Symmetry considerations on the magnetization process of the Heisenberg   model on the pyrochlore lattice
  We present a detailed symmetry analysis of the degeneracy lifting due to higher order spin exchanges in the pyrochlore lattice in applied magnetic field. Under the assumption of the 4 sublattice ordering, the criteria for a stable half-magnetization plateau are deduced. The higher order exchange terms may originate from spin-lattice coupling, or can describe quantum and thermal fluctuations. 
Karlo Penc, Nic Shannon, Yukitoshi Motome and Hiroyuki Shiba