Spin-Selective Kondo Insulator: Cooperation of Ferromagnetism and the Kondo Effect

We propose the notion of a spin-selective Kondo insulator, which provides a fundamental mechanism to describe the ferromagnetic phase of the Kondo lattice model with antiferromagnetic coupling. This unveils a remarkable feature of the ferromagnetic metallic phase: the majority-spin conduction electrons show metallic while the minority-spin electrons show insulating behavior. The resulting Kondo gap in the minority-spin sector, which is due to the cooperation of ferromagnetism and partial Kondo screening, evidences a dynamically induced commensurability for a combination of minority-spin electrons and parts of localized spins. Furthermore, this mechanism predicts a nontrivial relation between the macroscopic quantities such as electron magnetization, spin polarization, and electron filling.

Figure 1

Spin-resolved spectral functions for the ferromagnetic state in the Kondo lattice model $J/W=0.25$. The inset shows a magnification around the Fermi energy for the spin-down component illustrating the gap in the spectral function.

Figure 2

Gap width $\Delta /W$ in the minority-spin spectral function depending on the spin-coupling $J$ and the occupation $n_{\downarrow }^c$. The temperature of the system is $T/W=3\times {10}^{-4}$. The lines in the left panel are fits as $\sim \exp (-a/J)$.

Figure 3

Upper panel: Magnetization and “commensurability” ($n_{\downarrow }^c+n_{\downarrow }^f$), for two different coupling strengths and different occupation numbers calculated for a Bethe lattice at $T/W=3\times {10}^{-4}$. The electron magnetization is shown as $⟨m⟩=n_{\uparrow }^c-n_{\downarrow }^c$, while the spin expectation value $⟨S_z⟩$ is shown mirrored as $-\text{}⟨Sz⟩$. The commensurability condition is explained in the text. Lower panel: sketch of the local configuration (see text).

Figure 4

Momentum-resolved spectral functions for the square lattice and $J/W=0.3$, $n=n_{\uparrow }^c+n_{\downarrow }^c=0.25$, $m=n_{\uparrow }^c-n_{\downarrow }^c=0.1$. The right side always shows a magnification of the left side around the Fermi energy $\omega =0$ represented by the green line. From top to bottom the figures show the majority-spin and the minority-spin spectral function, respectively.

Figure 5

Momentum-resolved occupation number $n(k)$ (same parameters as in Fig. 4). Left (right) panel shows the majority- (minority-) spin component. The dotted line represents the Fermi surface for noninteracting electrons (for the majority spin this line coincides with the shown surface). Note that for improving the contrast, the occupation for the minority-spin electrons is displayed in the interval $n(k)\in [0,0.3]$.