  Motivated by the recent progress of high-frequency ultrasonic measurements,
we propose a theory of magnetoacoustic resonance as a microscopic probe for
quadrupole degrees of freedom hidden in magnetic materials. A local strain
driven by an acoustic wave couples to electronic states of a magnetic ion
through various quadrupole-strain couplings, and this provides a periodically
time-dependent oscillating field. As a typical two-level system with the
quadrupole, we consider a non-Kramers doublet and investigate single- and
multiphonon-mediated transition processes on the basis of the Floquet theory.
An analytic form of the transition probability is derived within the weak
coupling theory, which helps us analyze the magnetoacoustic quadrupole
resonance. We apply the theory to realistic non-Kramers doublet systems for the
f2 configuration in Oh and D4h symmetries, and discuss how to identify the
relevant quadrupole by controlling the quadrupole-strain coupling with an
applied magnetic field in ultrasonic measurements.
