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 square fit method based on a fully relativistic embedded-cluster Green's function method first we determined the parameters of a classical vectorspin 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 • Néel 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.

Atomistic spin model based on a spin-cluster expansion technique: Application to the IrMn3/Co interface

“…For complex magnetic structures, however, the use of such a reference state might lead to incorrect results concerning, e.g., the magnetic ground state of the system. 13 Another drawback of RTM is that for systems with reduced point group symmetry the derivation of the anisotropy matrix, K i , might be quite a cumbersome task. More importantly, RTM is not directly applicable to the calculation of more complicated two-spin interactions, such as biquadratic coupling, or multispin interactions, known to be present in magnetic systems at the nano-scale.…”

“…More importantly, RTM is not directly applicable to the calculation of more complicated two-spin interactions, such as biquadratic coupling, or multispin interactions, known to be present in magnetic systems at the nano-scale. 13,14 The Spin-Cluster Expansion (SCE) developed by Drautz and Fähnle 15,16 in principle solves the problems mentioned above, in that it provides a systematic parametrization of the adiabatic magnetic energy of general classical spin-systems. In the following we briefly outline the method.…”

Chiral Asymmetry of the Spin-Wave Spectra in Ultrathin Magnetic Films

“…This method opened the way to atomistic spin-model simulations of nanostructures accounting for relevant relativistic interactions, such as the on-site magnetic anisotropy, the anisotropic symmetric exchange interaction and the antisymmetric exchange interaction. [18,21,30,31] By using the convention, H = − i =j J ij e i e j , our calculated isotropic exchange interactions for the first few neighbors are, J 01 = 10.84 meV, J 02 = −3.34 meV, J 03 = 3.64 meV and J 04 = 4.60 meV. Note that, in particular, the nearest neighbor interaction, J 01 , is about four times less in magnitude than the corresponding parameter in Ref.…”

From collinear to vortex magnetic structures in Mn corrals on Pt(111)

“…As concerns first principles theory, which is the focus of the present study, we note that previous studies have been made for supported clusters, both as concerns the electronic structure 7,8 as well as magnetic configurations, where in particular the possibility for non-collinear magnetic structures have been discussed [9][10][11][12][13] . In this paper we have extended our previous efforts in describing the electronic structure and magnetic properties of supported clusters, to investigate the magnetic ordering and interatomic exchange-interactions for corrals of Mn atoms, deposited on a Pt(111) surface.…”