Transport phenomena, especially electron transport, are fundamental processes that are widely studied due to their practical applications in daily life. The Hall effect, for instance, is commonly applied in electronic devices to detect magnetic fields.

The topological Hall effect is another such phenomenon, that occurs when electrons are coupled to a non-coplanar magnetic texture with non-zero spin chirality, such as those found in magnetic skyrmions. Magnetic skyrmions are of great interest due to their possible applications in low-power, ultra-high density magnetic storage devices.

Theoretically, so far, the topological Hall effect has been studied in the strong- and weak-coupling regimes separately, with the former in terms of the Berry phase, while the latter, which cannot be described by the Berry phase as adiabaticity and locality fail, is understood through the perturbation theory. However, a unified picture of the topological Hall effect remains elusive.

In a study published in the Journal of the Physical Society of Japan, researchers developed a unified theoretical description for the topological Hall effect covering the entire region from strong- to weak-coupling. They utilized the spin gauge field, considering not only the adiabatic, Berry phase component, but also the non-adiabatic components extending beyond it.

Their theory reveals that, while the adiabatic component is important for the strong coupling regime, it is completely canceled in the weak-coupling regime, where the topological Hall effect is governed by non-adiabatic components.

Furthermore, the researchers identified new weak-coupling regions that cannot be accessed by a simple perturbation theory. There, spin precession and spin diffusion play key roles. The new theory also helped understand experimental observations of the topological Hall effect in a broader variety of materials, including correlated oxides.

In summary, this new theory significantly broadens our understanding of the topological Hall effect beyond the Berry phase theory. Considering this theoretical development, this paper was honored with the Outstanding Paper Award of the Physical Society of Japan.

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