Curvature-induced nonlinear anomalous Hall effect in thin magnetic shells

TL;DR

This paper demonstrates that curvature in thin magnetic shells can induce nonlinear anomalous Hall effects by manipulating the quantum geometric tensor components, enabling new control over nonlinear transport properties.

Contribution

It introduces a method to engineer and probe the quantum metric and Berry curvature in centrosymmetric ferromagnets through geometric bending and strain gradients.

Findings

Curvature induces strain gradients that break inversion symmetry and activate orbital Rashba coupling.

Nonlinear anomalous Hall effect is maximized when magnetization aligns with the electric field.

Breaking rotational symmetry reveals an additional effect governed by the Berry curvature dipole.

Abstract

Optoelectronic and nonlinear transport experiments probe the quantum geometric tensor of Bloch states, whose real and imaginary components -- the quantum metric and the Berry curvature -- are typically constrained by symmetry. Here, we show that geometric bending provides a route to engineer such responses in centrosymmetric ferromagnets. Curvature-induced strain gradients across the shell thickness break inversion symmetry and activate an orbital Rashba coupling. In the presence of in-plane magnetization and spin-orbit coupling, this generates spin textures with a nontrivial quantum geometry, leading to an intrinsic nonlinear anomalous Hall effect (NAHE) governed by the quantum metric and maximized when the magnetization aligns with the applied electric field. When geometric deformations further break twofold rotational symmetry around the out-of-plane axis, an additional NAHE emerges, maximal for magnetization perpendicular to the driving electric field and governed by the Berry curvature dipole, thus giving access to the imaginary component of the quantum geometric tensor. These results establish curved ferromagnetic shells as a platform for engineering anisotropic nonlinear transport and for selectively probing both components of the quantum geometric tensor.