  The mechanisms of magnetoelastic interaction in MnF$_2$ are studied using the
method of acoustoelectric transformation. The temperature dependence of the
piezomagnetic coupling coefficient and its anisotropy are determined in the
antiferromagnetic phase. We observe a new effect consisting in the appearance
of a non-diagonal component of the magnetic susceptibility tensor, which is
proportional to the square of the order parameter, under the action of the
shear wave. A phenomenological interpretation of the effect, which takes into
account a small-angle rotation of the crystal lattice, is presented. In the
paramagnetic state, the effect of acoustic deformation is reduced to the
modulation of the diagonal component of the susceptibility tensor.
