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

Abstract

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 Jxc/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.