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

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 squares fit method based on results obtained by means of a fully relativistic embedded-cluster Green's function method, first we determined the parameters of a classical spin vector model containing second- and fourth-order interactions. The developed method requires no a priori assumed symmetry constraints; therefore, it is applicable throughout for small nanoparticles of arbitrary geometry. The magnetic ground states were then found by solving the Landau-Lifshitz-Gilbert equations. In all cases considered, the configurational energy of the Cr trimers is dominated by large antiferromagnetic nearest neighbor interactions, while the biquadratic spin interactions provide the second largest contributions to the energy. We find that an equilateral Cr trimer exhibits a frustrated $120\ifmmode^\circ\else\textdegree\fi{}$ N\'eel type of ground state with a small out-of-plane component of the magnetization. Furthermore, 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 the magnetization lying parallel to the surface.