Magnetic Behavior of Cobalt in Garnets. I. Spin Resonance in Cobalt-Doped Yttrium Gallium Garnet

We have studied the spin resonance at 24 and 56 kMc/sec of cobalt in single crystals of yttrium gallium garnet (YGaG). We find resonances associated with four different combinations of site and charge state. Tetrahedral ${\mathrm{Co}}^{2+}$ has the ${}_{}{}^4{}_{}{}^{}A_2^{}{}_{}{}^{}$ ground term with the tetragonal splitting parameter $2D=-36$ ${\mathrm{cm}}^{-1\mathrm{}}$. Octahedral ${\mathrm{Co}}^{2+}$ has the ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}$ ground term with the trigonal splitting ${\Delta }_t=+650\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. It is seen in otherwise pure YGaG, as well as in crystals counterdoped with ${\mathrm{Si}}^{4+}$. Tetrahedral ${\mathrm{Co}}^{3+}$ has the ${}_{}{}^5{}_{}{}^{}E$ ground term, with $D\sim 14$ ${\mathrm{cm}}^{-1\mathrm{}}$, $\mathrm{}\left|a\right|=0.66\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. This value of $a$, the fourth-order cubic field-splitting parameter, is exceptionally large and makes possible strong magnetic-dipole transitions between states with $S_z=\pm 2$. Electric-dipole transitions are also observed between these states. Octahedral ${\mathrm{Co}}^{4+}$ has the strong-field ${}_{}{}^2{}_{}{}^{}T_2^{}{}_{}{}^{}$ ground term, with ${\Delta }_t=+1000\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$; its spectrum is very weak relative to ${\mathrm{Co}}^{3+}$, even in crystals counterdoped with ${\mathrm{Ca}}^{2+}$. The absence of a resonance from octahedral ${\mathrm{Co}}^{3+}$ implies that this ion has the strong-field ${}_{}{}^1{}_{}{}^{}A_1^{}{}_{}{}^{}$ ground term. Cobalt does not appear to enter the dodecahedral site in our crystals. Our results are complementary to, and on the whole consistent with, the optical data of Wood and Remeika. We review the information available on crystal fields at the octahedral and tetrahedral sites in garnet, and on the hyperfine structure of cobalt.