# Comparison of first-principles methods to extract magnetic parameters in ultra-thin films: Co/Pt(111)

## TL;DR

This study compares three first-principles computational methods to accurately determine magnetic interactions in a Co monolayer on Pt(111), revealing differences in parameters depending on the magnetic structure and providing insights into magnetic properties at the nanoscale.

## Contribution

It systematically compares different first-principles approaches for magnetic parameter extraction in ultra-thin films, highlighting their consistency and differences in various magnetic regimes.

## Key findings

- Methods (i) and (ii) yield consistent micromagnetic parameters.
- Calculated spin stiffness and Curie temperature are significantly higher than bulk Co.
- Nearest-neighbor exchange interaction in the monolayer is increased by 50%.

## Abstract

We compare three distinct computational approaches based on first-principles calculations within density functional theory to explore the magnetic exchange and the Dzyaloshinskii-Moriya interactions (DMI) of a Co monolayer on Pt(111), namely (i) the method of infinitesimal rotations of magnetic moments based on the Korringa-Kohn-Rostoker (KKR) Green function method, (ii) the generalized Bloch theorem applied to spiraling magnetic structures and (iii) supercell calculations with non-collinear magnetic moments, the latter two being based on the full-potential linearized augmented plane wave (FLAPW) method. In particular, we show that the magnetic interaction parameters entering micromagnetic models describing the long-wavelength deviations from the ferromagnetic state might be different from those calculated for fast rotating magnetic structures, as they are obtained by using (necessarily rather small) supercell or large spin-spiral wave-vectors. In the micromagnetic limit, which we motivate to use by an analysis of the Fourier components of the domain-wall profile, we obtain consistent results for the spin stiffness and DMI spiralization using methods (i) and (ii). The calculated spin stiffness and Curie temperature determined by subsequent Monte Carlo simulations are considerably higher than estimated from the bulk properties of Co, a consequence of a significantly increased nearest-neighbor exchange interaction in the Co-monolayer (+50%). The calculated results are carefully compared with the literature.