point (${\bm k}=0$) in the Brillouin zone.

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Quantum confinement of carriers in the type-I quantum wells structure Xinxin Li(李欣欣), Zhen Deng(邓震), Yang Jiang(江洋), Chunhua Du(杜春花), Haiqiang Jia(贾海强), Wenxin Wang(王文新), and Hong Chen(陈弘) Chin. Phys. B, 2024, 33 (9):  097301.  DOI: 10.1088/1674-1056/ad5d99 Abstract ( 59 )   HTML ( 0 )   PDF (630KB) ( 48 )   Quantum confinement is recognized to be an inherent property in low-dimensional structures. Traditionally, it is believed that the carriers trapped within the well cannot escape due to the discrete energy levels. However, our previous research has revealed efficient carrier escape in low-dimensional structures, contradicting this conventional understanding. In this study, we review the energy band structure of quantum wells along the growth direction considering it as a superposition of the bulk material dispersion and quantization energy dispersion resulting from the quantum confinement across the whole Brillouin zone. By accounting for all wave vectors, we obtain a certain distribution of carrier energy at each quantized energy level, giving rise to the energy subbands. These results enable carriers to escape from the well under the influence of an electric field. Additionally, we have compiled a comprehensive summary of various energy band scenarios in quantum well structures relevant to carrier transport. Such a new interpretation holds significant value in deepening our comprehension of low-dimensional energy bands, discovering new physical phenomena, and designing novel devices with superior performance.

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MHz cut-off frequency and permeability mechanism of iron-based soft magnetic composites Xiao-Wei Jin(金校伟), Tong Li(李通), Hui-Gang Shi(史慧刚), and De-Sheng Xue(薛德胜) Chin. Phys. B, 2024, 33 (9):  097501.  DOI: 10.1088/1674-1056/ad57aa Abstract ( 96 )   HTML ( 0 )   PDF (1567KB) ( 30 )   The lack of soft magnetic composites with high power density in MHz frequency range has become an obstacle in the efficient operation of the electrical and electronic equipments. Here, a promising method to increase the cut-off frequency of iron-based soft magnetic composites to hundreds of MHz is reported. The cut-off frequency is increased from 10 MHz to 1 GHz by modulating the height of the ring, the distribution of particles, and the particle size. The mechanism of cut-off frequency and permeability is the coherent rotation of domain modulated by inhomogeneous field due to the eddy current effect. An empirical formula for the cut-off frequency in a magnetic ring composed of iron-based particles is established from experimental data. This work provides an effective approach to fabricate soft magnetic composites with a cut-off frequency in hundreds of MHz.

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Induced magneto-conductivity in a two-node Weyl semimetal under Gaussian random disorder Chuanxiong Xu(徐川雄), Haoping Yu(于昊平), Mei Zhou(周梅), and Xuanting Ji(吉轩廷) Chin. Phys. B, 2024, 33 (9):  097502.  DOI: 10.1088/1674-1056/ad59fc Abstract ( 83 )   HTML ( 0 )   PDF (722KB) ( 92 )   Measuring the magneto-conductivity induced from impurities may help determine the impurity distribution and reveal the structure of a Weyl semimetal sample. To verify this, we utilize the Gaussian random disorder to simulate charged impurities in a two-node Weyl semimetal model and investigate the impact of charged impurities on magneto-conductivity in Weyl semimetals. We first compute the longitudinal magnetic conductivity and find that it is positive and increases proportionally with the parameter governing the Gaussian distribution of charged impurities, suggesting the presence of negative longitudinal magneto-resistivity. Then we consider both the intra-valley and inter-valley scattering processes to calculate the induced transverse magneto-conductivity in the model. Our findings indicate that both inter-valley and intra-valley scattering processes play important roles in the transverse magneto-conductivity. The locations of Weyl nodes can also be determined by magneto-conductivity measurements. This is possible if the magnetic field strength and the density of charged impurities are known. Alternatively, the measurement of magnetic conductivity may reveal the distribution of charged impurities in a given sample once the locations of the Weyl nodes have been determined. These findings can aid in detecting the structure of a Weyl semimetal sample, enhancing comprehension of magnetotransport in Weyl semimetals and promoting the development of valley electronics.

