# Metadynamics study of the temperature dependence of magnetic anisotropy and spin-reorientation transitions in ultrathin films

## TL;DR

This study uses metadynamics simulations to explore how magnetic anisotropy and spin orientations in ultrathin ferromagnetic films change with temperature, providing insights into phase transitions and magnetic behavior.

## Contribution

It introduces a systematic simulation approach combining first-principles parameters to analyze temperature-dependent magnetic phenomena in ultrathin films.

## Key findings

- Reproduces the power-law behavior of magnetic anisotropy energy.
- Identifies spin-reorientation transitions consistent with experimental data.
- Demonstrates the effectiveness of metadynamics in magnetic studies.

## Abstract

We employ metadynamics simulations to calculate the free energy landscape of thin ferromagnetic films and perform a systematic study of the temperature dependence of magnetic anisotropy and of the spin-reorientation transitions. By using a simple spin model we recover the well-known power-law behavior of the magnetic anisotropy energy against magnetization and present a rather detailed analysis of the spin-reorientation transitions in ultrathin films. Based on tensorial exchange interactions and anisotropy parameters derived from first-principles calculations we perform simulations for Fe double layers deposited on Au(001) and W(110). In case of Fe$_2$W(110) our simulations display an out-of-plane to in-plane spin-reorientation transition in agreement with experiments.