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

Abstract

Motivated by recent experiments on an S = 1/2 antiferromagnet on the kagomé lattice, we investigate the Heisenberg J1 − J2 model with ferromagnetic J1 and antiferromagnetic J2. Classically the ground state displays Néel 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 Z2 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 Z2 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 J2/|J1| ≃ 3, consistently with exact spectra studies, which indicate a gapped phase. I. THEORETICAL AND EXPERIMENTAL ISSUESWhatever the nature of the spin, classical or quantum, the first neighbor Heisenberg antiferromagnet on the kagomé lattice fails to display Néel-like long-range order. Classically, it is characterized by an extensive entropy 1,2 at T = 0. Quantum mechanically the spin-1/2 system has an exceptionally large density of low lying excitations 3,4 reminiscent of the classical extensive entropy. It is still debated whether and eventually how this degeneracy is lifted in the quantum limit 5,6 . An essential issue concerns the influence of perturbations: classically the effect of a second neighbor coupling J 2 has been very early studied by Harris and co-workers 7 . They showed that an infinitesimal J 2 is sufficient to drive the system toward an ordered phase with the three spins around a triangle pointing 120 • from each other. Antiferromagnetic second-neighbor coupling (J 2 > 0) favors the q = 0 Néel order of this pattern on the Bravais lattice, whereas there are nine spins per unit cell for J 2 < 0 (q = √ 3 × √ 3 order). The effect of Dzyaloshinsky-Moriya interactions has also been analyzed 8 . To our knowledge the reduction of the order parameter by quantum fluctuations has only been studied through exact diagonalizations 9 . This approach points to an immediate transition from the "disordered phase" at the pure J 1 > 0 point, to the semiclassical Néel phases.Up until now the J 1 − J 2 model on the kagomé lattice has only been studied for antiferromagnetic J 1 . Many magnetic compounds 10-13 with this geometry have been studied so far, but most of them have spin S = 3/2. A few compounds with S = 1/2 Cu ions have recently been synthetized [14][15][16] . None of them can be described by a pure isotropic first neighbor antiferromagnetic Heisenberg model. Recent experimental work on an organic compound with copper ions on a kagomé lattice 17 gives indication of competing ferromagnetic and antiferrom...

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