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Hi,

Could anyone help me understand this basic issue?

When I calculate systems with an electronic band gap, i always obtain an integer value for the total difference between alpha and beta electrons in the cell (magnetisation), even when I don't fix NUPDOWN.

But this does not happen for bulk metal calculations when I don't fix NUPDOWN... in this cases I obtain fractional values sometimes. My question is: Is this because of the smearing? Or even in the limit sigma-> 0 the difference between alpha and beta electrons can be non-integer for a conducting system?

Many thanks for any explanation!

the magnetization is calculated from the differences of the spin up and down charges in your cell. Hence, it may differ from integer numbers, depending on the quality of your k-mesh, the BZ-integration you chose and the smearing parameter.
Please also check the charge density congvergence of your calculation in OSZICAR (rms(c)-column). If this convergence is bad, please decrease the charge- and spin density mixing parameters (AMIX, BMIX, AMIX_MAG, BMIX_MAG)

If one the bands for one spin component are fully occupied you always get an integer magnetic moment (M = Nup - Ndown; N = Nup + Ndown; because N is an integer, if Nup or Ndown is an integer also M is an integer.) If you're calculating an insulator or semiconductor, it is likely that either Nup or Ndown must be an integer because you have a fully occ band. In the case of metals both up and down bands are partially filled, so there's no reason for either of them to have integer occupation. I don't see what this has to do with BZ integration.