Electronic Raman Studies of Antiferromagnetic Dysprosium Aluminum Garnet belowTNand with and without an Applied Magnetic Field

Electronic Raman transitions within the ${}_{}{}^6{}_{}{}^{}H_{\frac{15}{2}}^{}{}_{}{}^{}$ and to the ${}_{}{}^6{}_{}{}^{}H_{\frac{13}{2}}^{}{}_{}{}^{}$ manifolds of antiferromagnetic dysprosium aluminum garnet (DyAlG) at 1.5 K ($T_N=2.5\mathrm{} \mathrm{K}$) have been observed. Comparison of the Raman spectra obtained when a magnetic field (18 kOe) was applied along the [001] direction and when $H_{\mathrm{app}}=0\mathrm{}$ yielded estimations for the following: (a) the internal field splittings and consequently the exchange fields of the first two excited Kramers doublets in ${}_{}{}^6{}_{}{}^{}H_{\frac{15}{2}}^{}{}_{}{}^{}$; and (b) the Zeeman splittings of these levels. Using wave functions from our crystal-field analysis (Wadsack et al.), the $g$ values of all the levels in the ${}_{}{}^6{}_{}{}^{}H_{\frac{15}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^6{}_{}{}^{}H_{\frac{13}{2}}^{}{}_{}{}^{}$ manifolds have been calculated. These compared well with the $g$ values previously observed (Aoyagi et al.) and with our Raman determination of $g_z=14.7\mathrm{}\pm 1$ for the lowest level in ${}_{}{}^6{}_{}{}^{}H_{\frac{13}{2}}^{}{}_{}{}^{}$. Contributions to the electronic Raman scattering tensors from the six magnetic sublattices were derived for the applied field along [001] and for the different combinations of incident and scattered polarizations. Using the crystal-field wave functions for DyAlG, the relative Raman intensities for the observed Raman transitions were calculated. These Raman intensities are as sensitive to the crystal-field wave functions as are the $g$ values. The calculated and observed Raman intensity ratios for various polarization combinations agreed only qualitatively. Breakdown of phonon polarization selection rules for the $E_g$ and $A_{1g}$, but not the $T_{2g}$ Raman-active phonons, was observed when $H_{\mathrm{app}}=18\mathrm{} \mathrm{kOe}$. No explanation was given for this observation.