Magnetic properties of ${\mathrm{}\left(\mathrm{VO}\right)\mathrm{}}_2{\mathrm{P}}_2{\mathrm{O}}_7$ from frustrated interchain coupling

Neutron-scattering experiments on ${\mathrm{}\left(\mathrm{VO}\right)\mathrm{}}_2{\mathrm{P}}_2{\mathrm{O}}_7$ reveal both a gapped magnon dispersion and an unexpected, low-lying second mode. The proximity and intensity of these modes suggest a frustrated coupling between the alternating spin chains. We deduce the minimal model containing such a frustration, and show that it gives an excellent account of the magnon dispersion, static susceptibility, and electron-spin resonance absorption. We consider two-magnon states which bind due to frustration, and demonstrate that these may provide a consistent explanation for the second mode.