We report the crystal structure and magnetic behavior of the $4d^3$ spin-$frac32$ silicophosphate MoP$_3$SiO$_{11}$ studied by high-resolution synchrotron x-ray diffraction, neutron diffraction, thermodynamic measurements, and ab initio band-structure calculations. Our data revise the crystallographic symmetry of this compound and establish its rhombohedral space group ($Rbar 3c$) along with the geometrically perfect honeycomb lattice of the Mo$^{3+}$ ions residing in disconnected MoO$_6$ octahedra. Long-range antiferromagnetic order with the propagation vector $mathbf k=0$ observed below $T_N=6.8$ K is a combined effect of the nearest-neighbor in-plane exchange coupling $Jsimeq 2.6$ K, easy-plane single-ion anisotropy $Dsimeq 2.2 $ K, and a weak interlayer coupling $J_csimeq 0.8$ K. The 12% reduction in the ordered magnetic moment of the Mo$^{3+}$ ions and the magnon gap of $Deltasimeq 7$ K induced by the single-ion anisotropy further illustrate the impact of spin-orbit coupling on the magnetism. Our analysis puts forward single-ion anisotropy as an important ingredient of $4d^3$ honeycomb antiferromagnets despite their nominally quenched orbital moment.
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