Quantum Landau-Lifshitz-Bloch equation and its comparison with the classical case

TL;DR

This paper derives the quantum Landau-Lifshitz-Bloch equation for spin systems, compares it with the classical version, and discusses differences in relaxation rates and magnetization dynamics.

Contribution

It provides a detailed derivation of the quantum LLB equation for spin-phonon and spin-electron interactions, highlighting differences from the classical model.

Findings

Quantum magnetization dynamics are slower than classical.

Temperature-dependent relaxation rates are analyzed for both mechanisms.

The quantum LLB equation is formulated for comparison with classical models.

Abstract

The detailed derivation of the quantum Landau-Lifshitz-Bloch (qLLB) equation for simple spin-flip scattering mechanisms based on spin-phonon and spin-electron interactions is presented and the approximations are discussed. The qLLB equation is written in the form, suitable for comparison with its classical counterpart. The temperature dependence of the macroscopic relaxation rates is discussed for both mechanisms. It is demonstrated that the magnetization dynamics is slower in the quantum case than in the classical one.