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...

We demonstrate the existence of a spin-nematic, moment-free phase in a quantum four-spin ring exchange model on the square lattice. This unusual quantum state is created by the interplay of frustration and quantum fluctuations which lead to a partial restoration of SU (2) symmetry when going from a four-sublattice orthogonal biaxial Néel order to this exotic uniaxial magnet. A further increase of frustration drives a transition to a fully gapped SU (2) symmetric valence bond crystal.PACS numbers: 75.10. Jm, 75.40.Mg, 75.40.Cx Broken symmetries are one of the central paradigms of magnetic ordering, and most antiferromagnetic systems are in Néel phases at low temperatures, characterized by a vectorial order parameter: their sublattice magnetic moment. This order parameter breaks the rotational SU (2) symmetry of the Hamiltonian and is accompanied by gapless excitations, the Goldstone modes of the broken symmetry [1]. In low-dimensional systems of Heisenberg spins frustrating couplings can drive transitions to gapful SU (2) symmetric quantum states, where the building blocks are local singlets (in the simplest examples, pairs of spin-1/2 in short-range singlet states). These quantum gapped phases may have long-ranged singlet order and break spatial symmetries of the lattice, called valence bond crystals (VBC) in the following. An even more exotic groundstate, a coherent superposition of all lattice-coverings by local singlets, a state known as a resonating valence bond (RVB) spin liquid, could also be found [2].Quantum Phase Transitions from Néel ordered phases to quantum gapped phases have been studied for a long time as prototypical examples of quantum phase transitions. The nature of the symmetry breaking Néel phase plays an important role in these scenarios and seems determinant as to whether the adjacent gapped phase will be a VBC or an RVB phase [3]. It was recently shown that the transition from the standard collinear (π, π) Néel state to a Valence Bond Crystal phase can actually be an exotic quantum critical point with deconfined excitations [4].The well-known (π, π) Néel state is a uniaxial magnet, with two gapless Goldstone modes, in which SU (2) is partially broken to U (1). More complete SU (2) breaking schemes do exist, for example in noncollinear magnets with more than two ferromagnetic sublattices or more generally in helicoidal antiferromagnets. In these systems, the order parameter can be described as biaxial (or as a top), the SU (2) symmetry is completely broken, and there are three Goldstone modes. Chandra and Coleman suggested that in such situations the restoration of the full SU (2) symmetry due to the interplay of quantum fluctuations and frustration could possibly occur in two steps: from a biaxial magnet via an intermediate uniaxial spin nematic magnet -still with gapless excitations -to a fully gapped paramagnetic phase without SU (2) symmetry breaking [5,6]. This speculated spin-nematic phase -first introduced by Andreev and Grishchuk [7] -has no net magnetic moment, but nevertheless ...

The phase diagram of the classical J 1 -J 2 model on the kagome lattice is investigated by using extensive Monte Carlo simulations. In a realistic range of parameters, this model has a low-temperature chiral-ordered phase without long-range spin order. We show that the critical transition marking the destruction of the chiral order is preempted by the first-order proliferation of Z 2 point defects. The core energy of these vortices appears to vanish when approaching the T = 0 phase boundary, where both Z 2 defects and gapless magnons contribute to disordering the system at very low temperatures. This situation might be typical of a large class of frustrated magnets. Possible relevance for real materials is also discussed.In classical spin systems, competing interactions commonly frustrate the conventional ͑ , ͒ Néel order, possibly leading to more exotic arrangements of the local spins. Prominent examples include helicoidal configurations, 1-3 which usually break space inversion and time reversal. Noticeably, such spin chirality is a sufficient condition for multiferroic behavior, i.e., nonzero coupling between magnetization and electric polarization. 4,5 However, it is not uncommon that nonplanar magnetic orders effectively relieve the frustration even more than helicoidal configurations do. The associated magnetic order parameter is then three dimensional and, hence, also chiral. To date, two such orders have been exhibited, both on triangular-based lattices with competing interactions: A 4-sublattice tetrahedral order was found on the triangular lattice, 6 while a 12-sublattice cuboctahedral order was more recently found on the kagome lattice. 7 In two dimensions, complex magnetic orders might seem of purely theoretical interest since gapless spin waves destroy the spin long-range order at arbitrarily low temperatures. However, this disordering process is soft in the sense that at low but finite temperatures, the spin-spin correlations remain large enough to sustain emergent long-range orders. This is exemplified by the two above-mentioned models, wherein chiral long-range order persists up to finite temperatures, whereas long-range order in the spins is lost. Interestingly, the emergent chiral order parameter is Ising-type and in a straightforward extrapolation, one expects that these chiral phases will disappear through a critical transition in the two-dimensional ͑2D͒ Ising universality class. However, Momoi et al. 6 showed that in the case of the tetrahedral order, this is only true in the "weak universality" sense.We point out that such three-dimensional magnetic orders completely break the SO͑3͒ symmetry of Heisenberg interactions. Hence, the order parameter space is SO͑3͒, which supports point defects, namely vortices in two dimensions, around which the order parameter is rotated by 2. However, note that the rotation of 4 is equivalent to the identity, so that the order parameter may only wind by Ϯ2, as can be more formally deduced from ⌸ 1 = Z 2 . This evidences the peculiar topology of SO͑3͒ vortices...

The magnetization process of an S = 1 2 antiferromagnet on the kagomé lattice, [Cu3(titmb)2(OCOCH3)6]·H2O{titmb= 1,3,5-tris(imidazol-1-ylmethyl)-2,4,6 trimethyl-benzene} has been measured at very low temperatures in both pulsed and steady fields. We have found a new dynamical behavior in the magnetization process. A plateau at one third of the saturation magnetization Ms appears in the pulsed field experiments for intermediate sweep rates of the magnetic field and disappears in the steady field experiments. A theoretical analysis using exact diagonalization yields, J1 = −19 ± 2K and J2 = 6 ± 2K, for the nearest neighbor and second nearest neighbor interactions, respectively. This set of exchange parameters explains the very low saturation field and the absence of the plateau in the thermodynamic equilibrium as well as the two-peak feature in the magnetic heat capacity observed by Honda et al. [ Z. Honda et al., J. Phys.: Condens. Matter 14, L625 (2002)]. Supported by numerical results we argue that a dynamical order by disorder phenomenon could explain the transient appearance of the Ms/3 plateau in pulsed field experiments.