A detailed zero- and transverse-field muon spin rotation investigation of magnetism and the magnetoelectric coupling in Cu${}_2$OSeO${}_3$ is reported. An internal magnetic field $B_{\mathrm{int}}(T=0)=85.37\left(25\right)$ mT was found, in agreement with a ferrimagnetic state below $T_{\mathrm{c}}=57.0\left(1\right)$ K. The temperature dependence of the magnetic order parameter is well described by the relation $B_{\mathrm{int}}=B\left(0\right)(1-{(T/T_{\mathrm{c}})}^2{)}^{\tilde{\beta }}$ with an effective exponent $\tilde{\beta }\simeq 0.39\left(1\right)$, which is close to the critical exponent $\beta \simeq 1/3$ for a three-dimensional (3D) magnetic system. Just above $T_{\mathrm{c}}$ the muon relaxation rate follows the power law $\lambda \left(T\right)\propto {(T/T_{\mathrm{c}}-1)}^{-\tilde{\omega }}$ with $\tilde{\omega }=1.06\left(9\right)$, which is characteristic for 3D ferromagnets. Measurements of $B_{\mathrm{int}}\left(T\right)$ with and without an applied electrostatic field $E=1.66\times {10}^5$ V/m suggest a possible electric-field effect of magnitude $\Delta B_V=B_V\left(0\mathrm{V}\right)-B_V\left(500\mathrm{V}\right)=-0.4\left(4\right)$ mT.

• Received 30 April 2011

DOI:https://doi.org/10.1103/PhysRevB.84.064433