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 Mn/W(110) 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.
@article{arxiv.1812.07892,
title = {Surface monolayers and magnetic field},
author = {S. V. Maleyev},
journal= {arXiv preprint arXiv:1812.07892},
year = {2019}
}