Non-equilibrium finite temperature dynamics of magnetic quantum systems: Applications to spin-polarized scanning tunneling microscopy

TL;DR

This paper develops a mathematical framework based on $C^*$-algebras to analyze the non-equilibrium finite temperature dynamics of quantum spin systems, with applications to spin-polarized scanning tunneling microscopy, and validates it against experimental data.

Contribution

It introduces a $C^*$-algebra approach to model quantum spin dynamics at finite temperatures, providing new insights into relaxation times and thermalization processes.

Findings

Time-averaged expectations match experimental magnetization data.

Predictions for relaxation times of single spins on surfaces.

Good agreement with experimental data from Fe and Co adatoms.

Abstract

We calculate the real time non-equilibrium dynamics of quantum spin systems at finite temperatures. The mathematical framework originates from the $C^*$-approach to quantum statistical mechanics and is applied to samples investigated by means of spin-polarized scanning tunneling microscopy. Quantum fluctuations around thermal equilibrium are analyzed and calculated. The time averaged expectation values agree with the time averaged experimental data for magnetization curves. The method is used to investigate the dynamics of a sample for shorter times than the resolution time of the experimental setup. Furthermore, predictions for relaxation times of single spins on metallic and semiconductor surfaces are made. To check the validity of our model we compare our results with experimental data obtained from Fe adatoms on InSb and Co adatoms on Pt(111) and find good agreement. Approximated thermalization is found numerically for the expectation values of the spin operators.