Current Control of Spin Helicity and Nonreciprocal Charge Transport in a Multiferroic Conductor

A multiferroic state with both electronic polarity (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 the 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, the current control of the multiferroics is reported in a helimagnetic metal YMn₆Sn₆ and its detection through nonreciprocal resistivity (NRR). The underlying concept is the coupling of the current with the toroidal moment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>T</mml:mi> <mml:mo>∼</mml:mo> <mml:mi>P</mml:mi> <mml:mo>×</mml:mo> <mml:mrow></mml:mrow> <mml:mi>M</mml:mi> <mml:mo>∼</mml:mo> <mml:mo>(</mml:mo> <mml:mover><mml:mi>q</mml:mi> <mml:mo>̂</mml:mo></mml:mover> <mml:mo>×</mml:mo> <mml:mrow></mml:mrow> <mml:msub><mml:mi>χ</mml:mi> <mml:mi>v</mml:mi></mml:msub> <mml:mo>)</mml:mo> <mml:mo>×</mml:mo> <mml:mrow></mml:mrow> <mml:mi>M</mml:mi></mml:mrow> <mml:annotation>$\bm{T}\sim \bm{P}\ensuremath{\times{}}\bm{M}\sim (\widehat{\bm{q}}\ensuremath{\times{}}{\bm{\chi}}_{v})\ensuremath{\times{}}\bm{M}$</mml:annotation></mml:semantics> </mml:math> as well as with the magneto-chirality χ_v · M, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mspace></mml:mspace> <mml:mover><mml:mi>q</mml:mi> <mml:mo>̂</mml:mo></mml:mover> </mml:mrow> <mml:annotation>$\hspace*{0.28em}\widehat{\bm{q}}$</mml:annotation></mml:semantics> </mml:math> and χ_v are the unit modulation wave vector and the vector spin chirality, respectively. An enhancement of NRR is furthermore observed by the spin-cluster scattering via χ_v and its fluctuation. These findings may pave the way to an exploration of multiferroic conductors and the application of the spin-helicity degree of freedom as a state variable.