Abstract
This thesis investigates nonlinear Hall phenomena driven by Berry curvature multipoles in topological quantum magnets, moving beyond the traditional paradigm that requires a net magnetization or an external magnetic field. We demonstrate that Berry curvature quadrupoles, second momentum-space derivatives of the Berry curvature, generate distinct third-order transverse responses in compensated magnetic systems where linear and second-order effects are symmetry-forbidden.
First, we report the room-temperature discovery of the anomalous in-plane Hall effect in the Weyl ferromagnet Fe3Sn. A small out-of-plane spin canting breaks a mirror symmetry, allowing an in-plane magnetic field to induce a transverse voltage with a cos ϕB angular dependence. Density functional theory identifies Weyl points near the Fermi energy as the microscopic source of the Berry curvature. The signal strength increases by nearly 40% when F\mathrm{\operatorname{e}}_\mathrm{3}Sn is coupled to a ferromagnetic CoFeB layer through a heterostructure design.
Second, we provide direct evidence for a Berry curvature quadrupole in the antiferromagnetic Kagome metal FeSn. While the second-order Hall signals remain absent, a robust first and third-order anomalous Hall effect emerges. Scaling analysis confirms that this response originates intrinsically from the Berry curvature quadrupole, with skew scattering playing only a minor role at room temperature.
Third, we explore the g-wave altermagnet CrSb, where inversion symmetry forbids both linear and second-order Hall effects. We observe a strong, anisotropic third-order Hall response only when the current flows along the crystallographic ‘XZ’-direction, consistent with symmetry predictions. Using this third-order nonlinearity, we demonstrate a room-temperature multiple-wave-mixing device that generates sum, difference, and full-wave mixing frequencies from two input signals.
These findings establish Berry curvature multipoles as a powerful framework for nonlinear transport in compensated magnets, opening routes toward altermagnetic frequency converters, terahertz electronics, and high-speed signal processing.