  The magneto-optical and opto-magnetic effects describe the interaction of
light with a magnetic medium. The most prominent examples are the Faraday and
Cotton-Mouton effects that modify the transmission of light through a medium,
and the inverse Faraday and inverse Cotton-Mouton effects that produce
effective magnetic fields for the spin in the material. Here, we introduce the
phenomenology of the analogous magneto-phononic and phono-magnetic effects, in
which vibrational quanta take the place of the light quanta. We show, using a
combination of first-principles calculations and phenomenological modeling,
that the effective magnetic fields exerted by the phonon analogs of the inverse
Faraday and inverse Cotton-Mouton effects on the spins of antiferromagnetic
nickel oxide yield magnitudes comparable to and potentially larger than those
of the opto-magnetic originals.
