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When non-collinear spin textures are driven by current, an emergent electric field arises due to the emergent electromagnetic induction. So far, this phenomenon has been reported in several materials, manifesting the current-nonlinear imaginary part of the complex impedance. Recently, Furuta et al. proposed a time-varying temperature increase due to Joule heating as an alternative explanation for these current-nonlinear complex impedances [arXiv:2407.00309v1]. In this study, we re-examine the nonlinear complex impedance in GdRuAl12 and YMn6Sn6, specifically addressing the impact of the time-varying temperature increase. Our findings reveal that the magnetic-field angle, frequency, and temperature dependence of nonlinear complex impedances in these two materials cannot be explained by the time-varying temperature increase. Instead, these dependencies of the imaginary part of the nonlinear impedance are consistent with the expected behaviour in the theory of emergent electromagnetic induction. Moreover, we observe a significant real part of the nonlinear complex impedance, likely resulting from the dissipation associated with the current-driven motion of helices and domain walls. Our findings highlight the diverse current-nonlinear transport phenomena of spin dynamical origin in helimagnets., Comment: Comment on arXiv:2407.00309

Ac current-driven motions of spiral spin textures can give rise to emergent electric fields acting on conduction electrons. This in turn leads to the emergent electromagnetic induction effect which may realize quantum inductor elements of micrometer size. ${\rm YMn}_{6}{\rm Sn}_{6}$ is a helimagnet with a short helical period (2-3 nm) that shows this type of emergent inductance beyond room temperature. To identify the optimized materials conditions for ${\rm YMn}_{6}{\rm Sn}_{6}$-type room-temperature emergent inductors, we have investigated emergent electromagnetic inductance (EEMI) as the magnetism is modified through systematic partial substitution of Y by Tb. By small angle neutron scattering and inductance measurements, we have revealed that the pinning effect on the spin-helix translational mode by Tb doping selectively and largely suppresses the negative component of EEMI, while sustaining the positive inductance arising from the spin tilting mode. We also find that in addition to the spin helix, even the spin-collinear antiferromagnetic structure can host the positive EEMI due to thermally enhanced spin fluctuations. The present study highlights the facile control of both the magnitude and sign of EEMI beyond room temperature, and thus suggests a route to expand the range of emergent inductor candidate materials., Comment: 20 pages, 13 figures

Nonreciprocal resistance, depending on both directions of current ($j$) and magnetic-field ($H$) or magnetization ($M$), is generally expected to emerge in a chiral conductor, and be maximized for $j$ $\parallel$ $H$($M$). This phenomenon, electrical magnetochiral effect (eMChE), is empirically known to increase with $H$ in a paramagnetic or fully ferromagnetic state on chiral lattice or to depend on fluctuation properties of a helimagnetic state. We report here the eMChE over a wide temperature range in the chiral-lattice magnet MnGe in which the spin hedgehog lattice (HL) forms with the triple spin-helix modulation vectors. The magnitude of nonreciprocal resistivity is sharply enhanced in the course of the field-induced structural transition of HL from cubic to rhombohedral form. This is attributed to the enhanced asymmetric electron scatterings by vector spin chirality in association with the large thermal fluctuations of spin hedgehogs., Comment: 8 pages, 7 figures

Emergent electromagnetic induction based on electrodynamics of noncollinear spin states may enable dramatic miniaturization of inductor elements widely used in electric circuits, yet many issues are to be solved toward application. One such problem is how to increase working temperature. We report the large emergent electromagnetic induction achieved around and above room temperature based on short-period ($\leq$ 3 nm) spin-spiral states of a metallic helimagnet ${\rm YMn}_{6}{\rm Sn}_{6}$. The observed inductance value $L$ and its sign are observed to vary to a large extent, depending not only on the spin helix structure controlled by temperature and magnetic field but also on the current density. The present finding on room-temperature operation and possible sign control of $L$ may provide a new step toward realizing microscale quantum inductors., Comment: 19 pages, 6 figures