Electric Control of Spin Currents and Spin-Wave Logic

Spin waves in insulating magnets are ideal carriers for spin currents with low energy dissipation. An electric field can modify the dispersion of spin waves, by directly affecting, via spin-orbit coupling, the electrons that mediate the interaction between magnetic ions. Our microscopic calculations based on the superexchange model indicate that this effect of the electric field is sufficiently large to be used to effectively control spin currents. We apply these findings to the design of a spin-wave interferometric device, which acts as a logic inverter and can be used as a building block for room-temperature, low-dissipation logic circuits.

Figure 1

A Mach-Zehnder spin-wave interferometer in the presence of radial $\mathbf{E}$ field. A weak magnetic field is applied perpendicular to the ring plane, tilting the equilibrium magnetization away from the ring but still in the tangential plane to the ring. ${\theta }_0$ denotes the orientation of the equilibrium magnetization.

Figure 2

Superexchange model: two half filled magnetic ions connected by an oxygen ligand.

Figure 3

(a) Dispersion of spin waves in the ferromagnetic ring in Fig. 1, taking into account the geometric phase and the phase induced by the electric field. Parameters we use [20]: $J^{\prime }=1.18\times {10}^{-4}\mathrm{eV}$, $K=1.53\times {10}^{-4}\mathrm{eV}$, $S=14.3$, $a=12.4\AA$, $r_0=50\mathrm{nm}$, $R=100\mathrm{nm}$, $B=0.05\mathrm{T}$. (b) Transmission probability of a spin wave in the ring interferometer as a function of input voltage and magnetic field at $\omega =43\mathrm{GHz}$.