2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126703We 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.10 pages, 4 figures, submitted to "Highly Frustrated Magnetism 2006" conference in OsakaStrongly Correlated Electronstext