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We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a special surface with Arf-Kervaire invariant one, and is interpreted as resulting from an obstruction to transform the surface into its chiral image with special continuous deformations. We also consider additional constraints on the dynamics and see how the surface is modified., Comment: 21 pages, 8 figures, Submission to SciPost

We classify the sectors of configurations that result from the dynamics of 2d crossing flux lines, which are the simplest degrees of freedom of the 3-coloring lattice model. We show that the dynamical obstruction is the consequence of two effects: (i) conservation laws described by a set of invariants that are polynomials of the winding numbers of the loop configuration, (ii) steric obstruction that prevents paths between configurations, for lack of free space. We argue that the invariants fully classify the configurations in five, chiral and achiral, sectors and no further obstruction in the limit of low-winding numbers., 25 pages, 12 figures, Submission to SciPost

Le magnetisme des isolants peut donner naissance a des etats quantiques macroscopiques appeles « liquides de spins ». Sans ordre a longue portee a temperature nulle, ces etats sont caracterises theoriquement par des excitations magnetiques fractionnaires de spin 1/2, consequences specifiques de l’intrication de leur etat fondamental. Les travaux theoriques des vingt dernieres annees permettent d’affirmer qu’un tel etat liquide de spins pourrait etre stabilise en deux dimensions sur un reseau triangulaire en etoile de David, le reseau kagome. Un compose modele pour cette physique, l’herbertsmithite , a pu etre synthetise et ouvre la voie aux etudes experimentales et aux premieres confrontations avec la theorie.

We define two classes of colorings that have odd or even chirality on hexagonal lattices. This parity is an invariant in the dynamics of all loops, and explains why standard Monte-Carlo algorithms are nonergodic. We argue that adding the motion of "stranded" loops allows for parity changes. By implementing this algorithm, we show that the even and odd classes have the same entropy. In general, they do not have the same number of states, except for the special geometry of long strips, where a Z$_2$ symmetry between even and odd states occurs in the thermodynamic limit., 18 pages, 13 figures

In this paper we would like to review the zero field inelastic neutron scattering results obtained by using both the thermal and cold neutron triple axis instrument. The first single triplet state at around 3 meV is split due to the Dzyaloshinski-Moriya (DM) inter-dimer interaction with both the out-of-plane and in-plane components. The splitting between the S z = ±1 states is of the order of 0.3 meV. The two triplets bound states also form a very flat bands at 4.9. 5.5 and 6.3 meV with finite line width of the order and/or twice of the DM splitting. Finally the higher energy range up to 13 meV can be also characterized by three rather broad, but flat bands at around 8, 10 and 12 meV with the line width roughly three times the DM splitting. These excitations can be probably assigned to three and more triplets bound state excitations.

Anisotropic spin-spin interactions of the symmetry described by Dzyaloshinsky and Moriya are generally considered weak, as they depend on the spin-orbit couplings. In frustrated spin systems with singlet ground states they can, however, have rather strong effects. We discuss recent results related to two gapped spin systems: $\rm CuGeO_3$ and $\rm SrCu_2(BO_3)_2$ in particular. In the first compound the Dzyaloshinsky-Moriya interactions effectively lower the symmetry of the magnetic unit cell and this leads to doubling of the low frequency mode. In the second case, the Dzyaloshinsky-Moriya interactions also split the lowest magnon mode linearly in the spin-orbit coupling. In addition, the relatively weak Dzyaloshinsky-Moriya interactions can dominate the dispersion. Consideration of the selection rules for optical transitions show that while the Dzyaloshinsky-Moriya interactions can explain much of the dynamics, they do not explain the observed transition amplitudes. This leads to a review of recent calculations of anisotropic spin-phonon couplings. We discuss how this leads to a novel mechanism to explain the ESR intensities in the spin gap systems discussed. Selection rules for this novel mechanism involving coupling to the electric field of the resonant probe are discussed and relation to polarised neutron experiments briefly mentioned., Comment: 9 pages, no figure, Proceedings of the Yukawa symposium, to appear in Progress in Theoretical Physics, 145 (2002)

While multiple time scales generally arise in the dynamics of disordered systems, we find multiple time scales in absence of disorder, in a simple model with hard local constraints. The dynamics of the model, which consists of local collective rearrangements of various scales, is not determined by the smallest scale but by a length $l^*$ that grows at low energies. In real space we find a hierarchy of fast and slow regions: each slow region is geometrically insulated from all faster degrees of freedom, which are localized in fast pockets below percolation thresholds. A tentative analogy with structural glasses is given, which attributes the slowing down of the dynamics to the growing size of mobile elementary excitations, rather than to the size of some domains., Comment: 10 pages, 9 figures, v2: publ

