Dzyaloshinsky-Moriya-induced order in the spin-liquid phase of theS=1∕2pyrochlore antiferromagnet

We show that the S=1/2 pyrochlore lattice with both Heisenberg and antisymmetric, Dzyaloshinsky-Moriya (DM) interactions, can order antiferromagnetically into a state with chiral symmetry, dictated by the distribution of the DM interactions. The chiral antiferromagnetic state is characterized by a small staggered magnetic moment induced by the DM interaction. An external magnetic field can also lead to characteristic field-induced ordering patterns, strongly dependent on the field direction, and generally separated by a quantum phase transition from the chiral ordered phase. The phase diagram at finite temperature is also discussed.