Magnetic pattern formation on the nanoscale due to relativistic exchange interactions

We present a multiscale study of the formation of magnetic patterns in Mn monolayers deposited on W(0 0 1) and W(1 1 0) surfaces. We derive the parameters of an extended classical Heisenberg Hamiltonian from relativistic spin-polarized first principle calculations. By using these parameters we perform Monte Carlo simulations to explore the low-temperature spin structures. We find that the antisymmetric Dzyaloshinskii-Moriya interactions induce spin-spirals propagating along an in-plane axis with a wavelength of about 2.2 and 7.2 nm, respectively.