Angular dependence of hump-shape Hall Effects for distinguishing between Karplus-Luttinger and Geometrical Origins

TL;DR

This paper clarifies the origin of hump-shaped Hall effects in magnetic heterostructures by analyzing their angular dependence, distinguishing between Karplus-Luttinger and Geometrical/Topological mechanisms through divergence exponents.

Contribution

It introduces a method using divergence exponents from Hall measurements to differentiate between two competing interpretations of hump-shaped Hall effects.

Findings

Divergence exponents vary with magnetic field rotation, revealing different sensitivities.

Higher uniaxial anisotropy is associated with Karplus-Luttinger effects.

A unified curve relates divergence exponent to collinear quality factor across materials.

Abstract

Among the vast magnetic heterostructures explored in Condensed Matter Physics, two contrasting interpretations of the hump-shaped Hall Effects remain ambiguous and debated, namely, the overlap of two opposite-signed Karplus-Luttinger Hall loops associated with inhomogeneous collinear domains with perpendicular anisotropy, or the Geometrical/Topological Hall Effect emanated from hexagnal close-packed lattice of Skyrmion ground state with smoothly varying non-collinear moments. Their similarity in topology implies difficulty in discrimination via magnetic imaging. Here, this ambiguity is overcome and clarified by the divergence exponent of hump peak fields extracted from Hall measurements with magnetic field rotation on several heterostructures. Their difference in sensitivity to in-plane fields reveals that the former mechanism involves higher uniaxial anisotropy than the latter, departing from the Skyrmion ground state regime by the Ginzburg-Landau framework of triple-q spin-wave superposition. Numerous material systems can be summarized into a single curve of divergence exponent versus the collinear quality factor, bridging the crossover of the two mentioned mechanisms.