Magnetic and electric hyperfine interactions in the rare-earth indium compoundsR2Instudied byCd111perturbed angular correlations

Abstract

The magnetic and electric hyperfine interactions of the probe nucleus $^{111}\mathrm{Cd}$ on the $\mathrm{In}$ site of the ferromagnetic rare-earth $(R)$ indium compounds ${R}_{2}\mathrm{In}$ ( $R=\mathrm{Pr}$, $\mathrm{Nd}$, $\mathrm{Sm}$, $\mathrm{Gd}$, $\mathrm{Dy}$, $\mathrm{Ho}$, $\mathrm{Er}$, and $\mathrm{Tm}$) have been investigated by perturbed angular correlation (PAC) spectroscopy. In the paramagnetic phase, the axially symmetric quadrupole interaction (QI) decreases by more than a factor of 20 from $R=\mathrm{Pr}$ to $R=\mathrm{Er}$ indicating a significant influence of the $4f$ electrons on the charge distribution at the $\mathrm{In}$ site. In the ferromagnetic phase, the spin and temperature dependence of the magnetic hyperfine field ${B}_{hf}$ and its orientation relative to the $c$ axis of hexagonal ${R}_{2}\mathrm{In}$ have been determined by measuring the combined magnetic and electric hyperfine interaction as a function of temperature for all $R$ constituents. The sign of ${B}_{hf}$, determined by applying an external field of $4\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, is positive for light and negative for heavy ${R}_{2}\mathrm{In}$. The comparison of the $^{111}\mathrm{Cd}$ hyperfine fields in ${R}_{2}\mathrm{In}$ and in $R$ metals suggests that the indirect $4f\ensuremath{-}4f$ coupling is mediated by intra-atomic $4f\ensuremath{-}5d$ exchange and$5d\ensuremath{-}5d$ interaction of neighboring $R$ atoms rather than by $4f$ exchange with the $s$-conduction electrons. The spin dependence of the saturation value of ${B}_{hf}(0)$ and of the Curie temperature in ${R}_{2}\mathrm{In}$ reflect a substantial difference of the $f\ensuremath{-}d$ exchange parameter $\ensuremath{\Gamma}$ between the light ( $LR=\mathrm{Pr}$, $\mathrm{Nd}$, $\mathrm{Sm}$) and the heavy ( $HR=\mathrm{Gd}$, $\mathrm{Tb}$, $\dots{}$) ${R}_{2}\mathrm{In}$ compounds: ${\ensuremath{\Gamma}}_{LR}∕{\ensuremath{\Gamma}}_{HR}=1.5(1)$. The deviation of the magnetic hyperfine field from its saturation value at low temperatures can be explained by the excitation of spin waves. $\mathrm{In}\phantom{\rule{0.3em}{0ex}}{\mathrm{Gd}}_{2}\mathrm{In}$, the low temperature decrease of ${B}_{hf}$ follows Bloch's ${T}^{3∕2}$ relation. In the other ${R}_{2}\mathrm{In}$ compounds with nonzero angular momentum of the $R$ constituent, the temperature dependence of ${B}_{hf}$ is best described by the modified power law ${T}^{3∕2}\mathrm{exp}(\ensuremath{-}\ensuremath{\Delta}∕{k}_{\mathrm{B}}T)$ which suggests the existence of an energy gap of about $\ensuremath{\Delta}∕{k}_{\mathrm{B}}\ensuremath{\approx}15--20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in the spin wave spectrum of these anisotropic ferromagnets. With the exception of ${\mathrm{Pr}}_{2}\mathrm{In}$ and ${\mathrm{Nd}}_{2}\mathrm{In}$, where the hyperfine field vanishes discontinuously at the Curie temperature, the magnetic phase transitions of ${R}_{2}\mathrm{In}$ are of second order. A critical increase of the linewidth of the magnetic interaction close to the phase transition indicates a spatial variation of the exchange interaction with a spread of the Curie temperature of about $2--5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The temperature-induced changes of the orientation of the $4f$ spins relative to the $c$ axis of ${R}_{2}\mathrm{In}$ have been deduced from the angle between ${B}_{hf}$ and the symmetry axis of the electric field gradient.