Anisotropic properties, charge ordering, and ferrimagnetic structures in the strongly correlated β−V2PO5 single crystal

Single crystal $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{V}}_{2}{\mathrm{PO}}_{5}$ was synthesized by chemical vapor transport method and characterized by transport, thermodynamic, neutron diffraction, nuclear magnetic resonance measurements and first-principles calculation. It was shown to be a semiconductor with a band gap of 0.48 eV, undergoing a charge ordering (unusual ${\mathrm{V}}^{2+}$ and ${\mathrm{V}}^{3+}$) phase transition accompanied by a tetragonal to monoclinic structural distortion at 610 K and a paramagnetic to ferrimagnetic phase transition at 128 K with a propagation vector of $\mathbf{k}=0$. The easy axis is in the monoclinic $ac$ plane pointing 47(9)${}^{\ensuremath{\circ}}$ away from the monoclinic $a$ axis. This collinear ferrimagnetic structure and anisotropic isothermal magnetization measurements suggest weak magnetic anisotropy in this compound. The first-principles calculations indicate that the intrachain interactions in the face-sharing ${\mathrm{VO}}_{6}$ chains dominate the magnetic hamiltonian and identify the ${\mathrm{\ensuremath{\Gamma}}}_{5}^{+}$ normal mode of the lattice vibration to be responsible for the charge ordering and thus the structural phase transition.