Ferromagnetism and possible heavy-fermion behavior in single crystals of $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$

Single crystals of the filled-skutterudite compound $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ have been investigated by means of electrical resistivity, magnetization, and specific heat measurements. The $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ crystals have the $\mathrm{La}{\mathrm{Fe}}_4{\mathrm{P}}_{12}$-type cubic structure with a lattice parameter of $9.3\mathrm{\AA }$. Possible heavy-fermion behavior is inferred from specific heat measurements, which reveal a large electronic specific heat coefficient $\gamma \approx 520\mathrm{mJ}∕\mathrm{mol}{\mathrm{K}}^2$, corresponding to an effective mass $m^{*}\approx 98m_e$. Features related to a ferromagnetic transition at $\sim 0.9\mathrm{K}$ can be observed in electrical resistivity, magnetization, and specific heat. Conventional Arrott-plot analysis indicates that $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ conforms to mean-field ferromagnetism.

Figure 1

(a) DC magnetic susceptibility ${\chi }_{\mathrm{dc}}$ versus temperature $T$ from $0\text{to}10\mathrm{K}$ measured at $500\mathrm{Oe}$. Fits of ${\chi }_{\mathrm{dc}}\left(T\right)$ to a CEF model in which the ground state is either ${\Gamma }_6$ (dashed line) or ${\Gamma }_8^{\left(2\right)}$ (solid line). Below $10\mathrm{K}$, these two lines overlap. (b) ${\chi }_{\mathrm{dc}}^{-1}$ versus $T$ from $0\text{to}300\mathrm{K}$. Fits of ${\chi }_{\mathrm{dc}}\left(T\right)$ and ${\chi }_{\mathrm{dc}}^{-1}\left(T\right)$ to a CEF model in which the ground state is either ${\Gamma }_6$ (dashed line) or ${\Gamma }_8^{\left(2\right)}$ (solid line).

Figure 2

(a) Magnetization $M$ versus magnetic field $H$ isotherms and the saturation magnetization $M_{\mathrm{sat}}$ determined from $M$ versus $H$ isotherms below the Curie temperature ${\Theta }_{\mathrm{C}}$. (b) $M^2$ versus $H∕M$ isotherms (Arrott plot) for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$. (c) Inverse initial magnetic susceptibility (open circles) determined from $M^2=0$ intercepts of $M^2$ versus $H∕M$ isotherms, compared to the ${\chi }_{\mathrm{dc}}^{-1}\left(T\right)$ data (pluses). The line is a Curie-Weiss fit. (d) $H∕M=0$ intercepts of $M^2$ versus $H∕M$ isotherms plotted versus $T$. Positive values correspond to the spontaneous magnetization $M_{\mathrm{sp}}$.

Figure 3

(a) Low-temperature electrical resistivity $\rho$ versus temperature $T$ for magnetic fields $H$ between 0 and $6\mathrm{T}$ for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$. The solid lines are guides to the eye. (b) Low-temperature electrical resistivity $\rho$ versus $T$ for magnetic fields $H$ between 8 and $18\mathrm{T}$ for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$. The solid lines are guides to the eye. (c) Position of the shoulder $T_{\mathrm{d}}$ in $\rho \left(T\right)$ (which corresponds to ${\Theta }_{\mathrm{C}}$) versus $H$, with vertical bars indicating the width of the transition at $T_{\mathrm{d}}$ as described in the text. (d) High-$T$ resistivity $\rho$ versus $T$ at $H=0$, 0.5, 1, 2, 4, 6, 8, and $9\mathrm{T}$.

Figure 4

(a) Low-$T$ electrical resistivity $\rho$ versus temperature $T$ with power-law (dashed line) and spin-wave (solid line) fits at various magnetic fields for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$. (b) Residual resistivity ${\rho }_0$ versus $H$. (c) Exponent $n$ of the power-law fit versus $H$. (d) Energy gap ${\Delta }_{\mathrm{spw}}$ from the spin-wave fit versus $H$.

Figure 5

(a) Zero-field resistivity $\rho$ and the estimated ${\rho }_{\mathrm{lat}}+{\rho }_{\mathrm{imp}}$ versus temperature $T$ for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$, where ${\rho }_{\mathrm{imp}}\sim 9.4\mu \Omega \mathrm{cm}$. (b) Temperature dependence of the incremental resistivity $\Delta \rho =\rho -{\rho }_{\mathrm{lat}}-{\rho }_{\mathrm{imp}}$ and CEF fits for two different ground states: ${\Gamma }_6$ (dashed line) and ${\Gamma }_8^{\left(2\right)}$ (solid line), where $x∕(1-x)$ is the ratio of s-f exchange to aspherical Coulomb scattering for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$.

Figure 6

(a) Isotherms of electrical resistivity $\rho$ versus magnetic field $H$ for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$. (b) and (c) Calculated $\rho$ versus $H$ isotherms including the effects of s-f exchange and aspherical Coulomb scattering using the CEF parameters determined from zero-field data.

Figure 7

Electrical resistivity $\rho$ versus temperature $T$ for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ at various pressures $P$ up to $28\mathrm{kbar}$. Inset (a): Expanded view of the resistive ferromagnetic transitions. Inset (b): Temperature of the drop in $\rho \left(T\right)$ due to the onset of ferromagnetism $T_{\mathrm{d}}$ (approximately corresponding to the Curie temperature ${\Theta }_{\mathrm{C}}$) versus $P$ with vertical bars indicating the width of the transition.

Figure 8

(a) Zero-field $C$ versus $T$ for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ and $\mathrm{La}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ below $20\mathrm{K}$. Inset: $\delta C∕T$ versus $T^2$ below $20\mathrm{K}$, where $\delta C\equiv C\left(\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}\right)-C\left(\mathrm{La}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}\right)$. The extrapolated values of the two dashed lines at $0\mathrm{K}$ set the lower and upper limits of $\gamma \left(\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}\right)-\gamma \left(\mathrm{La}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}\right)$. (b) A comparison between $C$ of $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ and a fit of $C_{\mathrm{el}}+C_{\mathrm{lat}}$, where $C_{\mathrm{el}}=\gamma T$ and $C_{\mathrm{lat}}$ is composed of $C_{\mathrm{Deb}}$ and $C_{\mathrm{Ein}}$ as described in the text. The electronic specific heat coefficient $\gamma$, the Debye temperature $\left({\Theta }_{\mathrm{D}}\right)$, the Einstein temperature $\left({\Theta }_{\mathrm{E}}\right)$, and the coupling constant $r$ for the Einstein oscillator are estimated as $520\mathrm{mJ}∕\mathrm{mol}{\mathrm{K}}^2$, 255 K, 39 K, and $0.48$ respectively. Inset: $C∕T$ versus $T^2$ for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$ below $20\mathrm{K}$ for $\mathrm{Nd}{\mathrm{Os}}_4{\mathrm{Sb}}_{12}$.

Figure 9

(a) Incremental specific heat $\Delta C$ $(\Delta C\equiv C-C_{\mathrm{el}}-C_{\mathrm{lat}})$ (left axis) and the magnetic entropy $S_{\mathrm{mag}}$ (right axis) versus temperature $T$. (b) Logarithmic plot of the power-law fit (dotted line) and the anisotropic-spin-wave fit (dashed line) to the incremental specific heat $\Delta C\left(T\right)$ after the electronic and lattice contributions have been removed (in a very limited measuring range below ${\Theta }_{\mathrm{C}}$).