Surface monolayers and magnetic field

Abstract: We study theoretically the magnetic properties of the surface monolayers with the antiferromagnetic (AF) and ferromagnetic (FM) exchange interactions where the Dzyaloshinskii-Moriya interaction (DMI) is a result of the mirror symmetry breaking. To study the DMI helices in magnetic field a method is proposed. In zero field the DMI gives rise a cycloid in both AF and FM cases. The cycloid orientation is determined by the DMI induced in-plane anisotropy with the symmetry of the layer lattice. As a result we have one, two and three chiral domains in the rectangular, square and triangular lattices respectively. The magnetic structure of the $M n/W(1 1 0)$ monolayer is explained. The out-of-plane anisotropy may restore a collinear magnetic order. The chiral domains are rotated by the in-plane field. In some field directions the spin flops are predicted. In the out-of-plane field the chirality follows the field direction. The length of the cycloid wave-vector decreases. In the perpendicular field there is the spin flop to the corresponding collinear state. A possibility of the layer electric polarization is discussed.