Coexistence of localized and delocalized f-electrons in $\alpha \text{−}\mathrm{Yb}\mathrm{Pd}\mathrm{Sn}$ from thermodynamic and transport measurements

We report the specific heat, magnetic susceptibility, and magnetization as well as resistivity of hexagonal $\alpha \text{−}\mathrm{Yb}\mathrm{Pd}\mathrm{Sn}$ polycrystals down to temperatures $T$ of $50\mathrm{mK}$ and fields up to $12\mathrm{T}$. In the susceptibility $\chi \left(T\right)$, several different temperature regimes can be distinguished. For $300\mathrm{K}>T>170\mathrm{K}$, a Curie-Weiss-like behavior is obtained with the effective moments close to that of ${\mathrm{Yb}}^{3+}$. The large Weiss temperature ${\Theta }_H\approx 150\mathrm{K}$ and the leveling off of $\chi$ toward low $T$ are indicative of valence fluctuations. Around $30\mathrm{K}$, crystal-field excitations manifest themselves in features of $\chi \left(T\right)$ and the resistivity $\rho \left(T\right)$. For $5\mathrm{K}>T>0.2\mathrm{K}$, a Curie-Weiss behavior with ${\mu }_{\mathit{eff}}=1.27{\mu }_B∕\mathrm{Yb}$ atom and ${\Theta }_L=0.41\mathrm{K}$ is found, signaling the occupation of the lowest crystal-field doublet. A sharp maximum in $\chi \left(T\right)$ and in the specific heat $C\left(T\right)$ indicates antiferromagnetic ordering at $250\mathrm{mK}$. The specific-heat peak develops into a broadened Schottky anomaly in moderate magnetic fields. The sizable linear specific-heat coefficient $\gamma =68\mathrm{mJ}∕\text{mole}{\mathrm{K}}^2$ is attributed to valence fluctuations. Likewise, the magnetization at 10 and $2.3\mathrm{K}$ measured up to $12\mathrm{T}$ can be decomposed into a contribution of delocalized electrons and localized magnetic moments. The data can be consistently interpreted in terms of a two-fluid model with $\sim 6\%$ localized and $\sim 94\%$ delocalized moments derived from (nearly) trivalent Yb.

Figure 1

(Color online) Specific heat of $\alpha \text{−}\mathrm{Yb}\mathrm{Pd}\mathrm{Sn}$ plotted as $C∕T$ vs $T^2$. Straight line is a linear fit to the data above $4\mathrm{K}$. Inset shows the low-$T$ anomaly which is attributed to magnetic order of ${\mathrm{Yb}}_2{\mathrm{O}}_3$ impurity phase. It is suppressed in a magnetic field of $12\mathrm{T}$.

Figure 2

(Color online) Specific heat of $\alpha \text{−}\mathrm{Yb}\mathrm{Pd}\mathrm{Sn}$ at temperatures below $1.5\mathrm{K}$. In zero field, a sharp maximum is observed at $200\mathrm{mK}$ indicating antiferromagnetic order. A magnetic field of $0.5\mathrm{T}$ suppresses the magnetic ordering.

Figure 3

(Color online) Specific heat $\Delta C$ attributed to localized ${\mathrm{Yb}}^{3+}$ moments plotted as function of $T∕B$ for several magnetic fields $B$. The solid line is a two-level Schottky anomaly (see text for details).

Figure 4

(Color online) Inverse magnetic susceptibility $[{\chi }^{-1}\approx {({\mu }_{0}M∕B)}^{-1}]$ measured for $B=1\mathrm{T}$ as a function of temperature between 2 and $300\mathrm{K}$. The line indicates a Curie-Weiss law observed between 170 and $300\mathrm{K}$ with ${\mu }_{\mathit{eff}}=3.96{\mu }_B∕\mathrm{Yb}$ atom and ${\Theta }_H=145\mathrm{K}$. Inset shows low-temperature data with ${\mu }_{\mathit{eff}}=1.27{\mu }_B∕\mathrm{Yb}$ atom and ${\Theta }_L=0.41\mathrm{K}$.

Figure 5

(Color online) Magnetic susceptibility $\chi$ as a function of temperature $T$ between $50\mathrm{mK}$ and $4\mathrm{K}$. Measurements have been performed at $100\mathrm{mT}$ with a vibrating sample magnetometer (VSM) above $2.3\mathrm{K}$ and with a SQUID magnetometer at lower temperatures and $B=100\mu \mathrm{T}$ in zero-field-cooled (zfc) and field-cooled (fc) modes. Inset shows $\chi \left(T\right)$ around the sharp maximum, signaling an antiferromagnetic transition, on an expanded scale.

Figure 6

(Color online) Magnetization $M$ of $\alpha \text{−}\mathrm{Yb}\mathrm{Pd}\mathrm{Sn}$ in ${\mu }_B∕\mathrm{f.u.}$ as a function of $B$ at $T=2.3$, 10, and $30\mathrm{K}$. Solid lines are fits of Eq. (1) to the data.

Figure 7

(Color online) Electrical resistivity $\varrho$ as a function of temperature $T$. The upper left-hand inset shows the resistivity at $T⩽50\mathrm{K}$ for magnetic fields $B=0$ and $12\mathrm{T}$. Lower right-hand inset shows $\Delta \rho ∕\rho =[\rho \left(12\mathrm{T}\right)-\rho \left(0\right)]∕\rho$.