We develop a plane-wave pseudopotential scheme for noncollinear magnetic structures, based on a generalized local spin-density theory in which the direction of the magnetization is a continuous variable of position. We allow the atomic and magnetic structures to relax simultaneously and self-consistently. Application to small Fe clusters yields noncollinear magnetic structures for ${\mathrm{Fe}}_3$ and ${\mathrm{Fe}}_5$. The components of the magnetization density vary smoothly with position. The spin direction undergoes sizable changes only in the regions of small charge and spin density between the atoms and is generally uniform in the magnetic regions of the atoms.

• Received 22 January 1998

DOI:https://doi.org/10.1103/PhysRevLett.80.3622