  Strain engineering is widely used to manipulate the electronic and magnetic
properties of complex materials. An attractive route to control magnetism with
strain is provided by the piezomagnetic effect, whereby the staggered spin
structure of an antiferromagnet is decompensated by breaking the crystal field
symmetry, which induces a ferrimagnetic polarization. Piezomagnetism is
especially attractive because unlike magnetostriction it couples strain and
magnetization at linear order, and allows for bi-directional control suitable
for memory and spintronics applications. However, its use in functional devices
has so far been hindered by the slow speed and large uniaxial strains required.
Here, we show that the essential features of piezomagnetism can be reproduced
with optical phonons alone, which can be driven by light to large amplitudes
without changing the volume and hence beyond the elastic limits of the
material. We exploit nonlinear, three-phonon mixing to induce the desired
crystal field distortions in the antiferromagnet CoF$_2$. Through this effect,
we generate a ferrimagnetic moment of 0.2 $\mu_B$ per unit cell, nearly three
orders of magnitude larger than achieved with mechanical strain.
