Magnetic properties of ${\mathrm{}\left(\mathrm{VO}\right)\mathrm{}}_2{\mathrm{P}}_2{\mathrm{O}}_7:$ Two-plane structure and spin-phonon interactions

Detailed experiments on single-crystal ${\mathrm{}\left(\mathrm{VO}\right)\mathrm{}}_2{\mathrm{P}}_2{\mathrm{O}}_7$ continue to reveal new and unexpected features. We show that a model composed of two, independent planes of spin chains with frustrated magnetic coupling is consistent with nuclear-magnetic-resonance and inelastic-neutron-scattering measurements. The pivotal role of ${\mathrm{PO}}_4$ groups in mediating intrachain exchange interactions explains both the presence of two chain types and their extreme sensitivity to certain lattice vibrations, which results in the strong magnetoelastic coupling observed by light scattering. We compute the respective modifications of the spin and phonon dynamics due to this coupling, and illustrate their observable consequences on the phonon frequencies, magnon dispersions, static susceptibility, and specific heat.