Ordered phases in the frustrated fcc lattice antiferromagnet

We study the ordered phases of the $S=1/2$ fcc Heisenberg antiferromagnet, with first- and second-neighbor interactions, using perturbative series expansions at zero temperature. From calculations of ground-state energies we determine the regions of stability of semiclassical AF1, AF2, and AF3 phases. For the pure nearest-neighbor case our results suggest that AF1 is favored over AF3, a result in disagreement with linear spin-wave theory, but in agreement with other more recent work. We also investigate the two possible AF2 phases and locate the crossover between AF3 and AF2 at ${J}₂/{J}₁\ensuremath{\sim}0.535$.