Growth-Induced Magnetic Anisotropy of Epitaxial Films of Mixed Garnets Containing Europium

We have measured the ferromagnetic resonance of three garnet films with the approximate composition $R_2\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{O}}_{12}$, where $R=\mathrm{Y}\mathrm{or}\mathrm{Lu}$ and $M=\mathrm{Al}\mathrm{or}\mathrm{Ga}$, grown by liquid-phase epitaxy on 001 and {111} gadolinium gallium garnet substrates. The anisotropy has a growth-induced component which anneals out at 1250°C. Measurements from $0.04T_C$ to $0.92T_C$ on a {111} film with $T_C=404\mathrm{} °$K show that this component is proportional to the calculated uniaxial anisotropy of a ${\mathrm{Eu}}^{3+}$ ion in garnet, up to $0.75T_C$. This proportionality is predicted by the site-preference theory of the growth-induced anisotropy. The calculation is based on the Wolf-Van Vleck model of europium iron garnet, extended to include spin-correlation effects on the $d$ sublattice in a heuristic manner. Anisotropic exchange is found to be the dominant source of the anisotropy. We find site preferences of about 20% in all three films. The calculation also accounts reasonably well for the temperature dependence of the magnetostriction of europium iron garnet.