Microscopic Origin of Piezomagnetism in Mn$_3$Sn: A Dual Real- and $k$-Space Picture

TL;DR

The study addresses the microscopic origin of the piezomagnetic effect in Mn3Sn, a non-collinear antiferromagnet with a sizable anomalous Hall response. Using first-principles DFT with spin–orbit coupling, it develops dual real-space and k-space pictures to explain how uniaxial strain induces magnetization without lowering magnetic symmetry. Real-space analysis shows Mn3–Mn6 moment rotations under strain generate a net magnetization of about 0.06 μB, while k-space analysis reveals strain-induced splitting of near-Fermi-surface bands and selective spin polarization contributing from Fermi-surface regions. This integrated framework links spin reorientation to electronic-structure changes and offers a microscopic route to strain-engineered spintronic functionality.

Abstract

We present a comprehensive first-principles study on the origin of the piezomagnetic effect in the non-collinear antiferromagnet Mn$_3$Sn, a material known for exhibiting a large anomalous Hall effect. We investigate strain-induced variations of electronic and magnetic states and elucidate the mechanism of the piezomagnetic effect from both real-space and momentum-space perspectives. In real space, the emergence of piezomagnetism is understood to arise from rotations of the magnetic moments at specific Mn sites, which directly couple to the strain. Through detailed electronic structure analysis, we identify the Fermi surfaces that play a crucial role in the emergence of piezomagnetism. Our results reveal that specific Fermi surface features undergo pseudo-degeneracy lifting under applied strain, which significantly contributes to the induced net magnetization. By combining these complementary real-space and momentum-space pictures, our dual-space analysis provides deep insight into the microscopic origins of strain-driven magnetization in Mn$_3$Sn.

Figures (10)

• Figure 1: Change in magnetic moments under the uniaxial pressure along $x$-axis.
• Figure 2: (a) Orthorombic magnetic Brillouin zone of Mn$_3$Sn. (b)-(d) Distribution of the x component of spin, $S_{x}({\bm k})$, (b) before and (c) after compression, and (d) the difference between the two within the Brillouin zone of Mn$_3$Sn. In Panel (a) The labeling of the high-symmetry points and lines in the Brillouin zone follows the convention used for base-centered orthorhombic lattices Bradley_book_2010.Panel (d) is obtained by mapping the compressed Brillouin zone onto the uncompressed one through reciprocal-lattice scaling, expressing $S_{x}(\mathbf{k})$ in the common $\mathbf{k}$ coordinates, and plotting their difference.
• Figure 3: Fermi Surface of Mn$_3$Sn before compression. Fermi surface color map plots the absolute value of Fermi velocity. This figure is created using FermiSurfer Kawamurafermisurf.
• Figure 4: (a) Changes in the Fermi surface due to compression and (b) Spin distribution calculated for two bands forming a split Fermi surface on the $k_xk_z$ plane containing $\Gamma$ and $Z$ points.
• Figure 5: (a) Changes in the Fermi surface due to compression and (b) Spin distribution calculated for the band forming the Fermi surface on the $k_xk_z$ plane containing $Y$ and $T$ points, and (c) its change in the spin distribution as Fig. \ref{['fig:BRZ+ST3D']}(d).