Magnetoelectric control of spin helicity and nonreciprocal charge transport in a multiferroic metal

Abstract: A multiferroic state with both electric polarization ($P$) and magnetization ($M$) shows the inherently strong $P$-$M$ coupling, when $P$ is induced by cycloidal (N\'eel-wall like) spin modulation. The sign of $P$ is determined by clockwise or counterclockwise rotation of spin, termed the spin helicity. Such a multiferroic state is not limited to magnetic insulators but can be broadly observed in conductors. Here, we report the current-induced magnetoelectric control of the multiferroics in a helimagnetic metal YMn$_6$Sn$_6$ and its detection through nonreciprocal resistivity (NRR). The underlying concept is the coupling of the current with the toroidal moment $T \sim P \times M \sim (\hat{q} \times \chi_v) \times M$ as well as with the magneto-chirality $\chi_v \times M$, where $\hat{q}$ and $\chi_v$ being the unit modulation wave vector and the vector spin chirality, respectively. We furthermore observe an enhancement of NRR by the spin-cluster scattering via $\chi_v$ and its fluctuation. These findings may pave a way to exploration of multiferroic conductors and application of the spin-helicity degree of freedom as a state-variable.