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

We calculated 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 was applied to the samples investigated by means of spin-polarized scanning tunneling microscopy. Quantum fluctuations around thermal equilibrium were analyzed and calculated. The time-averaged expectation values agree with the time-averaged experimental data for magnetization curves. The method was used to investigate the dynamics of a sample for shorter times than the resolution time of the experimental setup. Furthermore, predictions of the relaxation times of single spins on metallic and semiconductor surfaces are made. To check the validity of our model, we compared our results with experimental data obtained from Fe adatoms on InSb and from Co adatoms on Pt(111) and found good agreement. Approximated thermalization was found numerically for the expectation values of the spin operators.