V. N. Krivoruchko, A. S. Savchenko, and V. V. Kruglyak
Phys. Rev. B 98, 024427 (2018)

An external electric field can modify the strength of the spin-orbit interaction between spins of ions in magnetic crystals. This influence leads to a spin-wave frequency shift that is linear in both the applied electric field and the wave vector of the spin wave. Here we study theoretically the external electric field as a means of control of the spin-wave power flow in thin ferromagnets. The spin-wave group velocity and focusing patterns are obtained from the slowness (isofrequency) curves by evaluating their curvature at each point of the reciprocal space. We show that the combination of the magnetodipole interaction and the electric field can result in nonreciprocal unidirectional caustic beams of dipole-exchange spin waves. We demonstrate that the degree of asymmetry of the spin-wave power flow can be tuned with the external electric field. Our findings open a novel avenue for spin-wave manipulation and development of electrically tunable magnonic devices.

Fig.1. The group velocity overall patterns. Here each contour in the figure represents a slowness surfaces and each successive contour represents a frequency difference f = 0.2 GHz; the first isofrequency contour is at f = 7.8 GHz.  (left panel) E = +35 V/μm, and (right panel) E = −35 V/μm.