Neutron diffraction and scattering study of the weak ferromagnetism in ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$ skutterudite

A structural and magnetic investigation of ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$ with filled skutterudite structure is carried out by means of powder neutron diffraction and magnetization measurements in order to investigate the magnetic ground state of this compound. The existence of an ordered magnetic moment on the Fe site of $\approx 0.6{\mu }_B$/Fe atom is in good agreement with magnetization data. The ratio between the number of spins in the paramagnetic state and in the saturated ferromagnetic state is $\approx 1.7$, indicating some degree of delocalization of the Fe magnetic moment in ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$. Theoretical density-functional calculations of real-space spin-density maps are performed and compared to the experimental findings of weak ferromagnetism in ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$ ($T_C\approx 83$ K). Diffuse magnetic scattering with polarized neutrons revealed that a localized moment exists in the paramagnetic phase which decreases with increasing temperature. The results are discussed in the light of comparison with other intermetallic compounds.

Figure 1

Powder neutron diffraction data of ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$ obtained on the D1B diffractometer: (a) $T=2$ K, (b) $T=95$ K. The circles represent experimental data, and the continuous (red) curve the calculated diffractogram. Vertical ticks are the calculated ($hkl$) reflex positions: upper row (blue) for the Sb impurity, and lower row (black) for ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$. The bottom trace is the difference plot. Arrows indicate artifacts from the sample holder. (c) Difference plot between the patterns recorded at 2 and 95 K, evidencing the diffraction peaks of magnetic origin for ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$.

Figure 2

Fe $3d$ orbital-resolved density of states (DOS) of ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$. The three $t_{2g}$ and two $e_g$ orbitals are mutually degenerate. Negative DOS denotes the minority spin contribution.

Figure 3

Calculated real-space spin-density maps for ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$. Top: positive spin density, isosurface $0.5{\mu }_B$/Å${}^3$. Middle: crystal structure of ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$. Large (white) balls: Na; small (blue) balls centering the octahedra: Fe; small (red) balls at octahedral vertices: Sb atoms forming (${\mathrm{Sb}}_4$) rectangular units. Bottom: spin-density iso-surface $0.2{\mu }_B$/Å${}^3$. Large objects (turquoise): positive density; smaller objects (red): negative density.

Figure 4

Arrott plot of magnetization isotherms at the indicated temperatures in Kelvin for ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$ ($M$ per formula unit).

Figure 5

Polarized neutron diffraction and $xyz$ separation of scattering contributions of paramagnetic (red), nuclear coherent (black), and spin-incoherent scattering (blue) of ${\mathrm{NaFe}}_4{\mathrm{Sb}}_{12}$ at 300 K (open) and 90 K (filled symbols). Note the logarithmic scale of absolute intensities.