Emergent electric field from magnetic resonances in a one-dimensional chiral magnet

The emergent electric field (EEF) is a fictitious electric field acting on conduction electrons through the Berry phase mechanism. The EEF is generated by the dynamics of noncollinear spin configurations, and it becomes nonzero even in one dimension. Although the EEF has been studied for several one-dimensional chiral magnets, most of the theoretical studies were performed in limited situations with respect to the strength and direction of the magnetic fields. Furthermore, the effect of the edges of the system has not been clarified, whereas it can be crucial in nanoscale and microscale samples. Here, we perform a comprehensive theoretical study on the momentum-frequency profile of the EEF in a one-dimensional chiral magnet using the Landau-Lifshitz-Gilbert equation while changing the strength and direction of the static and ac magnetic fields for both bulk and finite-size chains with edges. From the bulk calculations under the periodic boundary condition, we find that the EEF is resonantly enhanced at the magnetic resonance frequencies; interestingly, the higher resonance modes are more clearly visible in the frequency profile of the EEF response than in the magnetic one. Furthermore, we show that the EEF is amplified along with the solitonic feature of the spin texture introduced by the static magnetic field perpendicular to the chiral axis. We also show that the static magnetic field parallel to the chiral axis drives the EEF in the field direction, in addition to much slower drift motion in the opposite direction associated with the Archimedean screw dynamics, suggesting a dc electric current generation. For the finite-size chains under the open boundary condition, we find additional resonance modes localized at the edges of the system that are also more clearly visible in the EEF response than the magnetic one. Moreover, we show that a substantial EEF is generated from the edges even in the forced-ferromagnetic phase, although it is absent in the bulk case. Our results reveal that the emergent electric phenomena in one-dimensional chiral magnets can be tuned by the magnetic field and the sample size, and they provide not only a good probe of the magnetic resonances but also a platform for the applications to electronic devices.