Electric-Field Coupling to Spin Waves in a Centrosymmetric Ferrite

We experimentally demonstrate that the spin-orbit interaction can be utilized for direct electric-field tuning of the propagation of spin waves in a single-crystal yttrium iron garnet magnonic waveguide. Magnetoelectric coupling not due to the spin-orbit interaction and, hence, an order of magnitude weaker leads to electric-field modification of the spin-wave velocity for waveguide geometries where the spin-orbit interaction will not contribute. A theory of the phase shift, validated by the experiment data, shows that, in the exchange spin wave regime, this electric tuning can have high efficiency. Our findings point to an important avenue for manipulating spin waves and developing electrically tunable magnonic devices.

Figure 1

Schematic of the YIG magnonic waveguide used in this experiment. $B$: bias magnetic field; $E$: electric field; $k$: wave vector.

Figure 2

(a) Dispersion relation of the spin wave in the YIG magnonic waveguide. Red squares and blue circles are the experimentally extracted dispersions with and without metal electrodes on the YIG surface, respectively. Solid lines are the theoretical calculations. Dashed black line is the linearized dispersion. (b) Vector network analyzer transmission characterization of the YIG magnonic waveguide with magnitude response shown in the top panel and phase response shown in the bottom panel. (c) Interferometry scheme for measuring spin wave phase accumulation; SG: signal generator; RF SG: radio frequency signal generator; Amp: amplifier; PM: power meter; LPF: low-pass filter; HV Amp: high-voltage amplifier.

Figure 3

(a) Measurement of the electric-field-induced phase (symbols) at various electric fields (bias magnetic field $B=60.1\mathrm{mT}$). Dashed lines show the linear fittings. (b) Dependence of ${\partial }_f\phi$ on the electric field with different bias magnetic fields. Solid lines show the theoretical predictions. (c) Dependence of ${\partial }_{f,E}^2\phi$ on the magnetic field. (d) Phase induced by the first-order ME effect at the FMR frequency (bias magnetic field $B=60.1\mathrm{mT}$).

Figure 4

(a) The measured phase shift with the electric field applied in the in-plane (blue circles) and out-of-plane (red squares) directions, under the same bias magnetic field ($B=60.1\mathrm{mT}$). Dashed black lines are the linear fittings. (b) Dependence of $\overline{{\partial }_f\phi }$ on the electric field for the in-plane (blue circles) and out-of-plane (red squares) electric field configurations. Solid lines show the model predictions.