Magnetic excitations in the isostructural spin-dimer systems ${\text{Sr}}_{3}$${\text{Cr}}_{2}$${\text{O}}_{8}$ and ${\text{Ba}}_{3}$${\text{Cr}}_{2}$${\text{O}}_{8}$ are probed by means of high-field electron spin resonance at subterahertz frequencies. Three types of magnetic modes were observed. One mode is gapless and corresponds to transitions within excited states, while two other sets of modes are gapped and correspond to transitions from the ground to the first excited states. The selection rules of the gapped modes are analyzed in terms of a dynamical Dzyaloshinskii-Moriya interaction, suggesting the presence of phonon-assisted effects in the low-temperature spin dynamics of ${\text{Sr}}_{3}$${\text{Cr}}_{2}$${\text{O}}_{8}$ and ${\text{Ba}}_{3}$${\text{Cr}}_{2}$${\text{O}}_{8}$.

The direct ESR absorption between the singlet ground and triplet excited states of the spin-gap systems is investigated. Such an absorption, which is forbidden by the conservation of the total spin quantum number in the ordinary Heisenberg-Hamiltonian, is caused by the Dzyaloshinskii–Moriya interaction. We show the selection rule in the presence of the interaction, using the exact diagonalization of the finite cluster of the quasi-one-dimensional bond-alternating spin system. The selection rule is also modified into a suitable form for the investigation of the recent experimental result for CuGeO3.

By considering the constrained motion of classical spins in a geometrically frustrated magnet, we find a dynamical freezing temperature below which the system gets trapped in metastable states with a "frozen" moment and dynamical heterogeneities. The residual collective degrees of freedom are strongly correlated, and by spontaneously forming aggregates, they are unable to reorganize the system. The phase space is then fragmented in a macroscopic number of disconnected sectors (broken ergodicity), resulting in self-induced disorder and "thermodynamic" anomalies, measured by the loss of a finite configurational entropy. We discuss these results in the view of experimental results on the kagome compounds, SrCr(9p)Ga(12-9p)O19, (H30)Fe3(SO4)2(OH)6, Cu3V2O7(OH)2.2H2O and Cu3BaV2O8(OH)2., 17 pages, 14 fig

We argue that the spin-wave breakdown in the Heisenberg kagome antiferromagnet signals an instability of the ground state and leads, through an emergent local constraint, to a quantum dynamics described by a gauge theory similar to that of chromodynamics. For integer spins, we show that the quantum fluctuations of the gauge modes select the sqrt(3)xsqrt(3) Neel state with an on-site moment renormalized by color resonances. We find non-magnetic low-energy excitations that may be responsible for a deconfinement "transition" at experimentally accessible temperatures which we estimate., 4 pages, 4 figures, v2: printable figs, v3: publ. version

The topology of the magnetic interactions of the copper spins in the nitrosonium nitratocuprate $(\text{NO})[\text{Cu}{({\text{NO}}_{3})}_{3}]$ suggests that it could be a realization of the Nersesyan-Tsvelik model [A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. B 67, 024422 (2003)], whose ground state was argued to be either a resonating valence-bond state or a valence-bond crystal. The measurement of thermodynamic and magnetic resonance properties reveals a behavior inherent to low-dimensional spin $S=\frac{1}{2}$ systems and provides indeed no evidence for the formation of long-range magnetic order down to 1.8 K.

We study the electron spin resonance of low-dimensional spin systems at high temperature and test the Kubo-Tomita theory of exchange narrowing. In finite-size systems (molecular magnets), we found a double-peak resonance which strongly differs from the usual Lorentzian. For infinite systems, we have predictions for the linewidth and line shape as a function of the anisotropy strength. For this, we have used an interpolation between a nonperturbative calculation of the memory function at short times (exact diagonalization) and the hydrodynamic spin diffusion at long times. We show that the Dzyaloshinskii-Moriya anisotropies generally induce a much larger linewidth than the exchange anisotropies in two dimensions, contrary to the one-dimensional case.

International audience; We have obtained the zero-temperature phase diagram of the kagomé antiferromagnet with Dzyaloshinskii-Moriya interactions in Schwinger-boson mean-field theory. We find quantum phase transitions (first or second order) between different topological spin-liquid and Néel-ordered phases (either the 3×3 state or the so-called Q=0 state). In the regime of small Schwinger-boson density, the results bear some resemblances with exact diagonalization results and we briefly discuss some issues of the mean-field treatment. We calculate the equal-time structure factor (and its angular average to allow for a direct comparison with experiments on powder samples), which extends earlier work on the classical kagomé to the quantum regime. We also discuss the dynamical structure factors of the topological spin-liquid and the Néel-ordered phases.

