A nontrivial crossover in topological Hall effect regimes

Area of Science:

• Condensed Matter Physics
• Spintronics
• Materials Science

Background:

• The topological Hall effect (THE) is crucial for understanding electron transport in magnetic materials with non-collinear spin textures.
• Magnetic skyrmions, as a prominent example of such textures, exhibit complex behaviors that require precise theoretical descriptions.
• Existing theories, like adiabatic Berry phase and perturbation theory, present apparent contradictions in explaining THE.

Purpose of the Study:

• To propose a novel theoretical framework for the topological Hall effect (THE) in systems featuring magnetic skyrmions.
• To resolve discrepancies between existing theoretical approaches to THE.
• To elucidate the transformation dynamics between the topological Hall effect and the spin Hall effect.

Main Methods:

• Exact analytical solution for electron scattering on magnetic skyrmions, considering arbitrary exchange interaction strength and skyrmion size.
• Comparative analysis of adiabatic Berry phase theory and perturbation theory for THE.
• Investigation of the transition from topological Hall effect to spin Hall effect.

Main Results:

• Existence of distinct regimes for the topological Hall effect (THE).
• Resolution of contradictions between adiabatic Berry phase and perturbation theories for THE.
• Demonstration of the transformation of topological charge Hall effect into spin Hall effect by varying exchange interaction or skyrmion size.
• Observation of oscillating charge and spin Hall currents during this transformation.

Conclusions:

• The developed theory accurately describes electron scattering in magnetic skyrmions.
• The transformation from THE to spin Hall effect, characterized by oscillating currents, serves as an experimental signature.
• This work provides a pathway to experimentally identify chirality-driven contributions to Hall response.