Nonequilibrium charge density wave ordering from anomalous velocity in itinerant helical magnets

The Karplus-Luttinger anomalous velocity is shown to lead to electric-field-induced charge accumulation in nearly ferromagnetic noncollinear magnets with itinerant electrons, like $MnSi$. For helical magnetic ordering, the balance between this accumulation and the Coulomb interaction leads to a nonequilibrium charge density wave state with the period of the helix, even when such accumulation is forbidden by an approximate gauge-like symmetry in the absence of electric field. We compute the strength of such charge accumulation as an example of how unexpected many-electron physics is induced by the inclusion of the one-electron Karplus-Luttinger term whenever the local exchange field felt by conduction electrons does not satisfy the current-free Maxwell equations.