  The purpose of this article is to extend the work by Anantharaman and
Canc\`es [1], and prove the existence of minimizers for the spin-polarized
Kohn-Sham model in the presence of a magnetic field within the local spin
density approximation. We show that for any magnetic field that vanishes at
infinity, the existence of minimizers is ensured for neutral or positively
charged systems. The proof relies on classical concentration-compactness
techniques.
