Anisotropic Piezomagnetism in Noncollinear Antiferromagnets

In 3d-electron magnetic systems, the magnetic structures that transform each other by spin rotation have very close degenerate energies due to small spin-orbit coupling and can be easily controlled by chemical substitution and external magnetic fields. We investigate anisotropic piezomagnetic effects, exhibiting the different magnetic responses depending on the type of strain and the magnetic structures, for non-collinear magnetic states in Mn$_3A$N ($A=$ Ni, Cu, Zn, Ga) and Mn$_3X$ ($X$= Sn and Ge) based on detailed symmetry analysis using spin group and magnetic group and first-principles calculations of piezomagnetic responses. In Mn$_3A$N, magnetization develops along two distinct directions under the same applied stress, corresponding to two AFM states connected by spin rotation. Analysis of the piezomagnetic tensor based on magnetic and spin point groups for the states with and without spin-orbit coupling, respectively, shows that the difference in the magnitude of magnetization along different directions is attributed to the spin-orbit coupling. Mn$_3X$ are known to stabilize different AFM structures in the directions of the applied in-plane magnetic fields. Under uniaxial stress along the orthorhombic $x$ and $y$ axes, magnetization is induced without breaking the magnetic symmetry, but it develops in the opposite direction due to exchange interaction. Our study demonstrates that the direction and sign of strain-induced magnetization in Mn$_3A$N and Mn$_3X$ can be effectively controlled by strain in combination with magnetic fields. These findings highlight the potential for strain-tunable magnetic devices in noncollinear AFMs.