Effects of Rashba and Dresselhaus spin-orbit interactions on the ground state of two-dimensional localized spins

Abstract

Starting with the indirect exchange model influenced by the Rashba and the Dresselhaus spin-orbit interactions, we derive the Dzyaloshinskii-Moriya interaction of localized spins. The strength of the Dzyaloshinskii-Moriya interaction is compared with that of the Heisenberg exchange term as a function of atomic distance. Using the calculated interaction strengths, we discuss the formation of various atomic ground states as a function of temperature and external magnetic field. By plotting the magnetic field-temperature phase diagram, we present approximate phase boundaries between the spiral, Skyrmion and ferromagnetic states of the two-dimensional weak ferromagnetic system.