Quantum-Classical Escape-Rate Transition of a Biaxial Spin System with a Longitudinal Field: a Perturbative Approach

TL;DR

This paper investigates the quantum-classical escape-rate transition in a biaxial spin system with a longitudinal field using a perturbative approach, revealing the conditions for first-order transitions and comparing with previous models.

Contribution

It introduces a perturbative method to analyze the transition, extending understanding of the boundary conditions for first-order escape-rate transitions in spin systems.

Findings

First-order transition occurs for B < B_c(H_z).

The boundary B_c/D scales as 1 - H_z/(2SD).

The transition temperature T_0 behaves linearly as 2SD - H_z.

Abstract

The quantum-classical transition of the escape rate of the spin model \cal H= -DS_z^2 - H_zS_z + B S_x^2 is investigated by a perturbative approach with respect to B [D. A. Garanin, J. Phys A {\bf 24}, L61 (1991)]. The transition is first order for B<B_c(H_z), the boundary line going to zero as B_c/D ~ 1 - H_z/(2SD) in the strongly biased limit. The range of the first-order transition is thus larger than for the model \cal H = -DS_z^2 - H_zS_z - H_x S_x studied earlier, where in the strongly biased case H_{xc}/(2SD) ~ [1-H_z/(2SD)]^{3/2}. The temperature of the quantum-classical transition, T_0, behaves linearly in the strongly biased case for both models: T_0 ~ 2SD - H_z.