Control of the Anomalous Hall Effect by Doping in ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$ Thin Films

The anomalous Hall effect (AHE) has been studied for epitaxial films of ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3$, in which band filling can be controlled by doping $x$ without undesired changes in magnetization. This system has a simple band structure near the conduction band bottom, which makes it possible to design the AHE. As expected, the anomalous Hall resistivity shows a nonmonotonic change as a function of the carrier density accompanied with the sign reversal around $n=2.4\times {10}^{20}{\mathrm{cm}}^{-3}$. This opens a possibility to control the AHE by devising the material, structure, and doping level.

Figure 1

Band structure of the Luttinger-type effective model (left-hand panel and middle panel). The right-hand panel shows the Hall conductivity ${\sigma }_{xy}$ and the longitudinal (ordinary) conductivity (${\sigma }_{xx}$) as a function of the Fermi level. Some reference values of the carrier density $n_e$ are indicated on the right vertical axis. The parameters are taken as $t=300\mathrm{meV}$, $\delta t=-100\mathrm{meV}$, ${\Delta }_{\mathrm{Zeeman}}=20\mathrm{meV}$, $V_{\mathrm{tetra}}=60\mathrm{meV}$, and $a=4\AA$. The energy broadening is introduced by the constant lifetime $\tau$ as $1/\tau =10\mathrm{meV}$.

Figure 2

Temperature dependence of magnetization at 500 Oe for a ${\mathrm{EuTiO}}_3/\mathrm{STO}(001)$ film. Inset: Magnetization curves for the film at 2 K. The magnetic field is applied parallel to in-plane [100] (red line) and out-of-plane [001] (blue) axes.

Figure 3

Temperature dependence of (a) resistivity and (b) carrier density for ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3/\mathrm{LSAT}(001)$ films from $x=0.01$ to 0.06. Inset of (a) shows the data for a pristine ${\mathrm{EuTiO}}_3/\mathrm{LSAT}(001)$ film. (c) Temperature dependence of resistivity for a ${\mathrm{Eu}}_{0.94}{\mathrm{La}}_{0.06}{\mathrm{TiO}}_3/\mathrm{LSAT}(001)$ film under 0 and 7 T below 80 K. The arrow indicates a magnetic transition at 8 K.

Figure 4

Carrier density dependence of anomalous Hall resistivity (${\rho }_{\mathrm{AH}}$) for ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3/\mathrm{LSAT}(001)$ films at 2 K. The number for each data point is the nominal electron concentration $x$ and the dotted curve is a guide to the eyes. The inset shows the magnetic field dependence of Hall resistivity for ${\mathrm{Eu}}_{1-x}{\mathrm{La}}_x{\mathrm{TiO}}_3/\mathrm{LSAT}(001)$ films with $x=0.03$ and $x=0.04$ at 2 K.