Fully unconstrained noncollinear magnetism within the projector augmented-wave method

Spin-polarized calculations in solids have generally been confined to a global quantization axis to simplify both the theoretical model and its implementation in self-consistent codes. This approximation is justified as many materials exhibit a collinear magnetic order. However, in recent years much interest has been directed towards noncollinear magnetism in which the magnetization density is a continuous vector variable of position. In this paper we develop the all-electron projector augmented-wave (PAW) method for noncollinear magnetic structures, based on a generalized local-spin-density theory. The method allows both the atomic and magnetic structures to relax simultaneously and self-consistently. The algorithms have been implemented within a powerful package called VASP (Vienna ab initio simulation package), which has been used successfully for a large variety of different systems such as crystalline and amorphous semiconductors, simple liquids, and transition metals. The approach has been used to study small clusters of Fe and Cr; some of these clusters show noncollinear magnetic arrangements.