Analysis of the spin exchange interactions in the three phases of vanadium pyrophosphate, (VO)2P2O7, in terms of spin-orbital interaction energy

The spin exchange interactions in the ambient-pressure orthorhombic (APO), high-pressure orthorhombic (HPO), and ambient-pressure monoclinic (APM) phases of the vanadium pyrophosphate, (VO)2P2O7, were analyzed by calculating the spin-orbital interaction energies delta e-delta e0 of their spin dimers. The anisotropy of the spin exchange interactions in the HPO phase is well explained by the delta e-delta e0 values. For the APO phase, the reported crystal structure does not provide accurate enough delta e-delta e0 values to conclude unambiguously which of the V1-V2 and V3-V4 chains has a larger spin gap and which of the bridged and edge-sharing spin dimers has a stronger spin exchange interaction in the V1-V2 and V3-V4 chains. The APM phase is predicted to exhibit essentially two spin gaps, with a large spin gap for the V8-V5-V7-V6 chain and a very small one for the V4-V2-V3-V1 chain.