Isotropic Heisenberg exchange naturally appears as the main interaction in magnetism, usually favouring long-range spin-ordered phases. The anisotropic Dzyaloshinskii-Moriya interaction arises from relativistic corrections and is a priori much weaker
, even though it may sufficiently compete with the isotropic one to yield new spin textures. Here, we challenge this well-established paradigm, and propose to explore a Heisenberg-exchange-free magnetic world. There, the Dzyaloshinskii-Moriya interaction induces magnetic frustration in two dimensions, from which the competition with an external magnetic field results in a new mechanism producing skyrmions of nanoscale size. The isolated nanoskyrmion can already be stabilized in a few-atom cluster, and may then be used as LEGO block to build a large magnetic mosaic. The realization of such topological spin nanotextures in sp- and p-electron compounds or in ultracold atomic gases would open a new route toward robust and compact magnetic memories.
We present theoretical studies of the intrinsic spin orbit torque (SOT) in a single domain ferromagnetic layer with Rashba spin-orbit coupling (SOC) using the non-equilibrium Greens function formalism for a model Hamiltonian. We find that, to the fir
st order in SOC, the intrinsic SOT has only the field-like torque symmetry and can be interpreted as the longitudinal spin current induced by the charge current and Rashba field. We analyze the results in terms of the material related parameters of the electronic structure, such as band filling, band width, exchange splitting, as well as the Rashba SOC strength. On the basis of these numerical and analytical results, we discuss the magnitude and sign of SOT. Our results show that the different sign of SOT in identical ferromagnetic layers with different supporting layers, e.g. Co/Pt and Co/Ta, could be attributed to electrostatic doping of the ferromagnetic layer by the support.
