Magnetic polaron effect in Sr${}_{8-x}$Eu${}_x$Ga${}_{16}$Ge${}_{30}$ clathrates probed by electron spin resonance

Single crystals of the type-I clathrate series Sr${}_{8-x}$Eu${}_x$Ga${}_{16}$Ge${}_{30}$ ($x=0.01$–8) were grown by Ga flux and systematically studied by magnetic susceptibility, electrical resistivity, and electron spin resonance (ESR) measurements. Both magnetic transition temperatures ($T_c$ and $T^{*}$) were mapped as a function of $x$. We found that the Curie temperature ($T_c$) and the magnetic anomaly temperature ($T^{*}$) decrease systematically as Eu is substituted by Sr until no ordering is observed above 2 K for $x=1.0$. For samples where the rattling Einstein temperature of ${\theta }_E\approx 25$–60 K lies above $T_c$, we have observed no features in the ESR data, suggesting that the Eu${}^{2+}$ 4$f$ spin dynamics is weakly coupled to the rattling modes. As the temperature is lowered and the magnetic field is increased, the ESR linewidth ($\Delta H$) behavior points to the formation of magnetic polarons.

Figure 1

(a) Temperature dependence of electrical in-plane resistivity normalized to the room-temperature value for Sr${}_{8-x}$Eu${}_x$Ga${}_{16}$Ge${}_{30}$$$. (b) Low-temperature resistivity showing the peaks associated with $T_c$ and $T^{*}$.

Figure 2

Magnetic susceptibility inverse as a function of temperature taken at low applied magnetic field $H=1$ kOe. The inset shows the first derivative of $\chi$, and both $T_c$ and $T^{*}$ are indicated by arrows.

Figure 3

Phase diagram of Sr${}_{8-x}$Eu${}_x$Ga${}_{16}$Ge${}_{30}$$$ single crystals.

Figure 4

$X$-band ESR lines at $T=300$ K.

Figure 5

Temperature dependence of the ESR linewidth and $g$ factor for Sr${}_{8-x}$Eu${}_x$Ga${}_{16}$Ge${}_{30}$$$single crystals.

Figure 6

Temperature dependence of the ESR linewidth in $X$ and $Q$ band for $x=6.0$.