Berry curvature induced anomalous Hall conductivity in the magnetic topological oxide double perovskite ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$

Oxide materials exhibit several structural, magnetic, and electronic properties. Their stability under ambient conditions, easy synthesis, and high transition temperatures provide such systems with an ideal ground for realizing topological properties and real-life technological applications. However, experimental evidence of topological states in oxide materials is rare. In this paper, we have synthesized single crystals of oxide double perovskite ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ and revealed its topological nature by investigating its structural, magnetic, and electronic properties. We observed that the system crystallized in the cubic space group $Fm\overline{3}m$, which is a half-metallic ferromagnet. Transport measurements show an anomalous Hall effect (AHE), and it is evident that the Hall contribution originates from the Berry curvature. Assuming a shift of the Fermi energy toward the conduction band, the contribution of the AHE is enhanced owing to the presence of a gapped nodal line. This paper can be used to explore and realize the topological properties of bulk oxide systems.

Figure 1

Powder x-ray diffraction pattern $\left({\mathrm{Y}}_{\mathrm{obs}}\right)$ obtained at 300 K is shown along with the calculated pattern $\left({\mathrm{Y}}_{\mathrm{cal}}\right)$ obtained by Rietveld analysis using space group $Fm\overline{3}m$. The difference pattern and the Bragg positions are also shown. No sign of any secondary phase is observed.

Figure 2

Isothermal magnetization at various temperatures with magnetic field along (a) $a$ axis and (b) $c$ axis. Inset of (b) shows the magnified hysteresis curve at 2 K.

Figure 3

(a) Temperature as a function of resistivity. (b) Variation of longitudinal resistivity ${\rho }_{xx}$, (c) Hall resistivity ${\rho }_{yx}$, and (c) Hall conductivity ${\sigma }_{xy}$ with magnetic field at several temperatures.

Figure 4

Temperature dependence of carrier concentration obtained from the ordinary Hall coefficient $R_{\mathrm{H}}$ at different temperatures.

Figure 5

Variation of the anomalous Hall conductivity (AHC) as a function of the temperature until 50 K. The extrinsic part of the AHC (${\sigma }_{xy}^{\mathrm{sk}}$) originated from skew scattering and intrinsic part of AHC (${\sigma }_{xy}^{\mathrm{int}}$) resulting from Berry phase and side jump are separately shown here.

Figure 6

Spin-polarized density of states, projected onto Fe $d$ (blue line), Mo $d$, (cyan line), and O $p$ (orange line) states.

Figure 7

(a) (left) Band structure of ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$ magnetic ground state considering the magnetization $M\parallel \left(001\right)$. (right) Computed intrinsic anomalous Hall conductivity (AHC) contribution. The green line marks the peak in the AHC at $E=259$ meV. (b) Three-dimensional (3D) band structure considering the two bands that form the nodal line in the $k_x-k_y$ and (c) $k_y-k_z$ planes. $M$ is the direction of the fully polarized magnetic moments with spin-orbit coupling (SOC). The insets show a cut in the respective planes, showing the (b) closed and (c) gaped nodal lines, depending on the alignment of the magnetic moments with the mirror planes [ $M\parallel \left(001\right)$].

Figure 8

(a) Bandgap of the two bands forming the nodal line in the $k_x=0$ plane with magnetization $M\parallel \left(001\right)$. (b) Berry curvature in the $k_x=0$ plane with $M\parallel \left(001\right)$.