Periodic Instanton and Phase Transition in Quantum Tunneling of Spin Systems

TL;DR

This paper investigates quantum-classical phase transitions in spin systems using the periodic instanton method, revealing conditions for first-order transitions in uniaxial and biaxial magnetic models.

Contribution

It introduces a novel application of the periodic instanton approach to analyze phase transitions in spin tunneling systems, expanding the effective free energy near the barrier top.

Findings

First-order transition occurs below h_x=1/4 in uniaxial spins.

Transition occurs beyond λ=1/2 in biaxial ferromagnets.

Results agree with previous theoretical predictions.

Abstract

The quantum-classical transitions of the escape rates in a uniaxial spin model relevant to the molecular magnet Mn$_{12}$Ac and a biaxial anisotropic ferromagnetic particle are investigated by applying the periodic instanton method. The effective free energies are expanded around the top of the potential barrier in analogy to Landau theory of phase transitions. We show that the first-order transitions occur below the critical external magnetic field $h_x = 1/4$ for the uniaxial spin model and beyond the critical anisotropy constant ratio $\lambda = 1/2$ for the biaxial ferromagnetic grains, which are in good agreement with earlier works.