Mini volume collapse as evidence for a three-body magnetic polaron in $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$

Samarium sulfide (SmS) is a nonmagnetic narrow-gap (0.06 eV) semiconductor that undergoes a transition to a metallic intermediate valence state at 6.5 kbar. Europium sulfide (EuS) is a ferromagnetic semiconductor with a Curie temperature of 16 K and a gap of 1.6 eV. Here we present a study of the lattice constant, magnetic susceptibility, and resistivity of the substitution series $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$ for $0<x<1$. We observe a smooth interpolation of magnetic and transport behavior across the series, consistent with a virtual crystal scenario and Vegard's law. Surprisingly, however, the lattice constant deviates below Vegard's law in a manner that suggests parametric control of the Sm-Sm distance by the Eu moment in the manner of a magnetic polaron.

Figure 1

Lattice constants of $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$ at 300 K vs. concentration $x$. The dashed line represents a lattice constant that varies as $a\left(x\right)=(a_{\mathrm{Sm}}{n}_{\mathrm{Sm}}+a_{\mathrm{Eu}}{n}_{\mathrm{Eu}})-\mathcal{A}{n}_{\mathrm{Sm}}^2{n}_{\mathrm{Eu}}$, as discussed in the text. The $x$ values determined using energy dispersive microprobe analysis and the errors reflect variations in concentration across the sample.

Figure 2

Magnetic susceptibility and inverse susceptibility of $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$.

Figure 3

Upper inset: Percent composition of Eu in $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$ based on the expected ${\mathrm{Eu}}^{2+}$ magnetic moment. Lower inset: The ac susceptibility of $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$ for $x=0.25$, 0.5, 0.75, and 1 (left to right) divided by the peak value at temperatures close to the ferromagnetic $T_{\mathrm{c}}$, indicated by arrows and given in Table 1. The deviation of the data from unity for $x=0.75$ and 1.0 below $T_{\mathrm{c}}$ have been multiplied by 10 and 100, respectively, to make the peak more apparent. Main figure: The values of $T_{\mathrm{c}}$ versus $x$ for $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$ for $x=0.25$, 0.50, 0.75, and 1.0. The dashed line is a guide to the eye and suggests a percolation threshold of approximately 0.20.

Figure 4

Resistivity of different concentrations of $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$. Data for $x=1$ were not obtainable due to an upper limit on the measured resistance of the apparatus.

Figure 5

Log of resistivity versus inverse temperature for $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$. The straight lines represent fits to $\rho \left(T\right)={\rho }_0{e}^{\left(\mathrm{\Delta }/2\right)/k_{B}T}$ and $\mathrm{\Delta }$ values are given in Table 1.

Figure 6

Circles: Transport gaps $\mathrm{\Delta }$, as a function of percent composition in $\mathrm{S}{\mathrm{m}}_{1-x}\mathrm{E}{\mathrm{u}}_x\mathrm{S}$. Stars: The Weiss constant ${\theta }_W$, as a function of $x$.