Two-step transition in a magnetoelectric ferrimagnet Cu${}_2$OSeO${}_3$

We report a detailed single-crystal investigation of a magnetoelectric ferrimagnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ using dc magnetization and ac susceptibility along the three principal directions [100], [110], and [111]. We have observed that in small magnetic fields two magnetic transitions occur, one at $T_c=57$ K and the second one at $T_N=58$ K. At $T_c$ the nonlinear susceptibility reveals the emergence of the ferromagnetic component and below $T_c$ the magnetization measurements show the splitting between field-cooled and zero-field-cooled regimes. Above 1000 Oe the magnetization saturates and the system is in a single domain state. The temperature dependence of the saturation below $T_c$ can be well described by $\mu \left(T\right)=\mu \left(0\right){[1-{(T/T_c)}^2]}^{\beta }$, with $\mu \left(0\right)=0.56{\mu }_B$/Cu, corresponding to the 3-up-1-down configuration. The dielectric constant measured on a thin single crystal shows a systematic deviation below the transition, indicating an intrinsic magnetoelectric effect.

Figure 1

Temperature dependence of the magnetization for (a) [100], (b) [110], and (c) [111] directions. Upper branches (solid symbols) correspond to the FC regime, while the lower branches (open symbols) correspond to the ZFC regime.

Figure 2

Average magnetic moment on the cooper ion vs magnetic field for (a) [100], (b) [110], and (c) [111] directions.

Figure 3

Temperature dependence of the saturated magnetization in 1000 Oe for the [110] direction. The line is a fit to Eq. (1).

Figure 4

Temperature dependence of the susceptibility around the transition for the [111] direction. (Top) Linear susceptibility (ac and dc). (Middle) A derivative of the linear ac susceptibility. (Bottom) The third harmonic of the ac susceptibility.

Figure 5

Temperature dependence of the inverse dc susceptibility. The line is a fit to Eq. (2).

Figure 6

The temperature dependence of the dielectric constant of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ measured at 10 kHz and 1 V.

Figure 7

Local environment around ${\mathrm{Cu}}^{\mathsf{I}}$ and ${\mathrm{Cu}}^{\mathsf{II}}$ ions in ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$.