Effective-Field Approach to Magnetic Properties of Spin-1 System in XXZ Model with Single-Ion Uniaxial Anisotropy

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Division of Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

Received September 16, 2019; Accepted January 6, 2020; Published February 5, 2020

In the XXZ Heisenberg model with the positive single-ion uniaxial anisotropy D, magnetic properties of the spin-1 system are studied by the one-site effective-field theory, which takes account of the effect of on-site spin fluctuations in the direction of the magnetization, neglected in the mean-field approximation. At temperatures above the transition point, a spin susceptibility is generally derived, and in the temperature range much above the exchange coupling constants and D, the susceptibility is shown to agree with that given by the mean-field approximation, leading to the correct Curie–Weiss law in accordance with the result in the high-temperature expansion. In the present case where the easy-plane of magnetization is xy-plane, the critical exchange coupling constant for the ferromagnetic order is J_x_c/D = 0.182, which is larger than the value by the mean-field approximation 0.125 due to the effect of quantum-spin fluctuations. Characteristic behaviors of the susceptibility in the absence of the ferromagnetic order are explored in detail. The results are applied to an analysis for spin–lattice relaxation rate \(T_{1}^{ - 1}\) in Li₉V₃(P₂O₇)₃(PO₄)₂, which is shown to be definitely linear in the square root of the susceptibility in the x-direction, \(T_{1}^{ - 1} \propto \chi _{\text{s}}^{x}{}^{1/2}\), consistent with the theory by Moriya.

https://doi.org/10.7566/JPSJ.89.034002

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Effective-Field Approach to Magnetic Properties of Spin-1 System in XXZ Model with Single-Ion Uniaxial Anisotropy

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