Anisotropy of the Europium-Iron Exchange Interaction in Rare-Earth Iron Garnets

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M\"ossbauer studies of the 21.6-keV transition of Eu¹⁵¹ and the 14.4-keV transition of Fe⁵⁷ in europium iron garnet, samarium iron garnet, and mixed samarium-europium iron garnets were performed at various temperatures. The recoilless absorption spectra of the 21.6-keV and 14.4-keV γ rays in SmIG and in SmₓEu_1-xIG at 4.2^∘{}K differ substantially from the spectra in EuIG and other rare-earth iron garnets. The main conclusions drawn from the experimental results are the following. (1) The Eu-Fe exchange interaction in the garnets is anisotropic. The principal values of the anisotropic exchange field acting on the Eu³⁺ ions (produced mainly by the Fe³⁺ ions in the tetrahedral sites) are βHₓhc=12.7 cm^-1, βHyhc=11.9 cm^-1, and βHzhc=20.3 cm^-1. (2) The anisotropic properties of the Eu³⁺ ions in the garnets are mainly produced by the anisotropy in the Eu-Fe exchange interaction and not by the crystalline-field interactions. (3) The direction of the tetrahedral iron sublattice magnetization (nd) in SmIG at 4.2 and 20^∘{}K and in mixed SmₓEu_1-xIG's with x≥0.05 at 4.2^∘{}K is close to the [110] direction of the cubic unit cell. The experimental results tend to indicate that the direction of nd in SmIG and in mixed Eu-Sm garnet at 4.2^∘{}K makes a small angle ({~}5^∘{}) with the [110] direction of the unit cell, and that the direction of nd at 85^∘{}K is slightly canted relative to the [111] direction.