Experimental and Theoretical Study of Perturbed Angular Correlations for a Rare-Earth Localized Moment in Iron

In order to study the static and dynamic properties of a localized moment in a ferromagnet, the temperature-dependent hyperfine interaction of dilute thulium in iron was measured between 4.2 and 450°K. Time-integral perturbed-angular-correlation (IPAC) experiments were performed simultaneously on two cascades in ${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}$, using a sum-coincidence technique. Samples were prepared by implantation of radioactive ${}_{}{}^{169}{}_{}{}^{}\mathrm{Yb}$ with an isotope separator. To analyze the results, the $-J_{\mathrm{sf}}\overrightarrow{\mathrm{s}}·\overrightarrow{\mathrm{S}}$ interaction is approximated by a molecular field model, in which the exchange field $H_{\mathrm{exch}}$ between Tm and Fe is proportional to the host magnetization. The electronic Larmor frequency is then proportional to the Brillouin function representing the rare-earth susceptibility $〈J_z〉$. Above ∼200°K, the IPAC data may be interpreted in terms of the generalized Abragam-Pound theory. Below ∼200°K, however, the electron-spin correlation time ${\tau }_c$ is of the order of the nuclear lifetime ${\tau }_N$, and the Abragam-Pound theory is not appropriate. We describe the application of a more general theory of perturbed angular correlations (Ref. 7), whose validity does not depend on the condition $\frac{{\tau }_c}{{\tau }_N}\ll 1$. Exact analytical expressions are obtained assuming negligible quadrupole interaction, an axially symmetric magnetic hyperfine interaction, and exponential decay of the electron-spin correlation functions (whose amplitude is defined by the molecular field model). Experimental results above ∼20°K are in good over-all agreement with this analysis. A strong temperature dependence of the hyperfine field is observed (about 600% variation over the temperature range). The deduced exchange field between Tm and Fe at 0°K is 2.5±0.5 MOe. It is found that ${\tau }_c\left(300\mathrm{}°\mathrm{K}\right)\sim 5\times {10}^{-12\mathrm{}}$ sec, in agreement with the Korringa limit, and results are consistent with a $\frac{1}{T}$ dependence of the electron correlation time. Below ∼20°K, results of the calculation are insensitive to the value of ${\tau }_c$; hyperfine field values are then deduced by assuming a static magnetic interaction. The hyperfine field at 0°K is 5.60±0.15 MOe. The discrepancy between this value and the sum of the free-ion field and the contact term (∼7.5 MOe) may be ascribed to ion-implantation problems or to crystalline electric field effects.