Spin-dependent balance equations in spintronics

doi:10.1088/1674-1056/27/1/016701

Abstract It is commonly known that the hydrodynamic equations can be derived from the Boltzmann equation. In this paper, we derive similar spin-dependent balance equations based on the spinor Boltzmann equation. Besides the usual charge current, heat current, and pressure tensor, we also explore the characteristic spin accumulation and spin current as well as the spin-dependent pressure tensor and heat current in spintronics. The numerical results of these physical quantities are demonstrated using an example of spin-polarized transport through a mesoscopic ferromagnet.

Keywords: spin-dependent balance equations spinor Boltzmann equation spintronics spin current

Received: 27 July 2017
Revised: 18 September 2017
Accepted manuscript online:

PACS:	67.10.Jn	(Transport properties and hydrodynamics)
	71.10.Ay	(Fermi-liquid theory and other phenomenological models)
	72.25.-b	(Spin polarized transport)
	72.10.Bg	(General formulation of transport theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11274378), the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB08-3), and the MOST of China (Grant No. 2013CB933401).

Corresponding Authors: Zheng-Chuan Wang
E-mail: wangzc@ucas.ac.cn

Cite this article:

Zheng-Chuan Wang(王正川) Spin-dependent balance equations in spintronics 2018 Chin. Phys. B 27 016701

[1]	Landau L D and Lifshitz E M 1959 Fluid Mechanics (Oxford: Pergamon Press)
[2]	Madelung E 1926 Z. Phys. 40 322
[3]	Jüngel A 2009 Transport Equations for Semiconductors (Berlin: Springer)
[4]	Landau L D 1956 Zh. Eksp. Teor. Fiz. 30 1058
[5]	Landau L D 1956 Sov. Phys.-JETP 3 920
[6]	Pines D and Nozieres P 1966 The Theory of Quantum Liquids (New York: Benjamin)
[7]	Smith H and Jensen H H 1989 Transport Phenomena (Oxford: Clarendon Press)
[8]	Galasiewicz Z M 1984 Journal of Low Temperature Physics 57 123
[9]	Galasiewicz Z M 1988 Journal of Low Temperature Physics 72 153
[10]	Silin V P 1957 Zh. Eksp. Teor. Fiz. 33 495
[11]	Silin V P 1958 Sov. Phys.-JETP 6 387
[12]	Abrikosov A A and Dzyaloshinskil I E 1958 Zh. Eksp. Teor. Fiz. 35 771
[13]	Abrikosov A A and Dzyaloshinskil I E 1959 Sov. Phys. JETP 8 535
[14]	Kondratenko S 1964 Zh. Eksp. Teor. Fiz. 46 1438
[15]	Kondratenko S 1964 Sov. Phys. JETP 19 972
[16]	Kondratenko S 1964 Zh. Eksp. Teor. Fiz. 47 1536
[17]	Kondratenko S 1965 Sov. Phys. JETP 20 1032
[18]	Julliere M, Baibich M N, et al. 1988 Phys. Rev. Lett. 61 2472
[19]	Slonczewski J C 1989 Phys. Rev. B 39 6995
[20]	Slonczewski J C 1996 J. Magn. Magn. Mater. 159 L1
[21]	Slonczewski J C 1999 J. Magn. Magn. Mater. 195 L261
[22]	Berger L 1996 Phys. Rev. B 54 9353
[23]	Berger L 2001 J. Appl. Phys. 89 5521
[24]	Valet T and Fert A 1993 Phys. Rev. B 48 7099
[25]	Wen H Y and Xia J B 2017 Chin. Phys. B 26 047501
[26]	Zhang S, Levy P M and Fert A 2002 Phys. Rev. Lett. 88 23601
[27]	Shapiro A and Levy P M 2000 Phys. Rev. B 63 014419
[28]	Wang Z C 2012 Commun. Theor. Phys. 58 909
[29]	Wang Z C 2017 Physica A 465 754
[30]	Wang Z C, Su G and Gao S 2001 Phys. Rev. B 63 224419
[31]	Breton J C Le, Sharma S, Saito H, Yuasa S and Jansen R 2011 Nature 475 10224
[32]	Bauer G E, Saitoh E and van Wees B J 2012 Nat. Mater. 23 3301
[33]	Czerner M, Bachmann M and Heiliger C 2011 Phys. Rev. B 83 132405
[34]	Zhang J, Levy P M, Zhang S and Antropov V 2004 Phys. Rev. Lett. 93 256602
[35]	Sheng L, Xing D Y, Wang Z D and Dong J 1997 Phys. Rev. B 55 5908
[36]	Kadanoff L P and Baym G 1962 Quantum Statistical Mechanics (New York: Benjamin)
[37]	Mahan G D 1987 Phys. Rep. 145 251
[38]	Sheng L, Teng H Y and Xing D Y 1998 Phys. Rev. B 58 6428
[39]	Wang Z C 2012 Euro. Phys. J. B 85 303

