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Achieving thermal equilibrium in two-dimensional lattices of interacting nanomagnets has been a key issue on the route to study exotic phases in artificial frustrated magnets. We revisit this issue in artificial one-dimensional kagom\'e spin chains. Imaging arrested micro-states generated by a field demagnetization protocol and analyzing their pairwise spin correlations in real space, we unveil a non-equilibrated physics. Remarkably, this physics can be reformulated into an at-equilibrium one by rewriting the associated spin Hamiltonian in such a way that one of the coupling constants is quenched. We ascribe this effective behavior to a kinetic hinderance during the demagnetization protocol, which induces the formation of local flux closure spin configurations that sometimes compete with the magnetostatic interaction., Comment: 8 pages, 5 figures

Under certain experimental conditions, the deposition of C60 molecules onto an atomically flat copper surface gives rise to the formation of corrugated islands. This corrugation, which reflects a molecular displacement perpendicular to the surface plane, presents an astonishing pattern: it is well described by a frustrated Ising spin Hamiltonian whose thermodynamics is compatible with a spin liquid about to transit towards an ordered zigzag state. Here we study the statistical properties of such a molecular corrugation using tools generally employed in frustrated magnetism. More specifically, the real and reciprocal space analysis of pairwise molecule correlations allows us to demonstrate that the C60/Cu system, in which magnetism is totally absent, has all the characteristics of a triangular Ising antiferromagnet. Our results indicate that the organization of two-dimensional matter, at the molecular length scale, sometimes turns out to be particularly close to that encountered in highly frustrated magnets., Comment: 10 pages, 8 figures

Analyzing the magnetic structure factor of a field demagnetized artificial square ice, qualitative deviations from what would predict the square ice model are observed. Combining micromagnetic and Monte Carlo simulations, we demonstrate that these deviations signal the presence of interactions between nanomagnets that extend beyond nearest neighbors. Including further neighbor, dipolar-like couplings in the square ice model, we find that the first seven or eight coupling strengths are needed to reproduce semi-quantitatively the main features of the magnetic structure factor measured experimentally. An alternative, more realistic numerical scenario is also proposed in which the ice condition is slightly detuned. In that case as well, the features evidenced in the experimental magnetic structure factor are only well-described when further neighbor couplings are taken into account. Our results show that long range dipolar interactions are not totally washed out in a field demagnetized artificial square ice, and cannot be neglected as they impact the magnetic correlations within or at the vicinity of the ice manifold., Comment: 9 pages, 8 figures

Arrays of interacting magnetic nanostructures were introduced recently as a powerful approach to investigate experimentally the exotic many-body physics of frustrated spin models. Following a similar strategy based on lithographically-patterned magnetic lattices, we provide a first attempt to fabricate a lab-on-chip platform to explore the physics of vertex models. The central idea of this work is to replace the spin degree of freedom of artificial frustrated spin systems by a local micromagnetic knob, which can be finely tuned by a proper design of the vertex geometry. This concept is demonstrated both numerically and experimentally on the celebrated six vertex model, and we show how all variants of this model can be apprehended through the engineering of magnetic square lattices. Our results open new avenues to design arrays of magnetic nanostructures not only to study a wide range of frustrated spin models, but to explore vertex models as well.

Since the seminal ideas of Berezinskii, Kosterlitz and Thouless, topological excitations are at the heart of our understanding of a whole novel class of phase transitions. In most of the cases, those transitions are controlled by a single type of topological objects. There are however some situations, still poorly understood, where two dual topological excitations fight to control the phase diagram and the transition. Finding experimental realization of such cases is thus of considerable interest. We show here that this situation occurs in BaCo$_2$V$_2$O$_8$, a spin-1/2 Ising-like quasi-one dimensional antiferromagnet when subjected to a uniform magnetic field transverse to the Ising axis. Using neutron scattering experiments, we measure a drastic modification of the quantum excitations beyond a critical value of the magnetic field. This quantum phase transition is identified, through a comparison with theoretical calculations, to be a transition between two different types of solitonic topological objects, which are captured by different components of the dynamical structure factor., Comment: 9 pages, 4 figures; 10 additional pages of supplemental information containing 6 figures

The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where frustration arises from the lattice geometry, here magnetic frustration originates from competing interactions between neighboring spins. By tuning continuously the strength and sign of these interactions, we show that different magnetic phases can be stabilized. Comparison between our experimental findings and predictions from the one-dimensional Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model reveals that artificial frustrated spin chains have a richer phase diagram than initially expected. Besides the observation of several magnetic orders and the potential extension of this work to highly-degenerated artificial spin chains, our results suggest that the micromagnetic nature of the individual magnetic elements allows observation of metastable spin configurations., Comment: 5 pages, 4 figures

The complexity embedded in condensed matter fertilizes the discovery of new states of matter, enriched by ingredients like frustration. Illustrating examples in magnetic systems are Kitaev spin liquids, skyrmions phases, or spin ices. These unconventional ground states support exotic excitations, for example the magnetic charges in spin ices, also called monopoles. Beyond their discovery, an important challenge is to be able to control and manipulate them. Here, we propose a new mechanism to inject monopoles in a spin ice through a staggered magnetic field. We show theoretically, and demonstrate experimentally in the Ho$_2$Ir$_2$O$_7$ pyrochlore iridate, that it results in the stabilization of a monopole crystal, which exhibits magnetic fragmentation. In this new state of matter, the magnetic moment fragments into an ordered part and a persistently fluctuating one. Compared to conventional spin ices, the different nature of the excitations in this fragmented state opens the way to novel tunable field-induced and dynamical behaviors.

