Anisotropic anomalous Hall effect in distorted kagome GdTi3Bi4

Technical Summary: Anisotropic Anomalous Hall Effect in Distorted Kagome GdTi3Bi4

Problem Statement
The intrinsic anomalous Hall effect (AHE) in magnetic topological materials is typically governed by the interplay of broken time-reversal symmetry (TRS), spin-orbit coupling (SOC), and band topology. While kagome lattices are known hosts for Dirac cones, flat bands, and van Hove singularities that generate significant Berry curvature (BC), the specific mechanism by which magnetic order in rare-earth kagome systems influences these topological features remains complex. In the titanium-based bilayer kagome metal series $LnTi_3Bi_4$, the coupling between the localized moments of the rare-earth ($Ln$) chain and the topological electronic states of the Ti-kagome layer is not fully understood. Specifically, there is a lack of experimental and theoretical clarity regarding how the orientation of magnetization relative to the crystal axes affects the AHE, particularly in systems where magnetization behavior appears similar across different directions.

Methodology
The study employs a combined experimental and theoretical approach using high-quality single crystals of GdTi3Bi4 synthesized via the Bi self-flux method.

• Experimental: The authors conducted axis-dependent magneto-electrical transport measurements on single crystals. Key measurements included isothermal magnetization, temperature-dependent resistivity, and Hall resistivity ($\rho_{xy}$) under magnetic fields applied along the $a$, $b$, and $c$ crystallographic axes (defined as $x$, $y$, and $z$ respectively) at temperatures ranging from 2 K to 30 K. The anomalous Hall conductivity (AHC, $\sigma_{xy}^A$) was extracted by separating ordinary and anomalous contributions and analyzing the scaling behavior of $\rho_{xy}^A$ versus resistivity ($\rho_{xx}$).
• Theoretical: First-principles spin-polarized density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP) with PBE-GGA functionals and a DFT+U scheme ($U_{eff} = 6$ eV for Gd-4f). The study modeled fully relativistic, saturated ferromagnetic (FM) configurations with magnetization constrained along the $a$-axis ($M \parallel x$) and $c$-axis ($M \parallel z$) to isolate the effects of the spin-quantization axis on the band structure and Berry curvature.

Key Results

1. Crystal and Magnetic Structure: GdTi3Bi4 crystallizes in an orthorhombic structure ($Fmmm$) featuring Ti-based kagome layers perpendicular to the $c$-axis and zigzag Gd chains along the $a$-axis. The material orders antiferromagnetically below $T_N \approx 14.7$ K. Magnetization measurements reveal similar metamagnetic behaviors for fields applied along both the $a$ and $c$ axes, including spin-flip transitions and a distinct 1/3 magnetization plateau, indicating comparable magnetic responses in both orientations.
2. Anisotropic Anomalous Hall Effect: Despite the similar magnetization curves, the AHE exhibits extreme anisotropy.
   • For $\mu_0H \parallel c$ ($z$-axis), a large anomalous Hall conductivity of 410 $\Omega^{-1}$ cm$^{-1}$ is observed at 2 K.
   • For $\mu_0H \parallel a$ ($x$-axis), the anomalous Hall effect is completely absent, with Hall resistivity showing only linear (ordinary) behavior.
3. Scattering Mechanisms: Analysis of the scaling relation between anomalous Hall resistivity and longitudinal resistivity ($\rho_{xy}^A \propto \rho_{xx}$ vs. $\rho_{xx}^2$) confirms that the AHE in GdTi3Bi4 lies within the intrinsic regime. The dominant contributions arise from the Berry curvature and side-jump scattering, rather than skew scattering.
4. Theoretical Origin: DFT calculations reveal that the anisotropy stems from the orientation-dependent mixing of Ti $t_{2g}$ orbitals mediated by SOC.
   • When $M \parallel c$, SOC-gapped anticrossings within the Ti $t_{2g}$ manifold (specifically involving $d_{xz}$ and $d_{yz}$ orbitals) occur near the Fermi energy ($E_F$), creating large "hot spots" of Berry curvature that integrate to a high net value.
   • When $M \parallel a$, the active SOC matrix elements couple different orbitals ($d_{xz}$ to $d_{xy}$, etc.), but the relevant band crossings are shifted away from $E_F$. Consequently, the Berry curvature contributions cancel out significantly, resulting in a negligible net AHC.

Significance and Claims
The paper establishes GdTi3Bi4 as a platform for investigating "directional AHE," a phenomenon where the magnitude of the effect is dictated by the magnetization direction relative to the crystal lattice, even when the magnetic moment magnitude is similar. The authors claim that the study elucidates the intricate coupling between magnetic and electronic structures in kagome systems. Specifically, they demonstrate that while the Gd-4f sublattice is responsible for breaking TRS and setting the magnetization direction, the SOC in the Ti-derived bands acts as the switch that converts this magnetic orientation into specific Berry curvature patterns. This work highlights that the interplay between the 1D zigzag magnetic chains and the 2D kagome lattice can produce orientation-selective topological transport properties, offering new insights into how magnetic textures control quantum phenomena in topological materials.