[1]	Magnetic triangular bubble lattices in bismuth-doped yttrium iron garnet Tao Lin(蔺涛), Chengxiang Wang(王承祥), Zhiyong Qiu(邱志勇), Chao Chen(陈超), Tao Xing(邢弢), Lu Sun(孙璐), Jianhui Liang(梁建辉), Yizheng Wu(吴义政), Zhong Shi(时钟), and Na Lei(雷娜). Chin. Phys. B, 2023, 32(2): 027505.
[2]	Magnetic van der Waals materials: Synthesis, structure, magnetism, and their potential applications Zhongchong Lin(林中冲), Yuxuan Peng(彭宇轩), Baochun Wu(吴葆春), Changsheng Wang(王常生), Zhaochu Luo(罗昭初), and Jinbo Yang(杨金波). Chin. Phys. B, 2022, 31(8): 087506.
[3]	Current spin polarization of a platform molecule with compression effect Zhi Yang(羊志), Feng Sun(孙峰), Deng-Hui Chen(陈登辉), Zi-Qun Wang(王子群), Chuan-Kui Wang(王传奎), Zong-Liang Li(李宗良), and Shuai Qiu(邱帅). Chin. Phys. B, 2022, 31(7): 077202.
[4]	The 50 nm-thick yttrium iron garnet films with perpendicular magnetic anisotropy Shuyao Chen(陈姝瑶), Yunfei Xie(谢云飞), Yucong Yang(杨玉聪), Dong Gao(高栋), Donghua Liu(刘冬华), Lin Qin(秦林), Wei Yan(严巍), Bi Tan(谭碧), Qiuli Chen(陈秋丽), Tao Gong(龚涛), En Li(李恩), Lei Bi(毕磊), Tao Liu(刘涛), and Longjiang Deng(邓龙江). Chin. Phys. B, 2022, 31(4): 048503.
[5]	Magnetoresistance effect in vertical NiFe/graphene/NiFe junctions Pei-Sen Li(李裴森), Jun-Ping Peng(彭俊平), Yue-Guo Hu(胡悦国), Yan-Rui Guo(郭颜瑞), Wei-Cheng Qiu(邱伟成), Rui-Nan Wu(吴瑞楠), Meng-Chun Pan(潘孟春), Jia-Fei Hu(胡佳飞), Di-Xiang Chen(陈棣湘), and Qi Zhang(张琦). Chin. Phys. B, 2022, 31(3): 038502.
[6]	Skyrmion transport driven by pure voltage generated strain gradient Shan Qiu(邱珊), Jia-Hao Liu(刘嘉豪), Ya-Bo Chen(陈亚博), Yun-Ping Zhao(赵云平), Bo Wei(危波), and Liang Fang(方粮). Chin. Phys. B, 2022, 31(11): 117701.
[7]	Spin current in a spinor Bose-Einstein condensate induced by a gradient magnetic field Li Tian(田丽), Ningxuan Zheng(郑宁宣), Jun Jian(蹇君), Wenliang Liu(刘文良), Jizhou Wu(武寄洲), Yuqing Li(李玉清), Yongming Fu(付永明), Peng Li(李鹏), Vladimir Sovkov, Jie Ma(马杰), Liantuan Xiao(肖连团), and Suotang Jia(贾锁堂). Chin. Phys. B, 2022, 31(11): 110302.
[8]	Negative tunnel magnetoresistance in a quantum dot induced by interplay of a Majorana fermion and thermal-driven ferromagnetic leads Peng-Bin Niu(牛鹏斌), Bo-Xiang Cui(崔博翔), and Hong-Gang Luo(罗洪刚). Chin. Phys. B, 2021, 30(9): 097401.
[9]	Ultra-low Young's modulus and high super-exchange interactions in monolayer CrN: A promising candidate for flexible spintronic applications Yang Song(宋洋), Yan-Fang Zhang(张艳芳), Jinbo Pan(潘金波), and Shixuan Du(杜世萱). Chin. Phys. B, 2021, 30(4): 047105.
[10]	Pure spin-current diode based on interacting quantum dot tunneling junction Zhengzhong Zhang(张正中), Min Yu(余敏), Rui Bo(薄锐), Chao Wang(王超), and Hao Liu(刘昊). Chin. Phys. B, 2021, 30(11): 117305.
[11]	Detection of spin current through a quantum dot with Majorana bound states Ning Wang(王宁), Xingtao An(安兴涛), and Shuhui Lv(吕树慧). Chin. Phys. B, 2021, 30(10): 100302.
[12]	Exploring ferromagnetic half-metallic nature of Cs₂NpBr₆ via spin polarized density functional theory Malak Azmat Ali, G Murtaza, A Laref. Chin. Phys. B, 2020, 29(6): 066102.
[13]	Tunneling magnetoresistance in ferromagnet/organic-ferromagnet/metal junctions Yan-Qi Li(李彦琪), Hong-Jun Kan(阚洪君), Yuan-Yuan Miao(苗圆圆), Lei Yang(杨磊), Shuai Qiu(邱帅), Guang-Ping Zhang(张广平), Jun-Feng Ren(任俊峰), Chuan-Kui Wang(王传奎), Gui-Chao Hu(胡贵超). Chin. Phys. B, 2020, 29(1): 017303.
[14]	Spin transport in antiferromagnetic insulators Zhiyong Qiu(邱志勇), Dazhi Hou(侯达之). Chin. Phys. B, 2019, 28(8): 088504.
[15]	Magnetization-direction-dependent inverse spin Hall effect observed in IrMn/NiFe/Cu/YIG multilayer structure Runrun Hao(郝润润), Ruxue Zang(臧如雪), Tie Zhou(周铁), Shishou Kang(康仕寿), Shishen Yan(颜世申), Guolei Liu(刘国磊), Guangbing Han(韩广兵), Shuyun Yu(于淑云), Liangmo Mei(梅良模). Chin. Phys. B, 2019, 28(3): 037202.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Spin-dependent balance equations in spintronics

Cite this article:

Online attention