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Preparation and magnetic hardening of low Ti content (Sm,Zr)(Fe,Co,Ti)12 magnets by rapid solidification non-equilibrium method Xing-Feng Zhang(张兴凤), Li-Bin Liu(刘立斌), Yu-Qing Li(李玉卿), Dong-Tao Zhang(张东涛), Wei-Qiang Liu(刘卫强), and Ming Yue(岳明) Chin. Phys. B, 2024, 33 (9):  097503.  DOI: 10.1088/1674-1056/ad58c4 Abstract ( 62 )   HTML ( 0 )   PDF (3456KB) ( 56 )   The Sm-Zr-Fe-Co-Ti quinary-alloys with ThMn$_{12}$ structure has attracted wide attention for ultra-high intrinsic magnetic properties, showing potentiality to be developed into rare-earth permanent magnets. The Ti element in alloys is crucial for phase stability and magnetic properties, and lower Ti content can increase intrinsic magnetic properties but reduce phase stability. In this study, the 1:12 single-phase melt-spun ribbons with low Ti content was successfully prepared using a rapid solidification non-equilibrium method for the Sm$_{1.1}$Zr$_{0.2}$Fe$_{9.2}$Co$_{2.3}$Ti$_{0.5}$ quinary-alloy. However, this non-equilibrium ribbon did not achieve good magnetic hardening due to the uneven microstructure and microstrain. Then, annealing was carried out to eliminate micro-strain and homogenize microstructure, therefore, remanence and coercivity were significantly improved even the precipitation of a small amount of $\alpha $-Fe phase which were not conducive to coercivity. The remanence of 86.1 emu/g and coercivity of 151 kA/m was achieved when annealing at 850 ${^\circ}$C for 45 min. After hot pressing, under the action of high temperature and pressure, a small portion of ThMn$_{12}$ phases in the magnet decompose into Sm-rich phases and $\alpha $-Fe, while remanence of 4.02 kGs (1 Gs = 10$^{-4}$ T), and coercivity of 1.12 kOe (1 Oe = 79.5775 A$\cdot$m$^{-1}$) were still acquired. Our findings can provide reference for exploring practical permanent magnets made of 1:12 type quinary-alloys.

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Phase structure evolution and its effect on magnetic and mechanical properties of B-doped Sm2Co17-type magnets with high Fe content Yao-Wen Li(李耀文), Zhuang Liu(刘壮), Hai-Chen Wu(吴海辰), Fang Wang(王芳), Chao-Qun Zhu(竺超群), Dong-Liang Tan(谭栋梁), Yu Liu(刘宇), Yang Yang(羊杨), Ming-Xiao Zhang(张明晓), Ren-Jie Chen(陈仁杰), and A-Ru Yan(闫阿儒) Chin. Phys. B, 2024, 33 (9):  097504.  DOI: 10.1088/1674-1056/ad5535 Abstract ( 67 )   HTML ( 1 )   PDF (5727KB) ( 24 )   The unique cellular microstructure of Fe-rich Sm$_{2}$Co$_{17}$-type permanent magnets is closely associated with the structure of the solid solution precursor. We investigate the phase structure, magnetic properties, and mechanical behavior of B-doped Sm$_{2}$Co$_{17}$-type magnets with high Fe content. The doped B atoms can diffuse into the interstitial vacancy, resulting in lattice expansion and promote the homogenization of the phase organizational structure during the solid solution treatment in theory. However, the resulting second phase plays a dominant role to result in more microtwin structures and highly ordered 2 : 17R phases in the solid solution stage, which inhibits the ordering transformation of 1 : 7H phase during aging and affects the generation of the cellular structure, and to result in a decrease in magnetic properties, yet the interface formed between it and the matrix phase hinders the movement of dislocations and enhances the mechanical properties. Hence, the precipitation of high flexural strain grain boundary phase induced by B element doping is also a new and effective way to improve the flexural strain of Sm$_{2}$Co$_{17}$-type magnets. Our study provides a new understanding of the phase structure evolution and its effect on the magnetic and mechanical properties of Sm$_{2}$Co$_{17}$-type magnets with high Fe content.

