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Chin. Phys. B, 2021, Vol. 30(5): 057503    DOI: 10.1088/1674-1056/abd768

Magnetization and magnetic phase diagrams of a spin-1/2 ferrimagnetic diamond chain at low temperature

Tai-Min Cheng(成泰民)1,2,†, Mei-Lin Li(李美霖)1,2, Zhi-Rui Cheng(成智睿)3, Guo-Liang Yu(禹国梁)1, Shu-Sheng Sun(孙树生)1, Chong-Yuan Ge(葛崇员)1, and Xin-Xin Zhang(张新欣)1
1 Department of Physics, College of Sciences, Shenyang University of Chemical Technology, Shenyang 110142, China;
2 School of Materials Science and Engineering, Shenyang University of Chemical Technology, Shenyang 110142, China;
3 School of Software Engineering, Shenyang University of Technology, Shenyang 110870, China
Abstract  We used the Jordan-Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities $H_{\rm CB}$, $H_{\rm CE}$ and $H_{\rm CS}$ were obtained, in which the $H_{\rm CB}$ and $H_{\rm CE}$ correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher $H_{\rm CS}$ correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation ${\hslash \omega }_{\sigma,k}\,\,{(\sigma =1, 2, 3)}$ present the extrema of zero at the three critical magnetic fields at 0 K, i.e., $\left[ {{\hslash }\omega }_{{3,}k}\left(H_{\rm {CB}} \right) \right]_{{\min}}{=0}$, $\left[ \hslash \omega _{{2,}k}\left(H_{\rm{CE}} \right) \right]_{{\max}}{=0}$ and $\left[ {{\hslash }\omega }_{{2,k}}\left(H_{\rm{CS}} \right) \right]_{{\min}}{=0}$, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system's magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the 1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.
Keywords:  invariant eigen-operator method      Jordan-Wigner transformations      critical magnetic field intensity      magnetic phase diagrams  
Received:  04 November 2020      Revised:  21 December 2020      Accepted manuscript online:  30 December 2020
PACS:  75.50.Gg (Ferrimagnetics)  
  68.65.-k (Low-dimensional, mesoscopic, nanoscale and other related systems: structure and nonelectronic properties)  
  75.30.Kz (Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.))  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11374215 and 11704262), the Scientific Study Project from Education Department of Liaoning Province of China (Grant No. LJ2019004), and the Natural Science Foundation Guidance Project of Liaoning Province of China (Grant No. 2019-ZD-0070).
Corresponding Authors:  Tai-Min Cheng     E-mail:,

Cite this article: 

Tai-Min Cheng(成泰民), Mei-Lin Li(李美霖), Zhi-Rui Cheng(成智睿), Guo-Liang Yu(禹国梁), Shu-Sheng Sun(孙树生), Chong-Yuan Ge(葛崇员), and Xin-Xin Zhang(张新欣) Magnetization and magnetic phase diagrams of a spin-1/2 ferrimagnetic diamond chain at low temperature 2021 Chin. Phys. B 30 057503

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