Dynamics of molecular nanomagnets in time-dependent external magnetic fields: Beyond the Landau-Zener-St\"{u}ckelberg model

TL;DR

This paper investigates the magnetization dynamics of molecular nanomagnets under time-dependent magnetic fields, revealing deviations from traditional models and introducing an efficient approximation method that accounts for both coherent and decoherent effects.

Contribution

It provides the first exact numerical solutions for the system's time evolution and develops a new approximation method that captures multilevel transition effects beyond the Landau-Zener-Stückelberg model.

Findings

Transition probabilities deviate from Landau-Zener predictions due to multilevel effects.

An efficient approximation reproduces exact numerical results accurately.

Decoherence reduces magnetization step size without altering the fundamental dynamics.

Abstract

The time evolution of the magnetization of a magnetic molecular crystal is obtained in an external time-dependent magnetic field, with sweep rates in the kT/s range. We present the 'exact numerical' solution of the time dependent Schr\"{o}dinger equation, and show that the steps in the hysteresis curve can be described as a sequence of two-level transitions between adiabatic states. The multilevel nature of the problem causes the transition probabilities to deviate significantly from the predictions of the Landau-Zener-St\"{u}ckelberg model. These calculations allow the introduction of an efficient approximation method that accurately reproduces the exact results. When including phase relaxation by means of an appropriate master equation, we observe an interplay between coherent dynamics and decoherence. This decreases the size of the magnetization steps at the transitions, but does not modify qualitatively the physical picture obtained without relaxation.