The free energy of twisting spins in Mn$_3$Sn

TL;DR

This paper reveals that in Mn$_3$Sn, a non-collinear antiferromagnet, the magnetic free energy includes superquadratic terms that significantly influence magnetocrystalline anisotropy, driven by field-induced spin texture deformation.

Contribution

The study uncovers superquadratic components in the free energy of Mn$_3$Sn and provides a theoretical framework to quantify key energy scales affecting its magnetic properties.

Findings

Detection of odd-in-field terms in free energy ($H^3$, $H^5$)

Observation of sixfold and twelve-fold torque oscillations

Theoretical explanation linking spin texture deformation to MAE

Abstract

The magnetic free energy is usually quadratic in magnetic field and depends on the mutual orientation of the magnetic field and the crystalline axes. Tiny in magnitude, this magnetocrystalline anisotropy energy (MAE) is nevertheless indispensable for the existence of permanent magnets. Here, we show that in Mn$_3$Sn, a non-collinear antiferromagnet attracting much attention following the discovery of its large anomalous Hall effect, the free energy of spins has superquadratic components, which drive the MAE. We experimentally demonstrate that the thermodynamic free energy includes terms odd in magnetic field ($\mathcal{O}(H^3)+\mathcal{O}(H^5)$) and generating sixfold and twelve-fold angular oscillations in the torque response. We show that they are quantitatively explained by theory, which can be used to quantify relevant energy scales (Heisenberg, Dzyaloshinskii-Moriya, Zeeman and single-ion anisotropy) of the system. Based on the theory, we conclude that, in contrast with common magnets, what drives the MAE in Mn$_3$Sn is the field-induced deformation of the spin texture.