NUPDOWN = difference between number of electrons in up and down spin component
Allows calculations for a specific spin multiplet, i.e. the the difference of the number of electrons in the up and down spin component will be kept fixed to the specified value. There is a word of caution required: If NUPDOWN is set in the INCAR file the initial moment for the charge density should be the same. Otherwise convergence can slow down. When starting from atomic charge densities (ICHARG=2), VASP will try to do this automatically by setting MAGMOM to NUPDOWN/NIONS. The user can of course overwrite this default by specifying a different MAGMOM (which should still result in the correct total moment). If one initializes the charge density from the one-electron wavefunctions, the initial moment is always correct, because VASP ``pushes'' the required number of electrons from the down to the up component. Initiallizing the chargedensity from the CHGCAR file (ICHARG=1), however, the initial moment is usually incorrect!
If no value is set (or NUPDOWN=-1) a full relaxation will be performed. This is also the default.