中国物理B ›› 2004, Vol. 13 ›› Issue (7): 1124-1128.doi: 10.1088/1009-1963/13/7/028

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Comparison of calculation methods for the tunnel splitting at excited states of biaxial spin models

崔晓波1, 陈芝得2   

  1. (1)Department of Physics and Institute of Modern Condensed Matter Physics, Guangzhou University, Guangzhou 510405, China; (2)Department of Physics, Jinan University, Guangzhou 510632, China
  • 收稿日期:2003-01-15 修回日期:2003-12-09 出版日期:2004-07-05 发布日期:2005-07-05

Comparison of calculation methods for the tunnel splitting at excited states of biaxial spin models

Cui Xiao-Bo (崔晓波)a, Chen Zhi-De (陈芝得)b   

  1. a Department of Physics and Institute of Modern Condensed Matter Physics, Guangzhou University, Guangzhou 510405, China; b Department of Physics, Jinan University, Guangzhou 510632, China
  • Received:2003-01-15 Revised:2003-12-09 Online:2004-07-05 Published:2005-07-05

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摘要： We present the calculation and comparison of tunnel splitting at excited levels of biaxial spin models by various methods, including the generalized instanton method, the generalized path integral method for coherent spin states, the perturbation method, and the exact method by numerical diagonalization of the Hamiltonian. It is found that, for integer spin with spin number around 10, tunnel splitting predicted by the generalized path integral for coherent spin states is about 10^{-n} times of the exact numerical result for the nth excited level, while the ratio of the results of the perturbation method and the exact numerical method diverges in the large spin limit. We thus conclude that the generalized instanton method is the best approximate way for calculating tunnel splitting in spin models.

关键词: tunnel splitting, biaxial spin models, single molecular magnet

Abstract: We present the calculation and comparison of tunnel splitting at excited levels of biaxial spin models by various methods, including the generalized instanton method, the generalized path integral method for coherent spin states, the perturbation method, and the exact method by numerical diagonalization of the Hamiltonian. It is found that, for integer spin with spin number around 10, tunnel splitting predicted by the generalized path integral for coherent spin states is about $10^{-n}$ times of the exact numerical result for the nth excited level, while the ratio of the results of the perturbation method and the exact numerical method diverges in the large spin limit. We thus conclude that the generalized instanton method is the best approximate way for calculating tunnel splitting in spin models.

Key words: tunnel splitting, biaxial spin models, single molecular magnet

中图分类号:  (Excited states: methodology)

  • 71.15.Qe
71.70.-d (Level splitting and interactions) 75.10.-b (General theory and models of magnetic ordering)