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Atomic relaxation around defects in magnetically disordered materials computed by atomic spin constraints within an efficient Lagrange formalism
Lattice and magnetic degrees of freedom are strongly coupled in magnetic materials. We propose a consistent first-principles framework to explore the joint configurational space. For this, we define atomic spin moments from the projector augmented-wave formalism of density-functional theory and control them via Lagrangian constraints. We demonstrate our approach for vacancy formation and migration in collinear paramagnetic bcc iron by implementing a relaxation scheme based on spin-space averaged forces (SSA relaxation). Based on these results we discuss the impact of the magnetic state on vacancy formation energies, migration barriers, and relaxations.