Temperature dependence of $\text{Eu}4f$ and $\text{Eu}5d$ magnetizations in the filled skutterudite ${\text{EuFe}}_4{\text{Sb}}_{12}$

The element-specific and shell-specific magnetism of Eu in the filled skutterudite ferrimagnet ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$ has been investigated using $\text{Eu}{M}_{4,5}$- and $\text{Eu}{L}_{2,3}$-edge x-ray magnetic circular dichroism (XMCD) spectroscopy as a function of temperature. $\text{Eu}{L}_3$-edge x-ray absorption spectroscopy shows that Eu is mostly in the divalent state. $\text{Eu}{M}_5$-edge x-ray absorption spectroscopy, measured by electron yield, shows nearly equal fractions of ${\text{Eu}}^{2+}$ and ${\text{Eu}}^{3+}$ states because it probes a significant portion of the surface volume which is dominated by the ${\text{Eu}}^{3+}$ impurity state. Sum-rule analysis of the $\text{Eu}{M}_{4,5}$-edge XMCD spectrum measured at 4.9 K yielded the $4f$ spin moment of $\left(7.15\pm 0.3\right){\mu }_B$ per ${\text{Eu}}^{2+}$ ion. By comparing the $\text{Eu}{L}_{2,3}$-edge XMCD spectrum in the ferrimagnetic state of ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$ to that of a divalent Eu reference compound, the clathrate ${\text{Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$, we show that the $5d$ spin polarization of Eu in the skutterudite is strongly enhanced by the exchange coupling with the $3d$ band electrons of Fe, which were shown to have an ordered moment of $-0.21{\mu }_B/\text{Fe}$ in our earlier $\text{Fe}{L}_{2,3}$ XMCD measurements. The temperature dependence of the magnetic order parameter, determined from the $\text{Eu}{L}_3$-edge XMCD intensity, yields a mean-field-like exponent $\left(\sim 0.52\right)$ in the skutterudite and a three-dimensional Heisenberg-type $\left(\sim 0.36\right)$ exponent in the clathrate.

Figure 1

(Color online) Crystal structures of the skutterudite and the clathrate. (a) Unit cell of the skutterudite ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$. Eu (large spheres) is at the corners and at the body center, Fe (smallest spheres) is located in the center of each octahedron (shown as semitransparent substructures), and Sb (medium sized spheres) is at the vertices of the octahedra. (b) The coordination polyhedra around Eu (not shown in figure) in the clathrate ${\text{Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$. A Ga or Ge atom $\left(X\right)$ is at each vertex of a polyhedron.

Figure 2

(Color online) Temperature dependence of reduced magnetization, $M\left(T\right)/M\left(0\right)$, in (a) ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$ and (b) ${\text{Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$, measured in a field of 1 T. The solid lines are best fits by the power law given in the figure (see text for the details of the fitting regions).

Figure 3

(Color online) (a) Normalized x-ray absorption spectra at $\text{Eu}{L}_3$ and $L_2$ edges in ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$ and ${\text{Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ at 4.8 K in an applied field of 0.5 T. Inset shows the XAS with a fit to two-component arctangent step function with Lorentzian. (b) Experimental (filled circles) and FEFF calculation (solid line) of $\text{Eu}{L}_3$-edge x-ray absorption spectrum in ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$.

Figure 4

(Color online) $\text{Eu}{M}_{4,5}$-edge (a) XAS and (b) XMCD in ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$ measured in a field of 2 T at 4.8 K. Inset shows the hysteresis of $M_5$-edge XMCD peak intensity at $E=1128.2\text{eV}$ measured at 4.8 K

Figure 5

(Color online) (a) $\text{Eu}{M}_5$-edge XMCD in ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$ measured in a field of 2 T in the temperature range of 5–130 K. (b) Temperature dependence of the integrated intensity from the 1128 eV $\left({\text{Eu}}^{2+}\right)$, 1130 eV $\left({\text{Eu}}^{3+}\right)$, and 1125.6 eV $\left({\text{Eu}}^{3+}\right)$ peaks in the $\text{Eu}{M}_5$-edge XMCD spectra in ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$.

Figure 6

(Color online) (a) XAS and (b) XMCD at the $\text{Eu}{L}_{2,3}$ edges in ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$ measured at 4.8 K in an applied field of 0.5 T.

Figure 7

(Color online) (a) XAS and (b) XMCD at the $\text{Eu}{L}_{2,3}$ edges in ${\text{Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ measured at 4.8 K in a field of 0.5 T.

Figure 8

(Color online) Temperature dependence of the $\text{Eu}{L}_3$-edge XMCD intensity, measured in a field of 0.5 T, shows the magnetic phase transitions in (a) ${\text{Eu}}_{0.95}{\text{Fe}}_4{\text{Sb}}_{12}$ and (b) ${\text{Eu}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$. The numbers in the brackets indicate the error in the last significant digits.