Gamma-Gamma Angular-Correlation Study ofTm169in Lutetium Iron Garnet

The attenuation and rotation of the integral angular correlation of the $\frac{7}{2}(177\mathrm{}-\mathrm{keV})\frac{7}{2}(131\mathrm{}-\mathrm{k}\mathrm{e}\mathrm{V})\frac{3}{2}\gamma -\gamma \mathrm{cascade}$ in ${\mathrm{Tm}}^{169}$ following electron capture of ${\mathrm{Yb}}^{169}$ was measured in dilute solutions of ${\mathrm{Yb}}^{169}$ in polycrystalline samples of lutetium iron garnet at room temperature and at liquid-nitrogen temperature with and without applied magnetic field. The same measurements were also performed on the $\frac{7}{2}(198\mathrm{}-\mathrm{k}\mathrm{e}\mathrm{V})\frac{5}{2}(110\mathrm{}-\mathrm{k}\mathrm{e}\mathrm{V})\frac{3}{2} \gamma -\gamma \mathrm{cascade}$ at liquid-nitrogen temperature. From these experiments the magnetic hyperfine field acting at the nuclei of the ${\mathrm{Tm}}^{3+}$ ions, the electronic relaxation time at the ${\mathrm{Tm}}^{3+}$ ions, and the ratio of the $g$ factors of the $\frac{7}{2}+$ and $\frac{5}{2}+$ spin states in ${\mathrm{Tm}}^{169}$ could be deduced. At room temperature the time-averaged magnetic hyperfine field in the direction of the magnetizing field $〈{H_{\mathrm{int}}}^z〉$ was 206 kOe and agreed within 10% with that calculated from molecular-field theory using the free-ion model with an exchange field of 196 kOe and neglecting inner-core exchange-polarization effects. The value of $〈{H_{\mathrm{int}}}^z〉$ at liquid-nitrogen temperature averaged over all sites was 523 kOe. Neglecting quadrupole effects, the electronic relaxation time of the ${\mathrm{Tm}}^{3+}$ electrons was estimated to be 3.8×${10}^{-13\mathrm{}}$ sec at room temperature and 1.8×${10}^{-12\mathrm{}}$ sec at liquid-nitrogen temperature, consistent with an inverse dependence of the relaxation time on the absolute temperature. The ratio of the $g$ factors was determined to be $\frac{g_{\frac{7}{2}}}{g_{\frac{5}{2}}}=1.28\mathrm{}\pm 0.12$.