First-Principles Evaluation of the Dzyaloshinskii--Moriya Interaction

Abstract

We review recent developments of formulations to calculate the Dzyaloshinskii--Moriya (DM) interaction from first principles. In particular, we focus on three approaches. The first one evaluates the energy change due to the spin twisting by directly calculating the helical spin structure. The second one employs the spin gauge field technique to perform the derivative expansion with respect to the magnetic moment. This gives a clear picture that the DM interaction can be represented as the spin current in the equilibrium within the first order of the spin-orbit couplings. The third one is the perturbation expansion with respect to the exchange couplings and can be understood as the extension of the Ruderman--Kittel--Kasuya--Yosida (RKKY) interaction to the noncentrosymmetric spin-orbit systems. By calculating the DM interaction for the typical chiral ferromagnets Mn${}_{1-x}$Fe${}_x$Ge and Fe${}_{1-x}$Co${}_x$Ge, we discuss how these approaches work in actual systems.

invited review paper

References in corpus (8)

• Spin current and magneto-electric effect in non-collinear magnets
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites
• Microscopic approach to current-driven domain wall dynamics
• Spin Accumulation and Equilibrium Currents at the Edge of 2DEGs with Spin-Orbit Coupling
• Equilibrium spin currents in the Rashba medium
• Mechanical measurement of equilibrium spin currents in the Rashba medium
• Magnetic Chirality Induced from Ruderman-Kittel-Kasuya-Yosida Interaction at an Interface of a Ferromagnet/Heavy Metal Heterostructure