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Simulation of magnetization process and Faraday effect of magnetic bilayer films Sheng Gao(高升), An Du(杜安), Lei Zhang(张磊), Tian-Guang Li(李天广), and Da-Cheng Ma(马大成) Chin. Phys. B, 2024, 33 (9):  097505.  DOI: 10.1088/1674-1056/ad5a76 Abstract ( 70 )   HTML ( 0 )   PDF (819KB) ( 15 )   We described ferromagnetic film and bilayer films composed of two ferromagnetic layers coupled through antiferromagnetic interfacial interaction by classical Heisenberg model and simulated their magnetization state, magnetic permeability, and Faraday effect at zero and finite temperature by using the Landau-Lifshitz-Gilbert (LLG) equation. The results indicate that in a microwave field with positive circular polarization, the ferromagnetic film has one resonance peak while the bilayer film has two resonance peaks. However, the resonance peak disappears in ferromagnetic film, and only one resonance peak emerges in bilayer film in the negative circularly polarized microwave field. When the microwave field's frequency exceeds the film's resonance frequency, the Faraday rotation angle of the ferromagnetic film is the greatest, and it decreases when the thickness of the two halves of the bilayer is reduced. When the microwave field's frequency remains constant, the Faraday rotation angle fluctuates with temperature in the same manner as spontaneous magnetization does. When a DC magnetic field is applied in the direction of the anisotropic axis of the film, the Faraday rotation angle varies with the DC magnetic field and shows a similar shape of the hysteresis loop.

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Mapping the antiparallel aligned domain rotation by microwave excitation Jing Zhang(张景), Yuanzhi Cui(崔远志), Xiaoyu Wang(王晓雨), Chuang Wang(王创), Mengchen Liu(刘梦晨), Jie Xu(徐洁), Kai Li(李凯), Yunhe Zhao(赵芸鹤), Zhenyan Lu(陆振烟), Lining Pan(潘丽宁), Chendong Jin(金晨东), Qingfang Liu(刘青芳), Jianbo Wang(王建波), and Derang Cao(曹德让) Chin. Phys. B, 2024, 33 (9):  097506.  DOI: 10.1088/1674-1056/ad5536 Abstract ( 68 )   HTML ( 0 )   PDF (4869KB) ( 27 )   The evolution process of magnetic domains in response to external fields is crucial for the modern understanding and application of spintronics. In this study, we investigated the domain rotation in stripe domain films of varying thicknesses by examining their response to microwave excitation in four different orientations. The resonance spectra indicate that the rotation field of stripe domain film under an applied magnetic field approaches the field where the resonance mode of sample changes. The saturation field of the stripe domain film corresponds to the field where the resonance mode disappears when measured in the stripe direction parallel to the microwave magnetic field. The results are reproducible and consistent with micromagnetic simulations, providing additional approaches and techniques for comprehending the microscopic mechanisms of magnetic domains and characterizing their rotation.

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Spin wave resonance frequency in bilayer ferromagnetic films with the biquadratic exchange interaction Xiaojie Zhang(张晓洁), Yuting Wang(王雨汀), Yanqiu Chang(常艳秋), Huan Wang(王焕), Jianhong Rong(荣建红), and Guohong Yun(云国宏) Chin. Phys. B, 2024, 33 (9):  097601.  DOI: 10.1088/1674-1056/ad50bc Abstract ( 77 )   HTML ( 0 )   PDF (714KB) ( 19 )   The dependences of spin wave resonance (SWR) frequency on the surface anisotropy field, interface exchange coupling, symmetry, biquadratic exchange (BQE) interaction, film thickness, and the external magnetic field in bilayer ferromagnetic films are theoretically analyzed by employing the linear spin wave approximation and Green's function method. A remarkable increase of SWR frequency, except for energetically lower two modes, can be obtained in our model that takes the BQE interaction into account. Again, the effect of the external magnetic field on SWR frequency can be increased by increasing the biquadratic to interlayer exchange ratio. It has been identified that the BQE interaction is of utmost importance in improving the SWR frequency of the bilayer ferromagnetic films. In addition, for bilayer ferromagnetic films, the frequency gap between the energetically highest mode and lowest mode is found to increase by increasing the biquadratic to interlayer exchange ratio and film thickness and destroying the symmetry of the system. These results can be used to improve the understanding of magnetic properties in bilayer ferromagnetic films and thus may have prominent implications for future magnetic devices.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

