Energy-efficient excitation, amplification, and routing of spin waves using spin-orbit torque and voltage-controlled magnetic anisotropy

Multilayer ferromagnetic nanostructures comprising nonmagnetic conducting and insulating materials, which provide the generation of a strong spin-orbit torque (SOT) by a charge flow and the emergence of voltage-controlled magnetic anisotropy (VCMA) of interfacial origin, are promising for the electrical excitation and control of spin dynamics at the nanoscale. Here we present a theoretical study of the SOT-induced generation of spin waves and their propagation in the Co₂₀Fe₆₀B₂₀ (CoFeB) nanolayer sandwiched between the topological insulator Bi₂Se₃ (BiSe) and the dielectric MgO creating VCMA. Using micromagnetic simulations, we first describe the spin dynamics excited in the narrow CoFeB waveguide by a radio-frequency electric current locally created in the underlying BiSe strip. Owing to giant efficiency of charge-to-spin density conversion in the BiSe/CoFeB bilayer, the current-induced SOT generates a large-angle magnetization precession even at low current densities in the excitation region. Moreover, high-amplitude traveling spin waves emerge in the CoFeB waveguide when the excitation frequency exceeds the frequency of uniform ferromagnetic resonance in the CoFeB strip. Next, we model the propagation of a monochromatic spin wave through the long waveguide in the presence of a direct electric current flowing along the BiSe strip. Remarkably, the simulations demonstrate that the current-induced SOT can provide temporal amplification of spin waves in the CoFeB waveguide even at room temperature. Finally, we study the spin-wave routing through the joint of one and three CoFeB waveguides covered by an MgO nanolayer with two gate electrodes. It is shown that the regulation of interfacial VCMA by appropriate dc voltages applied to these electrodes makes it possible to direct the incoming spin wave into any of the three outgoing waveguides. Our theoretical predictions offer guidelines for the development of electrically controlled magnonic devices providing information transmission and processing with a low power consumption.