Spin-Wave Transmission in Ferromagnetic Thin Films: Flexoelectric Control and Spin-Wave Drag

Spin waves in insulating ferromagnets have recently emerged as an effective low-dissipation carrier of spin currents. In this work we explore a novel form of control of spin waves by {\it flexoelectric interactions}, which couple an electric field to the spatial gradient of the magnetization. We show that not only the short-wavelength exchange spin waves, but also the long-wavelength magnetostatic spin waves in a thin-film of magnetic insulator can be effectively controlled by an electric field. In fact, the relative electric-field-induced phase shift is even larger for magnetostatic spin waves than for exchange spin waves. We further show that spin waves in an insulating ferromagnetic film can excite a spin current in an adjacent conducting or insulating film, by way of long-ranged dipole-dipole interaction between the layers, in a magnetic analogue of the electronic Coulomb drag.