# Spin-spiral formalism based on the multiple scattering Green's function technique with applications to ultrathin magnetic films and multilayers

## TL;DR

This paper introduces a Green's function-based computational method for analyzing spin-spiral magnetic states in layered systems, enabling detailed study of magnetic interactions and effects of spin-orbit coupling in ultrathin films and multilayers.

## Contribution

The paper develops a novel computational scheme combining non-relativistic and relativistic Green's function techniques to accurately model spin-spiral states and Dzyaloshinskii-Moriya interactions in layered magnetic systems.

## Key findings

- Successfully describes magnetic ground states of Mn/W(001) and Co/Pt(111).
- Reveals changes in magnetic interactions when capping Co/Pt(111) with Ru.
- Identifies long-wavelength spin-spiral ground states in multilayer systems.

## Abstract

Based on the Korringa-Kohn-Rostoker Green's function technique we present a computational scheme for calculating the electronic structure of layered systems with homogeneous spin-spiral magnetic state. From the self-consistent non-relativistic calculations the total energy of the spin-spiral states is determined as a function of the wave vector, while a relativistic extension of the formalism in first order of the spin-orbit coupling gives an access to the effect of the Dzyaloshinskii-Moriya interactions. We demonstrate that the newly developed method properly describes the magnetic ground state of a Mn monolayer on W(001) and that of a Co monolayer on Pt(111). The obtained spin-spiral energies are mapped to a classical spin model, the parameters of which are compared to those calculated directly from the relativistic torque method. In case of the Co/Pt(111) system we find that the isotropic interaction between the Co atoms is reduced and the Dzyaloshinskii-Moriya interaction is increased when capped by a Ru layer. In addition, we perform spin-spiral calculations on Ir/Fe/Co/Pt and Ir/Co/Fe/Pt multilayer systems and find a spin-spiral ground state with very long wavelength due to the frustrated isotropic couplings between the Fe atoms, whereas the Dzyaloshinskii-Moriya interaction strongly depends on the sequence of the Fe and Co layers.