Determination of Exchange Interactions between CoupledCo2+Ions in MgF2by Far-Infrared Spectroscopy

We report here a far-infrared spectroscopy experiment in which we observe absorption lines due to pairs and triads of magnetic ions. A crystal of Mg${\mathrm{F}}_2$ containing ${\mathrm{Co}}^{2+}$ ions substituted for ${\mathrm{Mg}}^{2+}$ is investigated and is found to show spectra due to next-nearest-neighbor ${\mathrm{Co}}^{2+}$ pairs, and also spectra due to groups of three ${\mathrm{Co}}^{2+}$ ions containing two next-nearest-neighbor bonds. The isotropic component of the pair exchange interaction is determined to be 9.8 ${\mathrm{cm}}^{-1\mathrm{}}$, and the anisotropic components are also evaluated. Identification and evaluation are carried out with the information obtained from the Zeeman effect. The exchange and Zeeman Hamiltonian matrices for pairs and triads are developed using symmetry considerations, and it is shown that magnetic dipole transitions are allowed and are of the correct strength to account for the observed spectra. It is also shown that the next-nearest-neighbor exchange constant found from the spinwave dispersion curve for Co${\mathrm{F}}_2$ is in close agreement with the spectroscopic value found here.