Characterization of Nuclear and Magnetic Structures of Wolframite-Type MgReO4 and ZnReO4

We utilized high-pressure methods to synthesize the oxides AReO$4$ (A=Zn, Mg) and characterized their crystal structures as monoclinic wolframite-type. By combining muon spin spectroscopy (${\mu }^{+}$SR) with DFT calculations for muon stopping sites, we identify two possible magnetic spin structures for both compounds: ${\mathrm{\Gamma }}_3$ with the propagation vector $\mathbf{k}=(0,1\mathrm{/}2,0)$ and ${\mathrm{\Gamma }}_4$ with $\mathbf{k}=(0,0,0)$. In both cases, the magnetic moments are canted from the principal axes within the $ac$-plane. The ordered moment of the proposed structures is $\mathbf{0.29}(\mathbf{5})\mathbf{\mu }\mathrm{B}$ for ${\mathrm{\Gamma }}_3$ and $\mathbf{0.25}(\mathbf{8}){\mathbf{\mu }}_{\mathrm{B}}$ for ${\mathrm{\Gamma }}_4$. The low moment is consistent with the absence of a magnetic contribution to the neutron powder diffraction (NPD) spectra. Bond valence sum (BVS) analysis supports the oxidation state of Re being Re${}^{6+}$ in the compounds, and we suggest that a combination of $t_{2\mathrm{g}}$ orbital splitting due to spin-orbit coupling (SOC) and $d$-$p$ orbital hybridization is responsible for the strongly suppressed ordered magnetic moment.