Spin-current order induced by a magnetic field

We consider a 2D itinerant fermion system on a hexagonal lattice, with the Fermi surface consisting of well separated electron and hole pockets of similar sizes, centered at high-symmetry-points in the Brillouin zone: one hole pocket at the origin and two electron pockets at ± K. We perform RG analysis to select between superconductivity, charge and spin orders. Over some range of intra- and inter-pocket interactions, magnetism wins. We show that the magnetic order is either 120° spin-density-wave, or collinear order with magnetization on two-thirds of lattice sites, and no magnetization on another one-third. We further show that an application of a Zeeman field does not give rise to canting of SDW spin configuration, but rather triggers spin-current order. We discuss the structure of spin-current state and experimental implications of such an order.