Magnetic Hyperfine Interaction and Electronic Relaxation in Rare-Earth Ions in Europium Iron Garnet

The attenuation and rotation of the integral angular correlation for the $2^{-}$(1409 keV)$2^{+}$(122 keV)$0^{+}$ $\gamma -\gamma$ cascade in ${\mathrm{Sm}}^{152}$ following $K$ capture in ${\mathrm{Eu}}^{152}$ and of the $1^{-}$(1280 keV)$2^{+}$(123 keV)$0^{+}$ $\gamma -\gamma$ cascade in ${\mathrm{Gd}}^{154}$ following beta decay in ${\mathrm{Eu}}^{154}$ was measured in polycrystalline samples of europium iron garnet from -25°C to above the Néel point with and without magnetizing field perpendicular to the counter plane. These data and differential angular correlation data, have been analyzed using an extension of the theory of Abragam and Pound to time-dependent magnetic hyperfine interactions in magnetic materials. Explicit formulas for the dependence of the angular correlation on the electronic relaxation time, the average effective field acting at the nucleus in the direction of the magnetizing field $〈{H_{\mathrm{int}}}^z〉$, and the mean square fluctuating field $〈{H_{\mathrm{int}}}^2〉$ are given. The sign, magnitude, and temperature dependence of $〈{H_{\mathrm{int}}}^z〉$ in ${\mathrm{Sm}}^{152}$ were in excellent agreement with the expectation value of ${H_{\mathrm{int}}}^z$ calculated from molecular field theory under the assumption that the electronic configuration following $K$ capture in ${\mathrm{Eu}}^{152}$ is that of the ${\mathrm{Sm}}^{+3\mathrm{}}$ ion. Crystalline field and quadrupole interaction effects have been neglected. The contribution of the magnetic hyperfine interaction arising from the exchange between the $4f$ and inner core $s$ electrons was small compared with that from the orbital and spin moments of the $4f$ shell. The value of the root-mean square hyperfine field was found to be 4.7×${10}^6$ Oe and that of the average effective field was 4×${10}^5$ Oe at room temperature. The electronic relaxation time was 4×${10}^{-12\mathrm{}}$ sec at room temperature and varied inversely with absolute temperature. The electronic state in ${\mathrm{Gd}}^{154}$ following beta decay in ${\mathrm{Eu}}^{154}$ has as yet not been determined. $〈{H_{\mathrm{int}}}^z〉$ was found to be 8×${10}^4$ Oe at room temperature.