Constrained density functional for noncollinear magnetism

Energies of arbitrary small-and large-angle noncollinear excited magnetic configurations are computed using a highly accurate constrained density functional theory approach. Numerical convergence and accuracy are controlled by the choice of Lagrange multipliers lambda(I) entering the constraining conditions. The penalty part E-p of the constrained energy functional at its minimum is shown to be inversely proportional to lambda(I), enabling a simple, robust, and accurate iterative procedure to be followed to find a convergent solution. The method is implemented as a part of ab initio VASP package, and applied to the investigation of noncollinear B2-like and < 001 > double-layer antiferromagnetic configurations of bcc iron, Fe-2 dimer, and amorphous iron. Forces acting on atoms depend on the orientations of magnetic moments, and the proposed approach enables constrained self-consistent noncollinear magnetic and structural relaxation of large atomic systems to be carried out.