Paramagnetic Resonance of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>in Octahedral and Tetrahedral Sites in Yttrium Gallium Garnet (YGaG) and Anisotropy of Yttrium Iron Garnet (YIG)

The electron paramagnetic resonance spectrum of a small ${\mathrm{Fe}}^{3+}$ impurity which enters substitutionally for the gallium in single crystals of yttrium gallium garnet (chemical formula ${\mathrm{Y}}_{3}$${\mathrm{Ga}}_{5}$${\mathrm{O}}_{12}$) has been examined at 24 kMc/sec at 295\ifmmode^\circ\else\textdegree\fi{}K and 1.6\ifmmode^\circ\else\textdegree\fi{}K. ${\mathrm{Fe}}^{3+}$ is studied for the first time in tetrahedral coordination. The results for the crystal field parameters that appear in the usual spin Hamiltonian for ${\mathrm{Fe}}^{3+}$ for the octahedral ($a$) and tetrahedral ($d$) sites are: ${a}_{a}=+0.0185$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${D}_{a}=\ensuremath{-}0.1294$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${F}_{a}=+0.0026$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${a}_{d}=+0.0062$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${D}_{d}=\ensuremath{-}0.0880$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${F}_{d}=\ensuremath{-}0.0037$ ${\mathrm{cm}}^{\ensuremath{-}1}$.The finding of $a$ positive in both types of sites where the cubic crystalline potential, $V$, has opposite signs indicates that in the mechanism responsible for this splitting terms proportional to even powers of $V$ are dominant. Using the experimentally determined crystal field parameters of ${\mathrm{Fe}}^{3+}$ in YGaG, the low-temperature anisotropy energy per unit cell in the isostructural ferrimagnet, YIG, is predicted as ${K}_{1}=\ensuremath{-}0.370$ ${\mathrm{cm}}^{\ensuremath{-}1}$. This is 50% larger than the experimental value ${K}_{1}=\ensuremath{-}0.250$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and several sources for the origin of this discrepancy are suggested.

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