Magnetoelectric Coupling in Single Crystal ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ Studied by a Novel Electron Spin Resonance Technique

The magnetoelectric (ME) coupling on spin-wave resonances in single-crystal ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ was studied by a novel technique using electron spin resonance combined with electric field modulation. An external electric field $\mathbf{E}$ induces a magnetic field component ${\mu }_0{H}^i=\gamma E$ along the applied magnetic field $\mathbf{H}$ with $\gamma =0.7(1)\mu \mathrm{T}/(\mathrm{V}/\mathrm{mm})$ 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 $T_c$. The ratio $\gamma /J^M$ monotonically decreases with increasing temperature without an anomaly at $T_c$.

Figure 1

(a) Schematic view of the sample and the magnetic or electric field geometry. The ME sample and the marker sample DPPH are sandwiched between two gold plate electrodes (GPE). ${\mathbf{H}}^{\prime }$: static external magnetic field, ${\mathbf{H}}_m$: magnetic modulation field, ${\mathbf{E}}_m$: electric modulation field, ${\mathbf{H}}_1$: microwave field, and $\mathbf{H}={\mathbf{H}}^{\prime }+{\mathbf{H}}_m$: total external magnetic field. (b) Basic principle of EPR signal detection. Red curve represents the EPR absorption line $I(H)$. The modulation magnetic field $H_m\sin (2\pi {\nu }_{m}t)$ and the resulting modulated microwave absorption power $P_m\sin (2\pi {\nu }_{m}t)$ are also illustrated. (c) First derivative $D(H)$ signal of the EPR absorption line $I(H)$ after lock-in detection.

Figure 2

(a) FMR in the $55\mu \mathrm{m}$ thick single-crystal sample of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ at $T=14\mathrm{K}$ for $H_{\parallel }$ and $H_{\perp }$ using the conventional MFM technique. (b) SWR in the 25 and $55\mu \mathrm{m}$ thick single-crystal samples of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ at $T=14\mathrm{K}$ for $H_{\perp }$. The indices $0,1,2,\dots$ indicate the order of the SWR mode.

Figure 3

Temperature dependence of SWR signals of single-crystal ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ detected using the MFM technique (dotted line) and the EFM technique (solid line). The sharp peak visible at 340 mT and 54 K is the signal of the marker sample DPPH which is present only in the case of MFM. The inset shows the expanded spectra at 10 K around 415 mT. For better comparison, all the EFM signals are multiplied by a factor of 2.

Figure 4

(a) Spectrally resolved ME effect parameter $\alpha (H)$ in single-crystal ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ at $T=12$, 20, 40, 50, 56, and 60 K for $H_{\perp }$. (b) Temperature dependence of the average ME effect parameter $⟨\alpha ⟩$ and the signal intensities $J^E$ and $J^M$ detected by EFM and MFM, respectively. The inset shows the angular dependence of $⟨\alpha ⟩$ at 14 K. (c) Temperature dependence of the ratio $⟨\alpha ⟩/J^M$ showing no anomaly at $T_c$.

Figure 5

(a) Peak-to-peak amplitude $A_{\mathrm{pp}}$ of the zero order SWR mode extracted from $D(H)$ shown in (b) as a function of the EFM amplitude $E_m$ in ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$. Note that $A_{\mathrm{pp}}\propto E_m$ indicating that ME coupling is linear. (c) $A_{\mathrm{pp}}$ as a function of the EFM frequency ${\nu }_m$ at $T=25\mathrm{K}$ (dots) and 35 K (triangles).