Convergence of the Broyden Density Mixing Method in Noncollinear Magnetic Systems

In density functional theory, solutions of the Kohn-Sham equation correspond to stationary states of the energy functional. Most calculations converge to a minima of that functional, but in complex noncollinear magnetic systems the energy landscape shows many saddle points (or saddle-like points where the first variation of the energy functional is small) and it depends on the density mixing algorithm which stationary state is reached. This causes a convergence problem that frequently arises when the widely used Broyden algorithm is used to search the energy minima of noncollinear magnetic systems. Calculations of Fe and Mn systems illustrate how a small modification of the mixing algorithm allows to overcome this difficulty and to relax the magnetic moments' rotational degrees of freedom efficiently.