Electric-field control of magnetization promises to substantially enhance the energy efficiency of device applications ranging from data storage to solid-state cooling. However, the intrinsic linear magnetoelectric effect is typically small in bulk materials. In thin films electric-field tuning of spin-orbit interaction phenomena (e.g., magnetocrystalline anisotropy) has been reported to achieve a partial control of the magnetic state. Here we explore the piezomagnetic effect (PME), driven by frustrated exchange interactions, which can induce a net magnetization in an antiferromagnet and reverse its direction via elastic strain generated piezoelectrically. Our $ab~initio$ study of PME in Mn-antiperovskite nitrides identified an extraordinarily large PME in Mn$_3$SnN available at room temperature. We explain the magnitude of PME based on features of the electronic structure and show an inverse-proportionality between the simulated zero-temperature PME and the negative thermal expansion at the magnetic (Neel) transition measured by Takenaka et al. in 9 antiferromagnetic Mn$_3$AN systems.
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