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

Soichiro Kikuchi, Yuki Yanagi+2 more|arXiv (Cornell University)|Jan 23, 2026

Chemical and Physical Properties of Materials0 citations

TL;DR

The paper presents a first-principles analysis of the piezomagnetic effect in Mn3Sn, linking real-space spin rotations under strain to changes in the electronic structure and Fermi surface in k-space. It shows how strain-induced band splitting near the Fermi level contributes to induced magnetization.

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.

Motivation & Objective

• Clarify how uniaxial strain induces net magnetization in Mn3Sn without lowering magnetic symmetry.
• Identify real-space spin-rotation contributions on Mn sites under strain.
• Elucidate k-space electronic-structure changes, especially near the Fermi surface, that drive piezomagnetism.
• Connect real-space spin dynamics with band-structure shifts to provide a microscopic mechanism.

Proposed method

• Perform DFT calculations with VASP using GGA-PBE and self-consistent SOC.
• Apply uniaxial compressive strain (~0.4%) along the x-axis and relax atomic positions.
• Analyze spin moments in real space to observe strain-induced rotations of Mn spins.
• Map the spin distribution Sx(k) in the Brillouin zone to identify k-space regions contributing to magnetization.
• Examine Fermi surfaces and band shifts to link pseudo-degeneracy lifting under strain to magnetization.
• Decompose band characters by Mn sites and d-orbitals to connect orbital contributions with spin reorientation.

Figure 1: Change in magnetic moments under the uniaxial pressure along $x$ -axis.

Experimental results

Research questions

• RQ1 What is the microscopic mechanism by which uniaxial strain induces a net magnetization in Mn3Sn without altering magnetic symmetry?
• RQ2 How do real-space spin rotations of Mn atoms under strain relate to changes in the electronic structure near the Fermi surface?
• RQ3 Which features of the Fermi surface and which Mn-d orbital characters drive the piezomagnetic response?
• RQ4 How does band splitting and shifting under compression correlate with Mn1–Mn2 versus Mn3–Mn6 orbital contributions?
• RQ5 Can a dual real-space and k-space picture coherently explain the strain-induced magnetization in this non-collinear antiferromagnet?

Key findings

• Uniaxial compression along x rotates Mn3–Mn6 spin moments by about 0.4 degrees, increasing net magnetization Mx from 0.002 to 0.06 (in units implicit in the text).
• Sx(k) expands into negative regions in k-space under compression, with a significant Fermi-surface-localized contribution to magnetization.
• Two pseudo-degenerate Fermi-surface sheets near the Gamma–Z axis are split by compression, producing enhanced negative Sx(k) in the affected region.
• Bands dominated by Mn3–Mn6 d-orbitals experience a positive kz shift (Delta kz ~ +0.0078 per), while Mn1–Mn2 bands shift negatively (Delta kz ~ -0.0027 per), accounting for band splitting.
• The Mn3–Mn6–dominated band shows a kz shift and kz-dependent spin polarization linked to d_xz and d_xy orbital weights; Mn1/Mn2 bands show weaker changes, matching the observed spin rotations.
• The study links real-space spin rotations to specific k-space band shifts, providing a microscopic picture of stress-induced magnetization in Mn3Sn.

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