We give a physical picture of the low-energy sector of the spin-1 2 kagomé Heisenberg antiferromagnet ͑KAF͒. It is shown that the kagomé lattice can be presented as a set of stars which contain 12 spins and are arranged in a triangular lattice. Each of these stars has two degenerate singlet ground states which can be considered in terms of pseudospin. As a result of the interaction between stars we get the Hamiltonian of the Ising ferromagnet in a magnetic field. So in contrast to the common view there is a long-range order in KAF consisting of definite singlet states of stars.In spite of numerous theoretical and experimental studies in the last decade, some magnetic properties of kagomé antiferromagnets ͑KAF's͒ remain open problems. Experiments revealed an unusual low-temperature behavior of the specific heat and magnetic susceptibility in kagomé-like compounds. For example specific heat measurements in SrCr 9p Ga 12Ϫ9p O 19 (Sϭ3/2 kagomé material͒ have shown that there is a peak at TϷ5 K, CϰT 2 at TՇ5 K, and it appears to be practically independent of magnetic field up to 12 T. 1 Some of the experimental findings are in agreement with the results of numerical finite-cluster investigations. 2-6 They reveal a gap separating the ground state from the upper triplet levels and a band of nonmagnetic singlet excitations with a very small or zero gap inside the triplet gap. The number of states in the band increases with the number of sites N as ␣ N . For samples with up to 36 sites ␣ϭ1.15 and 1.18 for even and odd N, respectively. 2,5 This wealth of low-lying singlet excitations explains the peak of specific heat at low temperature and its independence of the magnetic field. 1,7 However, the origin of this band as well as the nature of the ground state has been unclear until now. Previous exact diagonalization studies 4,8 reveal an exponential decay of the spin-spin and dimer-dimer correlation functions. So the point of view that KAF is a spin liquid is widely accepted now. 2,4 -12 It seems the best candidate for a description of KAF low-energy properties is a quantum dimer model. 6,9,13 It should be mentioned that there has been a certain recent success in this field. In Ref. 14 an approach first pioneered by Subrahmanyam in Ref. 15 was developed in which a spin-1 2 kagomé lattice is considered as a set of interactive triangles with a spin in each apex. It was suggested there to work in the subspace where the total spin of each triangle is 1/2 ͓short-range resonant valance bond states ͑SRRVB͔͒ investigating low-lying excitations. It was shown that the lowenergy spectrum obtained with SRRVB on the samples with up to 36 cites and the number of singlet excitations in the band coincide with the results of exact diagonalization. Meanwhile, a further development of this approach is required to get a full physical description of KAF.Other types of frustrated magnets which possess a similar behavior as KAF and have many singlet states inside the triplet gap are pyrochlore 16 and CaV 4 O 9 . 17 Recently a model of frustrated ...

The spectrum of short-wavelength magnons in a two-dimensional quantum Heisenberg antiferromagnet on a square lattice is calculated to the third order in a 1/S expansion. It is shown that a 1/S series for S = 1/2 converges quickly in the whole Brillouin zone except in the neighborhood of the point k = (π, 0), at which absolute values of the third-and the second-order 1/S-corrections are approximately equal to each other. It is shown that the third-order corrections make deeper the roton-like local minimum at k = (π, 0), improving the agreement with recent experiments and numerical results in the neighborhood of this point. It is suggested that the 1/S series converges slowly near k = (π, 0) also for S = 1 although the spectrum renormalization would be small in this case due to the very small values of high-order 1/S corrections.

We present a theory describing spiral magnets with Dzyaloshinskii-Moriya interaction (DMI) subject to bond disorder at small concentration c of defects. It is assumed that both DMI and exchange coupling are changed on imperfect bonds. Qualitatively the same physical picture is obtained in two models which are considered in detail: B20 cubic helimagnets and layered magnets in which DMI leads to a long-period spiral ordering perpendicular to layers. We find that the distortion of the spiral magnetic ordering around a single imperfect bond is long-range: values of additional turns of spins decay with the distance r to the defect as 1/r 2 being governed by the Poisson's equation for electric dipole. At finite concentration of randomly distributed imperfect bonds, we calculate correction to the spiral vector. We show that this correction can change the sign of spin chirality even at c ≪ 1 if defects are strong enough. It is demonstrated that impurities lead to a diffuse elastic neutron scattering which has power-law singularities at magnetic Bragg peaks positions. Then, each Bragg peak acquires power-law decaying tails. Corrections are calculated to the magnon energy and to its damping caused by scattering on impurities.

