  We extend some of the well established self-interaction correction (SIC)
schemes of density-functional theory to the case of systems with noncollinear
magnetism. Our proposed SIC schemes are tested on a set of molecules and
metallic clusters in combination with the widely used local spin-density
approximation. As expected from the collinear SIC, we show that the
averaged-density SIC works well for improving ionization energies but fails to
improve more subtle quantities like the dipole moments of polar molecules. We
investigate the exchange-correlation magnetic field produced by our extension
of the Perdew-Zunger SIC, showing that it is not aligned with the local total
magnetization, thus producing an exchange-correlation torque.
