Interfaces play a substantial role for the functional properties of structured magnetic materials and magnetic multilayers. Modeling the functional behavior of magnetic materials requires the treatment of the relevant phenomena at the device level. Properties predicted from the electronic structure and spin dynamics at the atomistic level have to be properly transferred into a continuum level treatment. In this work we show how Co/Ru/Co three layers can be simulated with the continuum theory of micromagnetism, with interface coupling energies and bulk intrinsic properties properly derived from the results of ab initio and spin dynamics simulations atdifferent temperatures. In the following Dataset you will find the necessary data to reproduce the plots and figures of the publication arXiv:2501.08724 cond-mat.mtrl-sci. Below follow a more detailed list what you will find including the Figure captions: Figure 7 Magnetization configurations after relaxation steps for different temperatures of hcp Co bulk. Colored regions show the averaged magnetization over one atomic Co layer of around 100 separate spin-dynamics simulations. The dot-dashed lines highlight the average of those profiles for each specific temperature. Figure 9 Magnetization profiles across the Co/Ru/Co system for various temperatures and Ru spacer thicknesses. Left: Ru spacer thickness is 1 atomic layer, the coupling across the spacer is antiferromagnetic; Center: Ru spacer thickness is 2 atomic layers, the coupling across the spacer is antiferromagnetic; Right: Ru spacer thickness is 3 atomic layers, the coupling across the spacer is ferromagnetic. The dot-dashed lines highlight the average of those profiles for each specific temperature. Figure 12 Intrinsic material properties derived from the ASD simulations. Left: Reduced temperature dependent magnetization Ms(T)/Ms(0). Center: Anisotropy constant K(T). Right: Exchange stiffness constant A(T). Figure 13 The interface exchange coupling extracted from the ∆mz relation from the Eq. 35 in units of J/m2. Figure 14 Comparison of temperature dependent magnetization profiles obtained from the ASD and algebraic solution. The colored surfaces show the ensemble of all spin-dynamics simulations. The white dotted lines show the average values (see Fig. 9), the dashed white line demonstrate the results from algebraic solution. Left and Mid: Antiferromagnetic coupling across one and two monolayers Ru. Right: Ferromagnetic coupling across three monolayer Ru atoms. Note: We show only the right side of the profiles because of symmetry.
Kovacs et al. (Wed,) studied this question.