  The quantized surface acoustic wave (SAW) in the piezoelectric medium has
recently been studied, and is used to control electric dipoles of quantum
systems via the electric field produced through piezoelectric effect. However,
it is not easy and convenient to manipulate magnetic moments directly by the
electric field. We here study a quantum theory of SAW in the piezomagnetic
medium. We show that the intrinsic properties of the piezomagnetic medium
enable the SAW in the piezomagnetic medium to directly interact with magnetic
moments of quantum systems via magnetic field induced by piezomagnetic effect.
By taking the strip SAW waveguide made of piezomagnetic medium as an example,
we further study the coupling strengths between different magnetic quantum
systems with magnetic moments and the quantized single-mode SAW in the
waveguide. Based on this, we discuss the interaction between magnetic quantum
systems mediated by the quantized multi-mode SAW in piezomagnetic waveguide.
Our study provides a convenient way to directly control magnetic quantum
systems by quantized SAW, and offers potential applications to on-chip
information processing based on solid-state quantum systems via quantized
acoustic wave.
