This paper is concerned with the pure-state N-representability problem for systems under a magnetic field. Necessary and sufficient conditions are given for a spin-density 2x2 matrix R to be representable by a Slater determinant. We also provide sufficient conditions on the paramagnetic current j for the pair (R, j) to be Slater-representable in the case where the number of electrons N is greater than 12. The case N < 12 is left open.