Strong enhancement of the Edelstein effect in $f$-electron systems

The Edelstein effect occurring in systems with broken inversion symmetry generates a spin polarization when an electric field is applied, which is most advantageous in spintronics applications. Unfortunately, it became apparent that this kind of magnetoelectric effect is very small in semiconductors. We here demonstrate that correlation effects can strongly enhance the magnetoelectric effect. Particularly, we observe a strong enhancement of the Edelstein effect in $f$-electron systems close to the coherence temperature, where the $f$ electrons change their character from localized to itinerant. We furthermore show that this enhancement can be explained by a coupling between the conduction electrons and the still localized $f$ electrons.

Figure 1

Noninteracting momentum resolved spectral functions for (a) ${\alpha }_{ff}/t_f=0.5$, ${\alpha }_{cf}/t_f=0$, $V/t_f=0.5$ and (b) ${\alpha }_{ff}/t_f=0.5$, ${\alpha }_{cf}/t_f=0.5$, $V/t_f=0.5$.

Figure 2

(a) and (b) Noninteracting momentum resolved spectral functions. Model parameters are written above each panel. The Fermi energy corresponds to $\omega /t_f=0$. (c) ME effect for the parameter shown in (a) and (b).

Figure 3

Fermi surfaces of the noninteracting systems shown in Figs. 1 and 2. The arrows in the plot indicate the direction of the spin polarization in these bands, which is induced due to the Rashba spin-orbit interaction.

Figure 4

Conductivity ${\sigma }_{xx}$ (a) and magnetoelectric effect ${\mathrm{{\rm Y}}}_{xy}$ (b) for ${\alpha }_{ff}/t_f={\alpha }_{cf}/t_f=V/t_f=0.5$ and different interaction strengths and temperatures.

Figure 5

${\mathrm{{\rm Y}}}_{xy}/{\sigma }_{xx}$ for ${\alpha }_{ff}/t_f={\alpha }_{cf}/t_f=V/t_f=0.5$ for different interaction strengths and temperatures.

Figure 6

Momentum resolved spectral functions for $U/t_f=5$, ${\alpha }_{ff}/t_f={\alpha }_{cf}/t_f=V/t_f=0.5$, and different temperatures.

Figure 7

Momentum resolved ${\sigma }_{xx}^k$ and ${\mathrm{{\rm Y}}}_{yx}^k$ along the diagonal in the Brillouin zone for $U/t_f=5$, ${\alpha }_{ff}/t_f={\alpha }_{cf}/t_f=V/t_f=0.5$, and different temperatures.

Figure 8

Cuts of the momentum dependent density of states through the Brillouin zone at the Fermi energy. The color plot denotes the density of states at the fixed energy with a maximum intensity for yellow. The white arrows denote the calculated spin polarization. The parameters are ${\alpha }_{ff}/t_f=0.5{\alpha }_{cf}/t_f=0.5V/t_f=0.5$ and $U/t_f=5$. (a) $T/t_f=0.01$. (b) $T/t_f=0.15$. (c) $T/t_f=0.4$.

Figure 9

System with ${\alpha }_{ff}/t_f=0.5$, ${\alpha }_{cf}/t_f=0.5$, $V/t_f=0.5$, and $U/t_f=5$ at $T/t_f=1$ (left panels) and $T/t_f=0.005$ (right panels). The filling of the $c$-electron band is $n_c=0.6$. The $f$-electron band is half-filled. (a) Momentum-resolved spectral function for $T/t_f=1$. (b) Local density of states (DOS) for $T/t_f=1$. The black (red) lines correspond to the $c$ ($f$) electrons. (c) Momentum-resolved spectral function for $T/t_f=0.005$. (d) Local density of states (DOS) for $T/t_f=0.005$.

Figure 10

ME effect ${\mathrm{{\rm Y}}}_{yx}/{\sigma }_{xx}$ for ${\alpha }_{ff}/t_f=0.5$, ${\alpha }_{cf}/t_f=0.5$, $V/t_f=0.5$, and filling of the conduction electrons $n_c=0.6$.