Static and dynamical properties in the Pr-based filled skutterudite compound $\mathrm{Pr}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ revealed by a ${}^{31}\mathrm{P}$-NMR study

${}^{31}\mathrm{P}$-NMR studies have been carried out to investigate magnetic properties in the Pr-based filled skutterudite compound $\mathrm{Pr}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$. This compound shows an unusual phase transition at $T_A\sim 6.5\mathrm{K}$, which is now regarded as antiferroquadrupole (AFQ) ordering from neutron-diffraction experiments. Splitting of the P-NMR spectrum due to the appearance of two P sites with different hyperfine fields was observed below $T_A$. From the field dependence, the splitting seems to disappear in zero magnetic field, indicating that the different hyperfine fields are not due to magnetic order, but to the appearance of two inequivalent P sites below $T_A$. This is ascribed to the distortion of the P cage surrounding a Pr ion below $T_A$, which is associated with the Pr orbital ordering. The nuclear spin-lattice relaxation rate $(1∕T_1)$ shows the typical behavior of Kondo systems, where onset of local-moment screening due to the coupling between conduction and localized $\mathrm{Pr}\text{−}4f$ electrons is observed below $50\mathrm{K}$. Far above a critical field $H_A\sim 50\mathrm{kOe}$, the Korringa behavior $T_{1}T=\mathrm{const}$ is observed below $2\mathrm{K}$ in $100\mathrm{kOe}$. The Korringa value below $2\mathrm{K}$ is one order of magnitude larger than that in $\mathrm{La}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$, which has no $4f$ electrons. Our NMR experiment shows that the heavy-fermion state is realized far above $H_A$ in $\mathrm{Pr}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$. The magnetic fluctuations in $\mathrm{Pr}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ are discussed from a comparison with typical heavy-fermion compounds. In magnetic fields below $H_A$, $1∕T_1$ shows a sharp decrease below $T_A$, however, in smaller magnetic fields less than $10\mathrm{kOe}$, $1∕T_1$ stays constant far below $T_A$ with a relatively large value. The temperature and field dependence of $1∕T_1$ reveals the presence of low-energy spin fluctuations in the low-temperature and low-field region. These unusual magnetic fluctuations are considered to originate from the magnetic dynamics of Pr-nuclear spins since the fluctuating magnetic field $\sim 1.4\mathrm{Oe}$ and frequency $\sim 3.5\mathrm{MHz}$ are so small. The nuclear ordering temperature is estimated to be $\sim 0.08\mathrm{mK}$ using the nuclear exchange fluctuations derived from the observed $1∕T_1$ of P. We show that $\mathrm{Pr}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ is a quite unique compound in which nuclear magnetism can be detected by P NMR thanks to the nonmagnetic ground state of the $\mathrm{Pr}\text{−}4f$ moments.

Figure 1

Temperature dependence of Knight shift parallel and perpendicular to the principal axis of the Knight-shift tensor. The inset shows the powder pattern spectrum (upper) and the derivative of the spectrum (bottom) seen above $T_A$ in $\mathrm{Pr}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$.

Figure 2

$K_{\perp }$ and $K_{\Vert }$ above $T_A$ are plotted against bulk susceptibility $\chi$ with temperature as an implicit parameter. The inset shows the temperature dependence of bulk susceptibility in various fields.

Figure 3

The upper (bottom) panel shows the P-NMR spectrum at $T>T_A(T<T_A)$. The spectrum at $T<T_A$ can be interpreted by the overlap of two powder-pattern spectra which have an identical shape as shown by the fitting. The intensity of two powder-pattern spectra is adjusted to attain the reasonable fitting. The interval of two peaks is defined as $2\Delta H_{\mathit{int}}$.

Figure 4

Temperature dependence of $\Delta H_{\mathit{int}}$ in various magnetic field. The curves are a guide to the eyes.

Figure 5

Dependence of $\Delta H_{\mathrm{int}}$ at $1.5\mathrm{K}$ on magnetic field. The inset shows the dependence of the additional hyperfine field appearing in the AFQ ordering state.

Figure 6

Temperature dependence of $1∕T_1$ in various field smaller than $H_A$. $1∕T_1$ in $\mathrm{La}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$ is shown for a comparison.

Figure 7

Temperature dependence of $1∕T_1$ in various field larger than $H_A$, along with $1∕T_1$ in $10\mathrm{kOe}$. The inset shows the temperature dependence of $1∕T_{1}T$ of same data.

Figure 8

Temperature dependence of the characteristic energy of the spin fluctuations $\Gamma \left(T\right)$. The solid line shows the relation of $\Gamma \sim T$, and the dotted curve shows the calculated temperature dependence of $\Gamma$ based on the impurity Kondo model by Cox et al. with the characteristic temperature $T_0\sim 6.5\mathrm{K}$. The fairly nice fitting is seen in $6<T<20\mathrm{K}$ (see text).

Figure 9

Field dependence of $1∕T_1$ at $1.5\mathrm{K}$. The dotted curve of the fitting by $1∕T_1=2{\Delta }^2\omega ∕({\omega }^2+{\omega }_{\mathrm{res}}^2)$ with $\omega \sim 3.5\mathrm{MHz}$ (see text).

Figure 10

Temperature dependence of $1∕T_1$ in a small field of $950\mathrm{Oe}$ down to $65\mathrm{mK}$.