Double Exchange Model for Magnetic Hexaborides

A microscopic theory for rare-earth ferromagnetic hexaborides, such as ${\mathrm{E}\mathrm{u}}_{1-\mathrm{x}}{\mathrm{C}\mathrm{a}}_{\mathrm{x}}{\mathrm{B}}_6$, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as the Hall effect, magnetoresistance, frequency dependent conductivity, and dc resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature $T_C$ as a function of the plasma frequency ${\omega }_p$.

Figure 1

Evolution of $n_e(T)$, assuming $n_e^0=0.003$ and $E_W=0.1t$. The inset shows the mobility edge $\widetilde{E_C}$ (circles) and mobility gap $\Delta$ (squares) as functions of the normalized magnetization $M$.

Figure 2

Result for ${\omega }_p^2(M)$ obtained from the sum rule (circles) and experimental data (diamonds). The experimental ($H=0$) points were obtained combining ${\omega }_p^2(T)$ at zero field from Ref. 7 with the zero field $M(T)$ from Ref. 5.

Figure 3

Schematic phase diagram for ${\mathrm{E}\mathrm{u}}_{1-\mathrm{x}}{\mathrm{C}\mathrm{a}}_{\mathrm{x}}{\mathrm{B}}_6$ in the $T-x$ plane in standard notation: PM stands for paramagnetic metal, PI for paramagnetic insulator; FM means ferromagnetic metal and FI ferromagnetic insulator.