Exchange Interaction and Energy Transfer for3d3Ions:A24−E2Transition for KMgF3:V2+

The energy levels of exchange-coupled pairs of $3d^3$ ions, each in the ${}_{}{}^4{}_{}{}^{}A_2^{}{}_{}{}^{}$ or ${}_{}{}^2{}_{}{}^{}E$ state, are derived, taking into account the orbitally anisotropic nature of the exchange interaction. Specific analysis is made of the spectrum of collinear pairs of vanadium ions in a KMg${\mathrm{F}}_3$ host. It is found that the Davydov-type splittings in the excited levels of the pairs, which are caused by the exchange orbital anisotropy, are 2-6 times greater than the ground-state-ground-state exchange matrix elements. Using a semiquantitative method for estimating the diminution of exchange as one increases the number of ligand linkages between the magnetic ions, the magnitude of energy-transfer integrals for ${\mathrm{V}}^{2+}$ ions separated by three ${\mathrm{F}}^{-}$ ions is found sufficient to cause rapid single-ion-single-ion energy transfer (∼1 μsec). This result indirectly supports the argument that the Davydov-like terms for weakly coupled ${\mathrm{Cr}}^{3+}$ pairs are responsible for energy transfer in dilute ruby.