Magnetoelastic anisotropy in Heusler-type Mn$_{2-\delta}$CoGa$_{1+\delta}$ films

TL;DR

This study investigates the magnetoelastic anisotropy in Mn$_{2- ext{δ}}$CoGa$_{1+ ext{δ}}$ Heusler films, revealing significant perpendicular magnetic anisotropy linked to tetragonal distortion and spin-orbit coupling effects.

Contribution

It demonstrates the emergence of perpendicular magnetic anisotropy in inverse-type Heusler alloy films due to tetragonal distortion and provides insights into its microscopic origin through experiments and first-principles calculations.

Findings

Large uniaxial magnetocrystalline anisotropy constant (~10^5 J/m^3) at room temperature.

Positive correlation between c/a ratio and magnetic anisotropy.

Magnetic domain patterns change with anisotropy, confirmed by Kerr microscopy.

Abstract

Perpendicular magnetization is essential for high-density memory application using magnetic materials. High-spin polarization of conduction electrons is also required for realizing large electric signals from spin-dependent transport phenomena. Heusler alloy is a well-known material class showing the half-metallic electronic structure. However, its cubic lattice nature favors in-plane magnetization and thus minimizes the perpendicular magnetic anisotropy (PMA), in general. This study focuses on an inverse-type Heusler alloy, Mn$_{2-\delta}$CoGa$_{1+\delta}$ (MCG) with a small off-stoichiometry ($\delta$) , which is expected to be a half-metallic material. We observed relatively large uniaxial magnetocrystalline anisotropy constant ($K_\mathrm{u}$) of the order of 10$^5$ J/m$^3$ at room temperature in MCG films with a small tetragonal distortion of a few percent. A positive correlation was confirmed between the $c/a$ ratio of lattice constants and $K_\mathrm{u}$. Imaging of magnetic domains using Kerr microscopy clearly demonstrated a change in the domain patterns along with $K_\mathrm{u}$. X-ray magnetic circular dichroism (XMCD) was employed using synchrotron radiation soft x-ray beam to get insight into the origin for PMA. Negligible angular variation of orbital magnetic moment ($\Delta m_\mathrm{orb}$) evaluated using the XMCD spectra suggested a minor role of the so-called Bruno's term to $K_\mathrm{u}$. Our first principles calculation reasonably explained the small $\Delta m_\mathrm{orb}$ and the positive correlation between the $c/a$ ratio and $K_\mathrm{u}$. The origin of the magnetocrystalline anisotropy was discussed based on the second-order perturbation theory in terms of the spin--orbit coupling, claiming that the mixing of the occupied $\uparrow$- and the unoccupied $\downarrow$-spin states is responsible for the PMA of the MCG films.