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Effect of antioxidants on the efficiency of jet milling and the powder characteristics of Sm2Co17 permanent magnets Da-Shuai Xu(许大帅), Lei Liu(刘雷), Jian-Hui Yuan(袁建辉), Bo Zhou(周波), Chuang-Hui Dong(董创辉), Feng-Qing Wang(王凤青), Yong Ding(丁勇), Ying-Li Sun(孙颖莉), and A-Ru Yan(闫阿儒) Chin. Phys. B, 2024, 33 (9):  098103.  DOI: 10.1088/1674-1056/ad5537 Abstract ( 78 )   HTML ( 0 )   PDF (1409KB) ( 74 )   This study investigated the effect of antioxidants on the grinding efficiency, magnetic powder characteristics, microstructure, and magnetic properties of 2:17 type SmCo permanent magnet materials. The results show that adding antioxidants helps improve the dispersion among magnetic powders, leading to a 33.3% decrease in jet milling time and a 15.8% increase in magnet powder production yield. Additionally, adding antioxidants enhances the oxidation resistance of the magnetic powders. After being stored in a constant temperature air environment at 25 ${^\circ}$C for 48 h, the O content in the powder decreased by 33% compared to samples without antioxidants. While in the magnet body, the O content decreased from 0.21 wt.% to 0.14 wt.%, which helps increase the effective Sm content and domain wall pinning uniformity in the magnet. Excellent magnetic properties were obtained in the magnet with added antioxidants: $B_{\rm r} = 11.6$ kGs, ${\rm SF} = 79.6 $%, $H_{\rm cj} = 16.8$ kOe, and $(BH)_{\max} = 32.5 $ MGOe.

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Pressure generation under deformation in a large-volume press Saisai Wang(王赛赛), Xinyu Zhao(赵鑫宇), Kuo Hu(胡阔), Bingtao Feng(丰丙涛), Xuyuan Hou(侯旭远), Yiming Zhang(张羿鸣), Shucheng Liu(刘书成), Yuchen Shang(尚宇琛), Zhaodong Liu(刘兆东), Mingguang Yao(姚明光), and Bingbing Liu(刘冰冰) Chin. Phys. B, 2024, 33 (9):  098104.  DOI: 10.1088/1674-1056/ad58c6 Abstract ( 78 )   HTML ( 1 )   PDF (1437KB) ( 40 )   Deformation can change the transition pathway of materials under high pressure, thus significantly affects physical and chemical properties of matters. However, accurate pressure calibration under deformation is challenging and thereby causes relatively large pressure uncertainties in deformation experiments, resulting in the synthesis of complex multiphase materials. Here, pressure generations of three types of deformation assemblies were well calibrated in a Walker-type large-volume press (LVP) by electrical resistance measurements combined with finite element simulations (FESs). Hard Al$_{2}$O$_{3}$ or diamond pistons in shear and uniaxial deformation assemblies significantly increase the efficiency of pressure generation compared with the conventional quasi-hydrostatic assembly. The uniaxial deformation assembly using flat diamond pistons possesses the highest efficiency in these deformation assemblies. This finding is further confirmed by stress distribution analysis based on FESs. With this deformation assembly, we found shear can effectively promote the transformation of C$_{60}$ into diamond under high pressure and realized the synthesis of phase-pure diamond at relatively moderate pressure and temperature conditions. The present developed techniques will help improve pressure efficiencies in LVP and explore the new physical and chemical properties of materials under deformation in both science and technology.

