We study in this paper magnetic properties of a system of quantum Heisenberg spins interacting with each other via a ferromagnetic exchange interaction J and an in-plane Dzyaloshinskii-Moriya interaction D. The non-collinear ground state due to the competition between J and D is determined. We employ a self-consistent Greenfunction theory to calculate the spin-wave spectrum and the layer magnetizations at finite T in two and three dimensions as well as in a thin film with surface effects. Analytical details and the validity of the method are shown and discussed.
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