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Composition-driven magnetic anisotropy and spin polarization in Mn$_2$Ru$_{1-x}$Ga Heusler alloy

Ramón Cuadrado

Abstract

We present a comprehensive investigation of the influence of Ru concentration on the lattice parameters, atomic magnetic moments, electronic structure, and magnetic anisotropy energy of the full Heusler L2$_1$-type Mn$_2$Ru$_{1-x_p}$Ga alloy, where x$_p$ = 0.0834 p with p=0,...,12. This study combines first-principles calculations with data-driven techniques from artificial intelligence, specifically principal component analysis (PCA), to reveal trends and correlations across multiple structural, magnetic, and electronic descriptors. For each composition, a set of inequivalent atomic configurations was fully optimized. Structurally, the relaxed lattices exhibit anisotropic expansion, with a pronounced elongation of the out-of-plane lattice parameter ($c$) relative to the in-plane lattice vectors, which promotes the development of perpendicular magnetic anisotropy. Our results reveal that an out-of-plane easy axis emerges at intermediate Ru concentrations (25-28%), while low and high Ru levels favor an in-plane orientation or even vanishing anisotropy. The half-metallic character is also modulated by Ru content, appearing selectively at both ends of the composition range. Additionally, the ferrimagnetic coupling between Mn(4a) and Mn(4c) sublattices leads to nearly compensated magnetic moments below 50% Ru content, with a net moment close to zero around 30%. These findings open a pathway toward the design of tunable spintronic materials with co-optimized perpendicular magnetic anisotropy and half-metallicity, making Mn$_2$RuGa a promising candidate for magnetic tunnel junctions, magnetoresistive random-access memory (MRAM) devices, and high-density magnetic storage applications.

Composition-driven magnetic anisotropy and spin polarization in Mn$_2$Ru$_{1-x}$Ga Heusler alloy

Abstract

We present a comprehensive investigation of the influence of Ru concentration on the lattice parameters, atomic magnetic moments, electronic structure, and magnetic anisotropy energy of the full Heusler L2-type MnRuGa alloy, where x = 0.0834 p with p=0,...,12. This study combines first-principles calculations with data-driven techniques from artificial intelligence, specifically principal component analysis (PCA), to reveal trends and correlations across multiple structural, magnetic, and electronic descriptors. For each composition, a set of inequivalent atomic configurations was fully optimized. Structurally, the relaxed lattices exhibit anisotropic expansion, with a pronounced elongation of the out-of-plane lattice parameter () relative to the in-plane lattice vectors, which promotes the development of perpendicular magnetic anisotropy. Our results reveal that an out-of-plane easy axis emerges at intermediate Ru concentrations (25-28%), while low and high Ru levels favor an in-plane orientation or even vanishing anisotropy. The half-metallic character is also modulated by Ru content, appearing selectively at both ends of the composition range. Additionally, the ferrimagnetic coupling between Mn(4a) and Mn(4c) sublattices leads to nearly compensated magnetic moments below 50% Ru content, with a net moment close to zero around 30%. These findings open a pathway toward the design of tunable spintronic materials with co-optimized perpendicular magnetic anisotropy and half-metallicity, making MnRuGa a promising candidate for magnetic tunnel junctions, magnetoresistive random-access memory (MRAM) devices, and high-density magnetic storage applications.

Paper Structure

This paper contains 11 sections, 3 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Theoretical Methods
  3. Scope and robustness of the computational approach
  4. Results and discussion
  5. DFT structural optimizations
  6. Magnetic moments
  7. Projected density of states
  8. Magnetic anisotropy energy
  9. Exploratory Analysis of Structural and Electronic Descriptors
  10. Conclusions
  11. Acknowledgments

Figures (11)

  • Figure 1: (Colour online) Schematic representation of the full Heusler L2$_1$--type Mn$_2$RuGa bulk alloy. Dark and light blue spheres represent Mn atoms occupying inequivalent crystallographic Wyckoff positions (4a and 4c, respectively), while light cyan and green spheres denote Ga (4b) and Ru (4d) atoms, respectively. Wyckoff positions are indicated in brackets, and arrows superimposed on Mn atoms illustrate the orientation of their local MMs.
  • Figure 2: (Colour online) Heat map of the PCA loadings for the selected descriptors of Mn$_2$Ru$_{1-x_p}$Ga. Each cell represents the contribution of a descriptor to a given principal component (PC1–PC10). High absolute values indicate strong influence on the corresponding component, allowing identification of the descriptors driving the observed trends in structural and electronic properties.
  • Figure 3: (Colour online) Schematic research workflow implemented in the present investigation. From left to right: (A) The full Heusler Mn$_2$RuGa simulation cell is first used to optimize atomic pseudopotentials and numerical orbitals, as well as to converge the $k$-point sampling and mesh cutoff; (B) Ru atoms (solid green spheres) are then selectively removed to generate thousands of possible geometric configurations for each Ru concentration. Single-point energy calculations are subsequently performed to identify and discard symmetrically equivalent structures, retaining only the inequivalent ones. The schematic yellow bars shown between steps B and C represent, in a qualitative manner, the number of inequivalent configurations obtained after this filtering procedure for each Ru composition, rather than the number of symmetry-equivalent vacancy arrangements; (C) These inequivalent configurations are fully relaxed through SR ionic optimization; (D) Once convergence is achieved, statistical averages can be computed for each Ru concentration $1-x_p$, or all configurations can be directly analyzed to extract trends in the targeted physical properties.
  • Figure 4: (Colour online) Schematic representation of the dependency of the in--plane and out--of--plane lattice parameters $a$ and $c$ with Ru content within the Mn$_2$Ru$_{1-x_p}$Ga supercell as a function of Ru content for two Boltzmann factors: $kT$=1 meV (50 K) and 1 eV (10 kK), red and green symbols, respectively. Solid lines are provided as guides to the eye.
  • Figure 5: (Colour online) (A) Average net MM per formula unit of Mn$_2$Ru$_{1-x_p}$Ga as a function of Ru content for two Boltzmann factors: $kT$=1 meV (50 K) and 1 eV (10 kK), empty red and filled green circles, respectively. The text reports the MM values associated with the two distinct magnetic phases that emerge at both intermediate and extreme Ru concentrations: ferrimagnetic and antiferromagnetic; (B) and (C) show the average MMs of Mn atoms occupying the 4a and 4c Wyckoff positions, respectively, as a function of Ru content with the same color code as in (A). Solid lines are provided as guides to the eye.
  • ...and 6 more figures