Dzyaloshinskii-Moriya-type interaction and Lifshitz invariant in Rashba 2D electron gas systems

The origin of chiral magnetic structures in ultrathin films of magnetic metals is analyzed. It is shown that the Lifshitz-type invariant term in the macroscopic thermodynamic potential can be derived from spin-orbit Rashba Hamiltonian in two dimensional electron gas (2DEG). The former is the prerequisite for existence of spin cycloid, skyrmions and other chiral phenomena observed in thin films. The estimation of the period of spin cycloid gives the value of an order of 10 nm that agrees well with the results of scanning probe microscopy observation reported in the literature.