Rare-Earth-Iron Exchange Interactions in Europium Iron Garnet

Abstract

Recoilless absorption measurements of the 14.4-keV $\ensuremath{\gamma}$ rays of ${\mathrm{Fe}}^{57}$ and the 21.6-keV $\ensuremath{\gamma}$ rays of ${\mathrm{Eu}}^{151}$ in europium iron-gallium garnets (${\mathrm{Eu}}_{3}{\mathrm{Ga}}_{x}{\mathrm{Fe}}_{5\ensuremath{-}x}{\mathrm{O}}_{12}$) were carried out at 4.2\ifmmode^\circ\else\textdegree\fi{}K for $x=0,0.66,1.28,1.60,2.37,\mathrm{and} 3.03$. The iron concentrations in the octahedral and tetrahedral sites were determined from the ${\mathrm{Fe}}^{57}$ spectra. The results show that about 80% of the Ga ions occupy tetrahedral sites (\ensuremath{\sim}85% for $x=0.66$ and \ensuremath{\sim}75% for $x=3.03$). The analysis of the ${\mathrm{Eu}}^{151}$ spectra shows that (88\ifmmode\pm\else\textpm\fi{}4)% of the exchange field acting on an ${\mathrm{Eu}}^{3+}$ ion in europium iron garnet is produced by the two nearest iron neighbors in the tetrahedral site, although the Eu-O-Fe angle for these ions is 92\ifmmode^\circ\else\textdegree\fi{}, an angle often considered unfavorable for superexchange interactions. Excellent agreement between theoretical and experimental spectra is obtained assuming that the remaining 12% of the exchange field is produced by the 4 third nearest neighbors in the tetrahedral site.