Ab initio treatment of noncollinear spin systems within the atomic-sphere approximation and beyond

The properties of noncollinear magnets are often calculated within the framework of density-functional theory in local-spin-density approximation with the additional use of the atomic-sphere approximation for the spin directions. Thereby the intra-atomic noncollinearity is neglected for the calculation of the exchange correlation energy by taking into account only those components of the spin density which are parallel to spin quantization axes (SQAs) defined for the whole atomic spheres. When the magnetic moment directions are calculated in a self-consistent manner, e.g., for systems with intrinsic noncollinearity or when calculating the response of the system to a weak external field with components perpendicular to the moment directions, the SQAs are conventionally chosen to be parallel to the magnetic moments. We present both theoretical arguments and test calculations showing that this choice of SQAs is not the best and may in certain situations lead to wrong results. As a consequence of our arguments we can suggest a better choice of SQAs. Furthermore, a version of the linear-muffin-tin-orbital method is presented where the atomic-sphere approximation for the spin directions and the introduction of local SQAs are not required so that the intraatomic noncollinearity appears already in the basis functions.