We show that the magnetic Raman response of a spin liquid is independent of the polarizations of the light for triangular symmetries. In contrast, a ground state that has a broken-symmetry shows characteristic oscillations when the polarizations are rotated. This would allow one to detect weak broken-symmetries and emergent order parameters. We focus on the kagome antiferromagnet wherein no conventional long-range order has been found so far and present the Raman cross section of a spin liquid and a valence bond crystal by using a random phase approximation.

International audience; We argue that the S=1/2 kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For DDc the system develops antiferromagnetic long-range order. The quantum critical point is found to be Dc≃0.1J using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ZnCu3(OH)6Cl3 may be in a quantum critical region controlled by this fixed point.

We argue, in contrast to recent studies, that the antiferromagnetic superexchange coupling between nearest neighbour spins does not fully destroy the ferromagnetism in dilute magnets with long-ranged ferromagnetic couplings. Above a critical coupling, we find a \textit{canted} ferromagnetic phase with unsaturated moment. We have calculated the transition temperature using a simplified local Random Phase Approximation procedure which accounts for the canting. For the dilute magnetic semiconductors, such as GaMnAs, using \textit{ab-initio} couplings allows us to predict the existence of a canted phase and provide an explanation to the apparent contradictions observed in experimental measurements. Finally, we have compared with previous studies that used RKKY couplings and reported non-ferromagnetic state when the superexchange is too strong. Even in this case the ferromagnetism should remain essentially stable in the form of a canted phase., 6 figures, submitted to Phys. Rev

We study the effects of short-range correlated disorder arising from chemical dopants or local lattice distortions, on the ferromagnetism of 3d double exchange systems. For this, we integrate out the carriers and treat the resulting disordered spin Hamiltonian within local random phase approximation, whose reliability is shown by direct comparison with Monte Carlo simulations. We find large scale inhomogeneities in the charge, couplings and spin densities. Compared with the homogeneous case, we obtain larger Curie temperatures ($T_{C}$) and very small spin stiffnesses ($D$). As a result, large variations of $\frac{D}{T_{C}}$ measured in manganites may be explained by correlated disorder. This work also provides a microscopic model for Griffiths phases in double exchange systems., accepted for publication in Phys. Rev. B (rapid comm.)

We discuss the phase diagram of the two-orbital model of half-doped manganites by calculating self-consistently the Jahn-Teller (JT) distortion patterns, charge, orbital and magnetic order at zero temperature. We analyse the instabilities of these phases caused by electron or hole doping away from half-doping, or by the application of a magnetic-field. For the CE insulating phase of half-doped manganites, in the intermediate JT coupling regime, we show that there is a competition between canting of spins (which promotes mobile carriers) and polaronic self-trapping of carriers by JT defects. This results in a marked particle-hole asymmetry, with canting winning only on the electron doped side of half-doping. We also show that the CE phase undergoes a first-order transition to a ferromagnetic metallic phase when a magnetic-field is applied, with abrupt changes in the lattice distortion patterns. We discuss the factors that govern the intriguingly small scale of the transition fields. We argue that the ferromagnetic metallic phases involved have two types of charge carriers, localised and band-like, leading to an effective two-fluid model., Comment: 22 pages, 28 figures

We show that a continuous set of degenerate critical soft modes strongly enhances the first-order character of a fluctuation-induced first-order transition in the pyrochlore dipolar Heisenberg antiferromagnet. Such a degeneracy seems essential to explain the strong first-order transition recently observed in Gd(2)Sn(2)O(7). We present some evidence from Monte-Carlo simulations and a perturbative renormalization group expansion., 8 pages, 9 figures, new version to appear in PRB, added refs

We argue that many properties of the half-doped manganites may be understood in terms of a new two-(eg electron)-fluid description, which is energetically favorable at intermediate Jahn-Teller (JT) coupling. This emerges from a competition between canting of the core spins of Mn promoting mobile carriers and polaronic trapping of carriers by JT defects, in the presence of CE, orbital and charge order. We show that this explains several features of the doping and magnetic field induced insulator-metal transitions, as the particle-hole asymmetry and the smallness of the transition fields., Comment: 4 pages, 4 figures

We present a mean-field theory for magnetic-field-driven transitions in dipolar coupled gadolinium titanate ${\mathrm{Gd}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ pyrochlore system. Low-temperature neutron scattering yields a phase that can be regarded as a eight sublattice antiferromagnet, in which long-ranged ordered moments and fluctuating moments coexist. Our theory gives parameter regions where such a phase is realized, and predicts several other phases, with transitions amongst them driven by magnetic field as well as temperature. We find several instances of local disorder parameters describing the transitions.

