Fast \textit{ab initio} design of high-entropy magnetic thin films

Abstract

We show that the magnetic properties of high-entropy alloys (HEAs) can be captured by \textit{ab initio} calculations within the coherent potential approximation, where the atomic details of the high-entropy mixing are considered as an effective medium that possesses the translational symmetry of the lattice. This is demonstrated using the face-centered cubic (FCC) phase of $\textrm{FeCoNiMnCu}$ and the $L1_0$ phase of $\textrm{(FeCoNiMnCu)Pt}$ by comparing the density functional theory (DFT) results with the experimental values. Working within the first Brillouin zone and the primitive unit cell, we show that DFT can capture the smooth profile of magnetic properties such as the saturation magnetization, the Curie temperature and the magnetic anisotropy, using only a sparse set of sampling points in the vast compositional space. The smooth profiles given by DFT indeed follow the experimental trend, demonstrating the promising potential of using machine learning to explore the magnetic properties of HEAs, by establishing reasonably large datasets with high-throughput calculations using density-functional theory.

Figures (4)

• Figure 1: (a) The Spectral function of $L1_0\textrm{-phase}$$\textrm{FePt}$ obtained by the Green's function implementation of DFT in Questaal. Coherent potential approximation was used assuming no random mixing to resolve the band structure. An overall broadening energy of $0.001\textrm{Ryd}$ was applied to visualize the spectral function. (b) The spectral function in the case of $[\textrm{Fe}_{0.8}\textrm{CoNiMnCu}_{0.2}]\textrm{Pt}$ with the random mixing slightly turned on for Fe sites. (c) The VASP result of pure FePt with eigenstates projected to Fe and Pt orbitals. The weight of the projection is denoted by the color scale. The energy cutoff was set to $400\textrm{eV}$, and the DFT-D3 dispersion correction with Becke-Johnson damping was usedgrimme_a_consistent_2010becke_a_density-functional_2005grimme_effect_2011. A $\Gamma$-centered $12\times12\times9$ mesh was used for the k-space integration. The convergence criterion was set to $10^{-7}\textrm{eV}.$
• Figure 2: Magnetic properties of the high-entropy crystal $\textrm{FeCoNiMnCu}$ in the FCC phase. (a) The conventional FCC unit cell with all atomic sites randomly occupied by the five different elements. (b) The saturation magnetization when modulating the concentration of one high-entropy element. All other high-entropy elements are adjusted proportionately to maintain a total concentration of $100\%$. The central composition of $0.2$ corresponds to the equiatomic case. (c) The modulation of Curie temperature corresponding to changes in the concentration of one element, according to the pattern described in (b).
• Figure 3: The saturation magnetization and the Curie temperature of high-entropy magnet $\textrm{(FeCoNiMnCu)Pt}$ in the $L1_0$ phase. (a) The primitive unit cell of the tetragonal lattice. (b) The saturation magnetization when modulating the concentration of one high-entropy element on the corner sites. All other corner sites are adjusted proportionately to maintain a total concentration of $100\%$. The body-center Pt site is assumed to be uniformly occupied. The $20\%$ concentration corresponds to the equiatomic case for all the corner sites. (c) The modulation of Curie temperature corresponding to changes in the concentration of one element, following the pattern described in (b).
• Figure 4: The magnetic anisotropy energy density (MAE) of the $L1_0$ high-entropy magnet $\textrm{(FeCoNiMnCu)Pt}$. (a) The variation of MAE for different compositions when each high entropy element is modulated following the pattern described in Figs. \ref{['fig:FCC']} and \ref{['fig:L10']}. (b) The compositions in (a) projected from $\mathbb{R}^{5}$ to $\mathbb{R}^{2}$ using Multidimensional Scaling (MDS), which preserves the Euclidean distances between points. Color saturation denotes the MAE values scaled between $0$ and $1$. The red and blue points denote the DFT and the experimental results, respectively. (c-d) Direct comparison between the theoretical and experimental results for the $5$ samples highlighted in (b). Here the $M_S$ comparison is shown in (c), whereas the MAE comparison is shown in (d). Note that $M_S$ is compared with the same scale in (c), whereas the MAE comparison is illustrated on different scales in (d).