First-principles calculations of magnetic interactions in correlated systems

We present a method to calculate the effective exchange interaction parameters based on the realistic electronic structure of correlated magnetic crystals in local approach with the frequency dependent self-energy. The analog of local force theorem in the density-functional theory is proven for highly correlated systems. The expressions for effective exchange parameters, Dzialoshinskii-Moriya interaction, and magnetic anisotropy are derived. The first-principles calculations of magnetic excitation spectrum for ferromagnetic iron, with the local correlation effects from the numerically exact QMC scheme, are presented.