Magnetic ordering of hyperfine-coupled nuclear and4f-electron moments in the clathrate compoundPr3Pd20Ge6

Abstract

Complex ac susceptibility, $\ensuremath{\chi}={\ensuremath{\chi}}^{\ensuremath{'}}\ensuremath{-}i{\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}$, measurements of the clathrate compound ${\mathrm{Pr}}_{3}{\mathrm{Pd}}_{20}{\mathrm{Ge}}_{6}$ were performed in static fields up to 10 mT for $H\ensuremath{\parallel}[001]$ and at temperatures down to $500 \ensuremath{\mu}\mathrm{K}$. Praseodymium (Pr) nuclear magnetic moments at the $8c$ site, where quadrupole moments of $4f$ electrons order at ${\mathit{\text{T}}}_{\text{Q1}}=250$ mK, were found to order antiferromagnetically at 9 mK, as shown by a peak in ${\ensuremath{\chi}}^{\ensuremath{'}}$ and a substantial increase in thermal relaxation time. The large enhancement factor $(1+{K}_{8c})$ obtained by calculation of the hyperfine-enhanced nuclear susceptibility of Pr at the $8c$ site accounts for the high transition temperature of Pr nuclear magnetic moments and the large ${\ensuremath{\chi}}^{\ensuremath{'}}$ below 30 mK. From analysis of the crystalline electric field and the mean-field approximation, we conclude that a $\ensuremath{\chi}$ peak at 77 mK can be ascribed to an antiferromagnetic ordering of magnetic moments of $4f$ electrons at the $4a$ site. We found that nuclear and $\mathit{\text{f}}$-electron moments order separately on two sublattices in this compound. The temperature and magnetic field dependence of ${\ensuremath{\chi}}^{\ensuremath{'}}$ and ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}$ between 30 and 60 mK are discussed in terms of dissipation phenomena.