Dissipationless Multiferroic Magnonics

We propose that the magnetoelectric effect in multiferroic insulators with a coplanar antiferromagnetic spiral order, such as ${\mathrm{BiFeO}}_3$, enables electrically controlled magnonics without the need of a magnetic field. Applying an oscillating electric field in these materials with a frequency as low as household frequency can activate Goldstone modes that manifest fast planar rotations of spin, whose motion is essentially unaffected by crystalline anisotropy. Combining with spin ejection mechanisms, such a fast planar rotation can deliver electricity at room temperature over a distance of the magnetic domain, which is free from energy loss due to Gilbert damping in an impurity-free sample.

Figure 1

Schematics of a 2D AF spiral in the (a) original $S$ frame and the (b) rotated $S^{\prime }$ frame. Red and blue arrows indicate the spins on the two sublattices. (c) Spin wave dispersion ${\omega }_{\mathbf{k}}^{+}$ (dashed line) and ${\omega }_{\mathbf{k}}^{-}$ (solid line) solved in the $S^{\prime }$ frame, with $D_a/J=0.14$, $D_c=0$. Inserts show their eigenmodes in the $S^{\prime }$ frame near $\mathbf{k}=(0,0)$ and $(\pi ,\pi )$, where the spin dynamics $d{\mathbf{S}}_i^{\prime }/dt$ is indicated by black arrows or symbols.

Figure 2

Experimental proposal of using an oscillating $\mathbf{E}$ field to induce spin dynamics in a CMI. The AF spiral order is shown in the $S^{\prime }$ frame. The $\mathbf{E}$ field is applied between ${\mathbf{S}}_0^{\prime }$ and ${\mathbf{S}}_N^{\prime }$, causing dynamics in the whole spin texture. Two ways for spin ejection out of ${\mathbf{S}}_{N+M}^{\prime }$ are proposed: (a) using SHE to convert it into a charge current and (b) using time-varying spin accumulation and inductance.