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

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 Fe2W(110) our simulations display an out-of-plane to in-plane spin-reorientation transition in agreement with experiments.

Spin reorientation transition in an ultrathin Fe film on W(110) induced by Dzyaloshinsky-Moriya interactions

“…(1) was confirmed by calculating the temperaturedependent magnetic anisotropy energy (MAE) K, defined as the free-energy difference per spin between in-plane and normal-to-plane magnetic configurations. This was performed via well-tempered metadynamics simulations [37][38][39], a Monte Carlo-based method enabling to sample the freeenergy surface. As shown in Fig.…”

“…The computational scheme is described in detail in Ref. [39]. During the simulations, the free energy is sampled along a collective variable η = M z /M, where M z = p,i (s piẑ ) is the z component of the magnetization, M = p,i s p,i , and M = |M|.…”

“…Following the notations used in Ref. [39], the height of the Gaussian bias potentials was w 0 = 0.04 mRy, their width was σ = 0.06, and the metadynamics temperature was set to T m = 10 400 K. The simulations were performed on a 64 × 64 × 2 lattice.…”