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Motivated by recent experiments on an S=1/2 antiferromagnet on the kagomelattice, we investigate the Heisenberg J1-J2 model with ferromagnetic J1 andantiferromagnetic J2. Classically the ground state displays Neel long rangeorder with 12 non-coplanar sublattices. The order parameter has the symmetry ofa cuboctahedron so that it fully breaks SO(3) as well as the spin-flipsymmetry, and we expect from the latter a Z2 symmetry breaking pattern. Asmight be expected from the Mermin-Wagner theorem in two dimensions, the SO(3)symmetry is restored by thermal fluctuations while the Z2 symmetry breakingpersists up to a finite temperature. A complete study of S=1/2 exact spectrareveals that the classical order subsists for quantum spins in a finite rangeof parameters. First order spin wave calculations give the range of existenceof this phase and the renormalisations at T=0 of the order parametersassociated to both symmetry breakings. This phase is destroyed by quantumfluctuations for a small but finite J2/|J1|\simeq3 consistently with exactspectra studies which indicate a gapped phase.Comment: Accepted for publication in Phys. Rev. B (2005

physical review. b, condensed matter and materials physics

Twelve sublattice ordered phase in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>model on the kagomé lattice

Twelve sublattice ordered phase in theJ1−J2model on the kagomé lattice