Magneto-Electric Coupling in Single Crystal Cu$_2$OSeO$_3$ Studied by a Novel Electron Spin Resonance Technique

The magneto-electric (ME) coupling on spin-wave resonances in single-crystal Cu$_2$OSeO$_3$ was studied by a novel technique using electron spin resonance combined with electric field modulation. An external electric field ${\bf E}$ induces a magnetic field component $\mu_0 H^i = \gamma E$ along the applied magnetic field ${\bf H}$ with $\gamma=0.7(1)~ \mu$T/(V/mm) at 10 K. The ME coupling strength $\gamma$ is found to be temperature dependent and highly anisotropic. $\gamma(T)$ nearly follows that of the spin susceptibility $J^M(T)$ and rapidly decreases above the Curie temperature $T_{\rm c}$. The ratio $\gamma/J^M$ monotonically decreases with increasing temperature without an anomaly at $T_{\rm c}$.