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.