Local symmetry and magnetic anisotropy in multiferroic ${\text{MnWO}}_4$ and antiferromagnetic ${\text{CoWO}}_4$ studied by soft x-ray absorption spectroscopy

Soft x-ray absorption experiments on the transition-metal $L_{2,3}$ edge of multiferroic ${\text{MnWO}}_4$ and antiferromagnetic ${\text{CoWO}}_4$ are presented. The observed linear polarization dependence, analyzed by full-multiplet calculations, is used to determine the ground-state wave function of the magnetic ${\text{Mn}}^{2+}$ and ${\text{Co}}^{2+}$ ions. The impact of the local structure and the spin-orbit coupling on the orbital moment is discussed in terms of the single-ion anisotropy. It is shown that the orbital moment in ${\text{CoWO}}_4$ is responsible for the collinear antiferromagnetism, while the small size of spin-orbit coupling effects make spiral magnetic order in ${\text{MnWO}}_4$ possible, enabling the material to be multiferroic.

Figure 1

(Color online) Top panel: experimental and theoretical $\text{Mn}{L}_{2,3}$ XAS spectra of ${\text{MnWO}}_4$ with the $\mathbf{E}$ vector of the light parallel to the $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ crystallographic axes. The spectrum of MnO is included as reference. Bottom panels: a closeup revealing the polarization dependence of the spectra.

Figure 2

(Color online) Experimental and theoretical $\text{Co}{L}_{2,3}$ XAS spectra of ${\text{CoWO}}_4$. The spectrum of multidomain CoO single crystal is included as reference.

Figure 3

(Color online) The structure of ${\text{MnWO}}_4$ and ${\text{CoWO}}_4$. For the calculations of the XAS spectra, a local coordinate system $\left(x,y,z\right)$ was introduced, in which the axes point roughly along the Mn/Co-O bonds. The global crystallographic coordinates system can be transformed into the local coordinate system by rotating along $b$ by $\approx 34°$ and then along the $c$ axis by $45°$ (see text for more details).

Figure 4

Energy-level diagrams for (a) and (b) ${\text{Mn}}^{+}$ $\left(3d^6\right)$ and (c) and (d) ${\text{Co}}^{2+}$ clusters, excluding and including the $3d$ spin-orbit coupling $\zeta$. Only the states up to 1 eV are shown.

Figure 5

(Color online) Calculated magnetic anisotropy of ${\text{Co}}^{2+}$ in ${\text{CoWO}}_4$. (a) Three-dimensional representation of the magnetic anisotropy in the unit cell. The surface depicts the expectation value of the magnetic moment $M_{\parallel }$ pointing parallel to a small exchange field applied to the ion. (b) Two-dimensional cut of $M_{\parallel }$ in the plane of easy and intermediate magnetic axis (corresponding approximately to the $xy$ plane in local coordinates). (c) Cut through the plane of hard and intermediate magnetic axis.