First principles calculation of spin-interactions and magnetic ground states of Cr trimers on Au(111)

TL;DR

This study uses first principles calculations to determine the magnetic ground states of Cr trimers on Au(111), revealing complex interactions and geometries influencing their magnetic configurations.

Contribution

It introduces a symmetry-independent method to calculate magnetic interactions and ground states of small nanoparticles with arbitrary geometries.

Findings

Cr trimers exhibit antiferromagnetic interactions dominated by nearest neighbors.

Equilateral Cr trimers have a frustrated 120° Ne9el ground state.

Dzyaloshinsky-Moriya interactions influence the chirality of the magnetic state.

Abstract

We present calculations of the magnetic ground states of Cr trimers in different geometries on top of a Au(111) surface. By using a least square fit method based on a fully relativistic embedded-cluster Green's function method first we determined the parameters of a classical vector-spin model consisting of second and fourth order interactions. The newly developed method requires no symmetry constraints, therefore, it is throughout applicable for small nanoparticles of arbitrary geometry. The magnetic ground states were then found by solving the Landau-Lifshitz-Gilbert equations. In all considered cases the configurational energy of the Cr trimers is dominated by large antiferromagnetic nearest neighbor interactions, whilst biquadratic spin-interactions have the second largest contributions to the energy. We find that an equilateral Cr trimer exhibits a frustrated 120$^\circ$ N\'eel type of ground state with a small out-of-plane component of the magnetization and we show that the Dzyaloshinsky-Moriya interactions determine the chirality of the magnetic ground state. In cases of a linear chain and an isosceles trimer collinear antiferromagnetic ground states are obtained with a magnetization lying parallel to the surface.