A Spin magnetic moment in half metals.

I read that the stoichiometric half-metallic compound has integer spin moment. For this, n(up)-n(down) should be integer. Since n(up) +n(down) is always integer, either n(up) or n(down) should be integer to make total spin moment integer. I could not understand how the presence of energy gap in one of the spin channel( property of Half Metal) makes the value n(up) or n(down) integer. Where n is the no. Of electrons per unit cell.
 
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