Photoinduced sign inversion of the anomalous Hall effect in EuO thin films

We report on the sign inversion of the anomalous Hall effect (AHE) in EuO thin films along with photoirradiation as well as a temperature scan across ∼25 K that is well below the Curie temperature ($T_{\mathrm{C}}\sim 80$ K). The former gives an enhancement of the mobile electron density ($n$) by more than 30%, but the latter gives a negligible modification of $n$ of only 3% with a significant enhancement in mobility. It is found, in addition to the universal scaling law between longitudinal conductivity (${\sigma }_{xx}$) and anomalous Hall conductivity (${\sigma }_{\mathrm{AH}}$) as $|{\sigma }_{\mathrm{AH}}|\propto {\sigma }_{xx}^{1.6}$, that there is a critical value of about 10${}^2$ S cm${}^{-1}$ in ${\sigma }_{xx}$ that gives a boundary in the sign inversion of ${\sigma }_{\mathrm{AH}}$. If $n$ solely governs the sign of ${\sigma }_{\mathrm{AH}}$, the phenomenon could be explained by a Fermi level shift across the singularity in the band structure. However, our band calculation shows that, within any realistic adjustment of band parameters, the sign inversion of AHE never occurs. Thus, we conclude that other mechanisms of AHE are necessary to account for the AHE of EuO.

Figure 1

(a) Temperature ($T$) dependence of resistivity (${\rho }_{xx}$) in the dark (green) and under illumination (orange) at $B$ = 0 T (solid curve) and 8 T (dotted curve). The box with dashed lines is the region magnified in Fig. 4. $T$ dependence of (b) carrier density ($n$) and (c) mobility (μ) below 60 K. Solid circles represent the data in the dark and open circles under illumination. The sign of the anomalous Hall conductivity (${\sigma }_{\mathrm{AH}}$), which will be discussed in Fig. 2, is classified by colors as blue and red symbols for negative and positive signs, respectively.

Figure 2

Magnetic field ($B$) dependence of nonordinary Hall resistivity (${\rho }_{xy}-R_{\mathrm{H}}B$) defined by Eq. (1) in the dark at (a) 30, (b) 25, and (c) 20 K. Reversible effects of illumination are shown by those at 30 K (d) under illumination and (e) in the dark after switching off the illumination. The illumination intensity was $5.5\times {10}^{-3}$ W/cm${}^2$ in this study. The inset of (a) shows the $B$ dependence of Hall resistivity (${\rho }_{xy}$) at 30 K. The black dashed line in the inset displays a slope of the ordinary Hall effect ($R_{\mathrm{H}}B$). The blue and red regions correspond to negative and positive signs of ${\sigma }_{\mathrm{AH}}$, respectively. The arrows indicate the field scan direction.

Figure 3

(a) Energy band calculation of EuO including the on-site Coulomb interaction ($U$ = 7 eV) and the spin-orbit interaction. The color code indicates the $z$-component projection of spins. (b) Anomalous Hall conductivity as a function of carrier density. Squares are results calculated from the band structure of (a) and the range of the carrier density in this experiment is colored as yellow.

Figure 4

(a) $T$ dependence of ${\rho }_{xx}$ below 60 K at $B$ = 0 T. Solid and open circles are the data taken in the dark and under illumination, respectively. Those in blue and red, respectively, represent the negative and positive signs of the anomalous Hall conductivity (${\sigma }_{\mathrm{AH}}$). The dashed curves are guides to the eyes. (b) The data are plotted in the relationship between the longitudinal conductivity at $B$ = 0 T (${\sigma }_{xx}$) and the absolute value of the anomalous Hall conductivity at 9 T ($|{\sigma }_{\mathrm{AH}}|$). Triangles represent the data at 30 K under illumination with a variety of light intensities spanning two orders of magnitude. The dashed line indicates $|{\sigma }_{\mathrm{AH}}|\propto {\sigma }_{xx}^{1.6}$. The green curve is a guide to the eyes.