Electric-field-induced modulation of the anomalous Hall effect in a heterostructured itinerant ferromagnet ${\mathrm{SrRuO}}_3$

We fabricated electric-field-effect transistor structures with a channel layer of an itinerant ferromagnet ${\mathrm{SrRuO}}_3$ (SRO) heterostructured with a cap layer of ${\mathrm{BaTiO}}_3$ and investigated the electric field effects on the anomalous Hall effect (AHE) in SRO. We show that by applying positive and negative gate voltages ($V_{\mathrm{G}}$), the anomalous Hall conductivity in the heterostructured SRO increases and decreases, respectively, regardless of its sign, while no change in the magnetic easy axis direction is observed. The results indicate that the observed $V_{\mathrm{G}}$-induced modulations of the AHE do not simply originate from changes in the magnetization and magnetic anisotropy and indicate that $V_{\mathrm{G}}$-induced changes in an integral of the Berry curvature over the filled electronic states play a key role in the observed electric field effects on the AHE in SRO. We also found that $V_{\mathrm{G}}$-induced modulations on the AHE are negligibly small for transistor structures with a SRO channel having no BTO cap layer. This implies that the cap-layer-induced modifications in the Ru-O-Ru bond angles in the channel affect the Berry phase, enhancing the electric field effects on the AHE in SRO.

Figure 1

(a) X-ray $2\theta /\theta$ profiles of the ${\mathrm{BaTiO}}_3$(BTO)/${\mathrm{SrRuO}}_3$(SRO)/${\mathrm{GdScO}}_3$(GSO) and SRO/GSO heterostructures. (b) Optical image and schematic of our fabricated field-effect transistor structures. (c) Temperature dependence of the electrical resistivity ${\rho }_{xx}$ for the BTO/SRO and SRO channels in the transistor structures. The data were recorded without the application of $V_{\mathrm{G}}$ ($V_{\mathrm{G}}=0$ V). The ferromagnetic transition temperatures ($T_{\mathrm{C}}$) indicated by arrows in the graph (135 K for the BTO/SRO channel and 142 K for the SRO channel) were determined from the temperature derivative of each ${\rho }_{xx}\text{−}T$ curve. (d) Magnetic field dependence of the anomalous Hall resistivity ${\rho }_{\mathrm{AHE}}$ for the BTO/SRO channel under $V_{\mathrm{G}}=0$. The data were recorded at 128.0 K (red), 126.4 K (green), and 125.0 K (blue).

Figure 2

Magnetic field dependence of the electrical resistivity ${\rho }_{xx}$ for the transistor structures with the (a) BTO/SRO and (b) SRO channels under various $V_{\mathrm{G}}$. The data were recorded at 128.0 K and 125.0 K for the transistor structures with the BTO/SRO and SRO channels, respectively.

Figure 3

Magnetic field dependence of ${\rho }_{\mathrm{AHE}}$ of the (a)–(c) BTO/SRO and (d)–(e) SRO channels under various $V_{\mathrm{G}}$. The data were recorded at temperatures (a), (d) above; (b), (e) at; and (c), (f) below $T_{\mathrm{S}}$. $T_{\mathrm{S}}$ is defined as the temperature at which ${\rho }_{\mathrm{AHE}}$ becomes zero (or negligibly small), and is 126.4 K for the BTO/SRO channel and 123.2 K for the SRO channel. In (b), the inset shows the vertically expanded view of the curves in the curves on Fig. 3.

Figure 4

$V_{\mathrm{G}}$ dependence of the anomalous Hall conductivity ${\sigma }_{\mathrm{AHE}}$ ($\sim {\rho }_{\mathrm{AHE}}/{\rho }_{xx}^2$) for the BTO/SRO channel (a) above, (b) at, and (c) below $T_{\mathrm{S}}$.

Figure 5

Magnetic field angle ${\theta }_{\mathrm{H}}$ dependence of the Hall resistivity ${\rho }_{xy}$ for the BTO/SRO channel. (a) Measurement configurations. (b) ${\theta }_{\mathrm{H}}$ dependence of ${\rho }_{xy}$ under $V_{\mathrm{G}}=0$ V at 128.0 K (red) and 125.0 K (blue). (c), (d) ${\theta }_{\mathrm{H}}$ dependence of ${\rho }_{xy}$ under $V_{\mathrm{G}}=+10$ V (red), 0 V (green), and $-10$ V (blue). The curves were recorded at (c) 128.0 K and (d) 125.0 K. In (b), (c), and (d), the arrows indicate the magnetic field rotation direction (clockwise and counterclockwise).