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Lewis acid-doped transition metal dichalcogenides for ultraviolet-visible photodetectors Heng Yang(杨恒), Mingjun Ma(马明军), Yongfeng Pei(裴永峰), Yufan Kang(康雨凡), Jialu Yan(延嘉璐), Dong He(贺栋), Changzhong Jiang(蒋昌忠), Wenqing Li(李文庆), and Xiangheng Xiao(肖湘衡) Chin. Phys. B, 2024, 33 (9):  098501.  DOI: 10.1088/1674-1056/ad597f Abstract ( 85 )   HTML ( 0 )   PDF (6804KB) ( 23 )   Ultraviolet photodetectors (UV PDs) are widely used in civilian, scientific, and military fields due to their high sensitivity and low false alarm rates. We present a temperature-dependent Lewis acid p-type doping method for transition metal dichalcogenides (TMDs), which can effectively be used to extend the optical response range. The p-type doping based on surface charge transfer involves the chemical adsorption of the Lewis acid SnCl$_{4}$ as a light absorption layer on the surface of WS$_{2}$, significantly enhancing its UV photodetection performance. Under 365 nm laser irradiation, WS$_{2}$ PDs exhibit response speed of 24 ms/20 ms, responsivity of 660 mA/W, detectivity of $3.3\times 10^{11}$ Jones, and external quantum efficiency of 226%. Moreover, we successfully apply this doping method to other TMDs materials (such as MoS$_{2}$, MoSe$_{2}$, and WSe$_{2})$ and fabricate WS$_{2}$ lateral p-n heterojunction PDs.

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Interfacial stress engineering toward enhancement of ferroelectricity in Al doped HfO2 thin films S X Chen(陈思学), M M Chen(陈明明), Y Liu(刘圆), D W Cao(曹大威), and G J Chen(陈国杰) Chin. Phys. B, 2024, 33 (9):  098701.  DOI: 10.1088/1674-1056/ad4ff4 Abstract ( 79 )   HTML ( 0 )   PDF (1754KB) ( 75 )   Ferroelectric HfO$_{2}$ has attracted much attention owing to its superior ferroelectricity at an ultra-thin thickness and good compatibility with Si-based complementary metal-oxide-semiconductor (CMOS) technology. However, the crystallization of polar orthorhombic phase (o-phase) HfO$_{2}$ is less competitive, which greatly limits the ferroelectricity of the as-obtained ferroelectric HfO$_{2}$ thin films. Fortunately, the crystallization of o-phase HfO$_{2}$ can be thermodynamically modulated via interfacial stress engineering. In this paper, the growth of improved ferroelectric Al doped HfO$_{2}$ (HfO$_{2}$:Al) thin films on (111)-oriented Si substrate has been reported. Structural analysis has suggested that nonpolar monoclinic HfO$_{2}$:Al grown on (111)-oriented Si substrate suffered from a strong compressive strain, which promoted the crystallization of (111)-oriented o-phase HfO$_{2}$ in the as-grown HfO$_{2}$:Al thin films. In addition, the in-plane lattice of (111)-oriented Si substrate matches well with that of (111)-oriented o-phase HfO$_{2}$, which further thermally stabilizes the o-phase HfO$_{2}$. Accordingly, an improved ferroelectricity with a remnant polarization (2$P_{\rm r}$) of 26.7 μC/cm$^{2}$ has been obtained. The results shown in this work provide a simple way toward the preparation of improved ferroelectric HfO$_{2}$ thin films.

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A solution method for decomposing vector fields in Hamilton energy Xin Zhao(赵昕), Ming Yi(易鸣), Zhou-Chao Wei(魏周超), Yuan Zhu(朱媛), and Lu-Lu Lu(鹿露露) Chin. Phys. B, 2024, 33 (9):  098702.  DOI: 10.1088/1674-1056/ad5a74 Abstract ( 88 )   HTML ( 0 )   PDF (1802KB) ( 40 )   Hamilton energy, which reflects the energy variation of systems, is one of the crucial instruments used to analyze the characteristics of dynamical systems. Here we propose a method to deduce Hamilton energy based on the existing systems. This derivation process consists of three steps: step 1, decomposing the vector field; step 2, solving the Hamilton energy function; and step 3, verifying uniqueness. In order to easily choose an appropriate decomposition method, we propose a classification criterion based on the form of system state variables, i.e., type-I vector fields that can be directly decomposed and type-I$\!$I vector fields decomposed via exterior differentiation. Moreover, exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition. Finally, we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior. This solution provides a new approach for deducing the Hamilton energy function, especially in high-dimensional systems.