We discuss spin-1 2 one-dimensional (1D) and quasi-1D magnets with competing ferromagnetic nearest-neighbor J1 and antiferromagnetic next-nearest-neighbor J exchange interactions in a strong magnetic field H. It is well known that due to attraction between magnons quantum phase transitions (QPTs) take place at H = Hs from the fully polarized phase to nematic ones if J > |J1|/4. Such a transition at J > 0.368|J1| is characterized by a softening of the two-magnon bound-state spectrum. Using a bond operator formalism we propose a bosonic representation of the spin Hamiltonian containing, aside from bosons describing one-magnon spin-1 excitations, a boson describing spin-2 excitations whose spectrum coincides at H ≥ Hs with the two-magnon bound-state spectrum obtained before. The presence of the bosonic mode in the theory that softens at H = Hs makes the QPT consideration substantially standard. In the 1D case at H < Hs, we find an expression for the magnetization which describes well existing numerical data. Expressions for spin correlators are obtained which coincide with those derived before either in the limiting case of J |J1| or using a phenomenological theory. In quasi-1D magnets, we find that the boundary in the H-T plane between the fully polarized and the nematic phases is given by Hs(0) − Hs(T ) ∝ T 3/2 . Simple expressions are obtained in the nematic phase for static spin correlators, spectra of magnons and the soft mode, magnetization and the nematic order parameter. All static two-spin correlation functions are short ranged with the correlation length proportional to 1/ ln(1 + |J1|/J). Dynamical spin susceptibilities are discussed and it is shown that the soft mode can be observed experimentally in the longitudinal channel. 1 1 ' , J J J 2 1 ' , J J J

We discuss Bose-Einstein condensation of magnons (BEC) in magnets with predominant ferromagnetic (FM) interaction in magnetic field H near saturation (Hc). Because Hc is independent of FM couplings, magnetic materials of this type can have small Hc that makes them promising candidates for experimental investigation of BEC. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe small effective interaction between magnons near the QCP in such magnets, in contrast to AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature Tc(H) ∝ (Hc − H) 1/φ from φ = 3/2 to φ = 1 in quasi-1D magnets, and from φ = 3/2 to φ ≈ 1 (Tc ln Tc ∝ Hc − H) in quasi-2D ones.

Erratum: Renormalization of the spin-wave spectrum in three-dimensional ferromagnets with dipolar interaction [Phys. Rev. B 74, 014435 (2006)]

The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar two-dimensional grating for the coherent neutron wave. The thickness of the film L ͑length of pores͒ plays important role in the transition from the weak to the strong scattering regimes. It is shown that the coherency of the standard small-angle neutron scattering setups suits to the geometry of the studied objects and often affects the intensity of scattering. The proposed theoretical solution can be applied in the small-angle neutron diffraction experiments with flux lines in superconductors, periodic arrays of magnetic or superconducting nanowires, as well as in small-angle diffraction experiments on synchrotron radiation.

We present a mean-field theory describing the influence of long-range dipolar forces on the temperature transition from the paramagnetic to ordered phases in frustrated Heisenberg spiral magnets. It is shown that the dipolar interaction produces a cascade of first- and second- order phase transitions between the paramagnetic and the spiral states upon temperature decreasing. Depending on system parameters, the following intermediate phases can arise: an incommensurate and a commensurate sinusoidally modulated states, spiral phases in which perpendicular spin components have different amplitudes and are modulated with the same and with different wave vectors. We distinguish six possible sequences of phase transitions upon temperature decreasing at least four of which were observed before experimentally in specific compounds. It is found that the action of dipolar forces cannot always be modeled even qualitatively by small one-ion anisotropic spin interactions. We demonstrate that the dipolar interaction is responsible for successive phase transitions in the triangular-lattice multiferroic MnI$_2$: almost all available experimental findings are described quantitatively within the mean-field theory by taking into account the exchange, the dipolar and small symmetry-allowed anisotropic spin interactions.Comment: 12 pages, 5 figure