The magnetic free energy is usually quadratic in the 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 ${\mathrm{Mn}}_3\mathrm{Sn}$, a noncollinear antiferromagnet that has attracted much attention following the discovery of its large anomalous Hall effect, the free energy of the spins has superquadratic components, which drive the MAE. We experimentally demonstrate that the thermodynamic free energy includes terms odd in the magnetic field [$F\left(H^3\right)+F\left(H^5\right)$] and generating sixfold and 12-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 to common magnets, what drives the MAE in ${\mathrm{Mn}}_3\mathrm{Sn}$ is the field-induced deformation of the spin texture.

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• Exchange interaction
• Frustrated magnetism
• Magnetic anisotropy
• Magnetic susceptibility
• Antiferromagnets
• Topological materials