  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.
