Hydrostatic-pressure studies of magnetic modes in the far infrared

Measurement of the frequency shifts of far-infrared-active magnetic modes as a function of applied hydrostatic pressure has permitted determination of the variation of the superexchange interaction with interionic spacing in MnO, Mn${\mathrm{F}}_2$, and Mn${\mathrm{F}}_2$:${\mathrm{Fe}}^{2+}$. In the pure crystals the antiferromagnetic resonance was used as the probe of the exchange interaction, while in Mn${\mathrm{F}}_2$:${\mathrm{Fe}}^{2+}$ observation of a localized magnetic-impurity mode above the host spin-wave band allowed the impurity-host exchange behavior to be determined. The experiments, which were the first hydrostatic-pressure studies of magnetic materials in the far infrared, were performed on crystals maintained at 4.2 °K and compressed by pressures up to 7.5 kbar with helium as the pressure-transmitting medium. The high resolution required to detect the small-frequency shifts was obtained by the use of Fourier-transform spectroscopic techniques and a ${\mathrm{He}}^3$-cooled bolometer detector. The use of resonance techniques for high-pressure studies is particularly noteworthy because it allows measurement of impurity effects in crystals which would be buried in bulk-property behavior. The experimental results were analyzed in terms of the covalent model of superexchange developed by Anderson. The pressure dependence of the covalent parameters was approximated by that of the two-center overlap integrals between wave functions of the completely ionized states. When only covalency between $3d$ metal states and $2p$, $2s$ ligand states is considered, the overlap calculations give a result for ${\gamma }_m\equiv -{\left(\frac{\partial \ln J}{\partial \ln V}\right)}_T$ consistently 30% higher than the measured values. If in addition spin transfer to vacant $4s$ metal states is considered, the calculated results are considerably improved and agree well with experiment for values of $f(2p-4s)$ suggested by Rimmer. The results have led us to suggest that the empirical "10/3 law" for ${\gamma }_m$ in many magnetic crystals may be a consequence of the dominance of $\sigma$ bonding in the superexchange process for such substances.