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Motivated by the recent progress of high-frequency ultrasonic measurements,we propose a theory of magnetoacoustic resonance as a microscopic probe forquadrupole degrees of freedom hidden in magnetic materials. A local straindriven by an acoustic wave couples to electronic states of a magnetic ionthrough various quadrupole-strain couplings, and this provides a periodicallytime-dependent oscillating field. As a typical two-level system with thequadrupole, we consider a non-Kramers doublet and investigate single- andmultiphonon-mediated transition processes on the basis of the Floquet theory.An analytic form of the transition probability is derived within the weakcoupling theory, which helps us analyze the magnetoacoustic quadrupoleresonance. We apply the theory to realistic non-Kramers doublet systems for thef2 configuration in Oh and D4h symmetries, and discuss how to identify therelevant quadrupole by controlling the quadrupole-strain coupling with anapplied magnetic field in ultrasonic measurements.

Analysis of Magnetoacoustic Quadrupole Resonance and Application to Probe Quadrupole Degrees of Freedom in Quantum Magnets