Self-Consistent Field Theory studies of the thermodynamics and quantum spin dynamics of magnetic Skyrmions

TL;DR

This paper develops a self-consistent field theory to analyze the thermodynamics and quantum spin dynamics of magnetic Skyrmions in an $S=1$ quantum spin system, revealing phase transitions and quantum annihilation processes.

Contribution

It introduces a novel self-consistent field approach to study Skyrmion thermodynamics and quantum dynamics, including phase transitions and electric field-driven annihilation.

Findings

Skyrmion undergoes a first-order phase transition to ferromagnetic phase with increasing temperature.

Surrounding ferromagnet exhibits a second-order phase transition to paramagnetic phase.

Quantum mechanical description of Skyrmion annihilation aligns with semi-classical spin dynamics trajectories.

Abstract

A self-consistent field theory is introduced and used to investigate the thermodynamics and spin dynamics of an $S = 1$ quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. It is shown that the Skyrmion carries a phase transition to the ferromagnetic phase of first order with increasing temperature, while the magnetization of the surrounding ferromagnet undergoes a phase transition of second order when changing to the paramagnetic phase. Furthermore, the electric field driven annihilation process of the Skyrmion is described quantum mechanical by solving the time dependent Schr\"odinger equation. The results are compared with the trajectories of the semi-classical description of the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.