Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice -: art. no. 024433

Motivated by recent experiments on an S=1/2 antiferromagnet on the kagome lattice, we investigate the Heisenberg J(1)-J(2) model with ferromagnetic J(1) and antiferromagnetic J(2), Classically the ground state displays Neel long-range order with 12 noncoplanar sublattices. The order parameter has the symmetry of a cuboctahedron, it fully breaks SO(3) as well as the spin-flip symmetry, and we expect from the latter a Z(2) symmetry breaking pattern. As might be expected from the Mermin-Wagner theorem in two dimensions, the SO(3) symmetry is restored by thermal fluctuations while the Z(2) symmetry breaking persists up to a finite temperature. A complete study of S=1/2 exact spectra reveals that the classical order subsists for quantum spins in a finite range of parameters. First-order spin wave calculations give the range of existence of this phase and the renormalizations at T=0 of the order parameters associated to both symmetry breakings. This phase is destroyed by quantum fluctuations for a small but finite J(2)/vertical bar J(1)vertical bar similar or equal to 3, consistently with exact spectra studies, which indicate a gapped phase.