We consider the absorption of light with emission of one S(tot)=1 magnetic excitation in systems with a spin gap induced by quantum fluctuations. We argue that an electric dipole transition is allowed on the condition that a virtual phonon instantaneously breaks the inversion symmetry. We derive an effective operator for the transition and argue that the proposed theory explains the polarized experiments in CuGeO(3) and SrCu(2)[BO(3)](2)., Comment: 9 pages, 4 figures

We adapt Takahashi's modified spin-wave theory to the context of nano-magnets, and apply it to the molecular compound based on the giant magnetic molecule Mo(72)Fe(30). This involves solving numerically the mean-field equations and then forcing the sublattice magnetizations to zero by means of local chemical potentials for the magnons. We have thus constructed a quantum state with no local magnetization at all temperatures, appropriate to a finite-size system, but with strong correlations. We compare theoretical results to specific heat and ESR measurements., Comment: 12 pages, 11 figures

The synthetic organic compound lambda-(BETS)2FeCl4 undergoes successive transitions from an antiferromagnetic insulator to a metal and then to a superconductor as a magnetic field is increased. We use a Hubbard-Kondo model to clarify the role of the Fe(3+) magnetic ions in these phase transitions. In the high-field regime, the magnetic field acting on the electron spins is compensated by the exchange field He due to the magnetic ions. This suggests that the field-induced superconducting state is the same as the zero-field superconducting state which occurs under pressure or when the Fe(3+) ions are replaced by non-magnetic Ga(3+) ions. We show how He can be extracted from the observed splitting of the Shubnikov-de Haas frequencies. Furthermore, we use this method of extracting He to predict the field range for field-induced superconductivity in other materials., Comment: 5 pages

We consider the possibility that the electrons injected into organic field-effect transistors are strongly correlated. A single layer of acenes can be modelled by a Hubbard Hamiltonian similar to that used for the kappa-(BEDT-TTF)(2)X family of organic superconductors. The injected electrons do not necessarily undergo a transition to a Mott insulator state as they would in bulk crystals when the system is half-filled. We calculate the fillings needed for obtaining insulating states in the framework of the slave-boson theory and in the limit of large Hubbard repulsion, U. We also suggest that these Mott states are unstable above some critical interlayer coupling or long-range Coulomb interaction., Comment: 9 pages, 7 figures

The Dzyaloshinski-Moriya interaction partially lifts the magnetic frustration of the spin-1/2 oxide SrCu(2)(BO(3))(2). It explains the fine structure of the excited triplet state and its unusual magnetic field dependence, as observed in previous ESR and new neutron inelastic scattering experiments. We claim that it is mainly responsible for the dispersion. We propose also a new mechanism for the observed ESR transitions forbidden by standard selection rules, which relies on an instantaneous Dzyaloshinski-Moriya interaction induced by spin-phonon couplings.

The direct electron spin resonance (ESR) absorption between a singlet ground state and the triplet excited states of spin gap systems is investigated. Such an absorption, which is forbidden by the conservation of the total spin quantum number in isotropic Hamiltonians, is allowed by the Dzyaloshinskii-Moriya interaction. We show a selection rule in the presence of this interaction, using the exact numerical diagonalization of the finite cluster of the quasi-one-dimensional bond-alternating spin system. The selection rule is also modified into a suitable form in order to interpret recent experimental results on CuGeO$_3$ and NaV$_2$O$_5$., 5 pages, Revtex, with 6 eps figures, to appear in J. Phys. Soc. Jpn. Vol. 69 No. 11 (2000)

We report high-resolution neutron inelastic scattering experiments on the spin excitations of NaV2O5. Below Tc, two branches associated with distinct energy gaps are identified. From the dispersion and intensity of the spin excitation modes, we deduce the precise zig-zag charge distribution on the ladder rungs and the corresponding charge order (about 0.6). We argue that the spin gaps observed in the low-T phase of this compound are primarily due to the charge transfer., Comment: 4 pages, 5 figures, to appear in Phys. Rev. Lett

We present a canonically invariant form for the generalized Langevin and Fokker-Planck equations. We discuss the role of constants of motion, and the construction of conservative stochastic processes., Comment: 3 pages, RevTeX. Submitted to J. Phys. A