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

A multiferroic state with both electric polarization ($P$) and magnetization ($M$) shows the inherently strong $P$-$M$ coupling, when $P$ is induced by cycloidal (Néel-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 $T\sim P\times M\sim (\widehat{q}\times {\chi }_v)\times M$ as well as with the magneto-chirality ${\chi }_v\times M$, where $\widehat{q}$ 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.