Ferrimagnetism of the magnetoelectric compound ${\text{Cu}}_2{\text{OSeO}}_3$ probed by ${}^{77}\text{S}\text{e}$ NMR

We present a thorough ${}^{77}\text{S}\text{e}$ nuclear-magnetic-resonance (NMR) study of a single crystal of the magnetoelectric compound ${\text{Cu}}_2{\text{OSeO}}_3$. The temperature dependence of the local electronic moments extracted from the NMR data is fully consistent with a magnetic phase transition from the high-$T$ paramagnetic phase to a low-$T$ ferrimagnetic state with 3/4 of the ${\text{Cu}}^{2+}$ ions aligned parallel and 1/4 aligned antiparallel to the applied field of 14.09 T. The transition to this 3up-1down magnetic state is not accompanied by any splitting of the NMR lines or any abrupt modification in their broadening, hence there is no observable reduction in the crystal symmetry from its high-$T$ cubic $P{2}_{1}3$ space group. These results are in agreement with high-resolution x-ray diffraction and magnetization data on powder samples reported previously by Bos et al. [Phys. Rev. B 78, 094416 (2008)]. We also develop a mean-field theory description of the problem based on a microscopic spin Hamiltonian with one antiferromagnetic $\left(J_{\text{afm}}\simeq 68\text{K}\right)$ and one ferromagnetic $\left(J_{\text{fm}}\simeq -50\text{K}\right)$ nearest-neighbor exchange interaction.

Figure 1

(Color online) Crystal structure of ${\text{Cu}}_2{\text{OSeO}}_3$ where Cu ions form a network of distorted corner-sharing tetrahedra. Only the ions inside the unit cell are shown (${\text{Cu}}_1$ in blue, ${\text{Cu}}_2$ in green, O in yellow, ${\text{Se}}_{\text{I}}$ in magenta, and ${\text{Se}}_{\text{II}}$ in red).

Figure 2

${}^{77}\text{S}\text{e}$ NMR line-shape measurements at 220 K in an external field of 14.09 T applied parallel to the [111], [110], and [100] crystallographic directions.

Figure 3

${}^{77}\text{S}\text{e}$ NMR line-shape measurements for selected temperatures measured at external field of 14.09 T applied parallel to the [111] and [110] crystallographic directions.

Figure 4

(Color online) Temperature dependence of the ${}^{77}\text{S}\text{e}$ NMR FWHM for each of the four spectral lines measured at 14.09 T along the [111] and [110] crystallographic directions. The FWHM for lines P1 and P3 along [111] are multiplied by a factor 0.9 and 0.7, respectively, in order to match the other curves. The temperature dependence of the magnetic susceptibility per copper mol (multiplied by a factor of 9.4) as measured with the magnetometer at 14 T is shown with a solid line.

Figure 5

(Color online) Temperature dependence of the relative NMR shifts $\Delta \nu /{\nu }_L$ at $H_0=14.09\text{T}$ and for each of the four spectral lines observed along the (a) [111] and (b) [110] crystallographic directions.

Figure 6

(Color online) The local environment of each ${\text{Se}}_{\text{I}}$ nuclear site. There is a threefold symmetry axis through the Se site which is vertical to the planes of the ${\text{Cu}}_1$ and ${\text{Cu}}_2$ ions. Note that the plane of the ${\text{Cu}}_2$ ions lies slightly above the plane of the ${\text{Cu}}_1$ ions. Shown distances are in units of $\text{Å}$.

Figure 7

(Color online) The local environment of ${\text{Se}}_{\text{II}}$ type ions. As in the case of ${\text{Se}}_{\text{I}}$ ions, there is a threefold symmetry axis through the Se site which is vertical to the planes of ${\text{Cu}}_2$ ions. Shown distances are in units of $\text{Å}$.

Figure 8

(Color online) A comparison of the values of the parameters given in Eqs. (10, 11, 12, 13) extracted from the NMR line shifts along the [111] direction with those extracted from the [110] direction.

Figure 9

(Color online) The fractional shift $\Delta {\nu }_{{\text{P}}_i}/{\nu }_L$ for each one of the four NMR peaks as measured along (a) [111] and (b) [110], vs the susceptibility $\chi$ measured with the magnetometer with $T$ being an implicit parameter. The dotted lines indicates the points where $T=170$ and 290 K.

Figure 10

(Color online) Comparison between the total magnetization measured by PPMS (corrected for the Van Vleck and diamagnetic contributions) and the local moments extracted from NMR (with two different values of the ratio $r_1$, cf. text) with the corresponding mean-field theory predictions. We also demonstrate how the value of the demagnetizing factor $N_d$ affects the sign of $M_1$ at high temperatures.

Figure 11

(Color online) Temperature dependence of the ${}^{77}\text{S}\text{e}$ NMR (a) spin-lattice $T_1^{-1}$ and (b) spin-spin $T_2^{-1}$ relaxation rates with the magnetic field of 14.09 T applied parallel to [111]. The inset shows $1/T_1$ vs 1/T for the line P1 and the corresponding fit (solid line) with the contribution from Raman scattering of magnons.