In the spinel compound GeCo$_2$O$_4$, the Co$^{2+}$ pyrochlore sublattice presents remarkable magnetic field-induced behaviors that we unveil through neutron and X-ray single-crystal diffraction. The N\'eel ordered magnetic phase is entered through a structural lowering of the cubic symmetry. In this phase, when a magnetic field is applied along a 2-fold cubic direction, a spin-flop transition of one fourth of the magnetic moments releases the magnetic frustration and triggers magnetostructural effects. At high field, these ultimately lead to an unusual spin reorientation associated to structural changes.

Fractionalised excitations that emerge from a many body system have revealed rich physics and concepts, from composite fermions in two-dimensional electron systems, revealed through the fractional quantum Hall effect, to spinons in antiferromagnetic chains and, more recently, fractionalisation of Dirac electrons in graphene and magnetic monopoles in spin ice. Even more surprising is the fragmentation of the degrees of freedom themselves, leading to coexisting and a priori independent ground states. This puzzling phenomenon was recently put forward in the context of spin ice, in which the magnetic moment field can fragment, resulting in a dual ground state consisting of a fluctuating spin liquid, a so-called Coulomb phase, on top of a magnetic monopole crystal. Here we show, by means of neutron scattering measurements, that such fragmentation occurs in the spin ice candidate Nd$_2$Zr$_2$O$_7$. We observe the spectacular coexistence of an antiferromagnetic order induced by the monopole crystallisation and a fluctuating state with ferromagnetic correlations. Experimentally, this fragmentation manifests itself via the superposition of magnetic Bragg peaks, characteristic of the ordered phase, and a pinch point pattern, characteristic of the Coulomb phase. These results highlight the relevance of the fragmentation concept to describe the physics of systems that are simultaneously ordered and fluctuating., Comment: accepted in Nature Physics

We have investigated the low-temperature thermodynamic properties of the dipolar kagome Ising antiferromagnet using at-equilibrium Monte Carlo simulations, in the quest for the ground-state manifold. In spite of the limitations of a single spin-flip approach, we managed to identify certain ordering patterns in the low-temperature regime and we propose a candidate for this unknown state. This novel configuration presents some intriguing features and passes several test-criteria, making it a very likely choice for the dipolar long-range order of this kagome Ising antiferromagnet., Comment: 8 pages, 5 figures

The quasi-one-dimensional antiferromagnetic Ising-like compound BaCo2V2O8 has been shown to be describable by the Tomonaga-Luttinger liquid theory in its gapless phase induced by a magnetic field applied along the Ising axis. Above 3.9 T, this leads to an exotic field-induced low-temperature magnetic order, made of a longitudinal incommensurate spin-density wave, stabilized by weak interchain interactions. By single-crystal neutron diffraction we explore the destabilization of this phase at a higher magnetic field. We evidence a transition at around 8.5 T towards a more conventional magnetic structure with antiferromagnetic components in the plane perpendicular to the magnetic field. The phase diagram boundaries and the nature of this second field-induced phase are discussed with respect to previous results obtained by means of nuclear magnetic resonance and electron spin resonance, and in the framework of the simple model based on the Tomonaga-Luttinger liquid theory, which obviously has to be refined in this complex system., Comment: 7 pages, 5 figures

In this work, we show that the zero field excitation spectra in the quantum spin ice candidate pyrochlore compound \ybti\ is a continuum characterized by a very broad and almost flat dynamical response which extends up to $1-1.5$ meV, coexisting or not with a quasi-elastic response depending on the wave-vector. The spectra do not evolve between 50 mK and 2 K, indicating that the spin dynamics is only little affected by the temperature in both the short-range correlated and ordered regimes. Although classical spin dynamics simulations qualitatively capture some of the experimental observations, we show that they fail to reproduce this broad continuum. In particular, the simulations predict an energy scale twice smaller than the experimental observations. This analysis is based on a careful determination of the exchange couplings, able to reproduce both the zero field diffuse scattering and the spin wave spectrum rising in the field polarized state. According to this analysis, \ybti\ lies at the border between a ferro and an antiferromagnetic phase. These results suggest that the unconventional ground state of \ybti\ is governed by strong quantum fluctuations arising from the competition between those phases. The observed spectra may correspond to a continuum of deconfined spinons as expected in quantum spin liquids.

We investigate experimentally magnetic frustration effects in thermally active artificial kagome spin ice. Starting from a paramagnetic state, the system is cooled down below the Curie temperature of the constituent material. The resulting magnetic configurations show that our arrays are locally brought into the so-called spin ice 2 phase, predicted by at-equilibrium Monte Carlo simulations and characterized by a magnetic charge crystal embedded in a disordered kagome spin lattice. However, by studying our arrays on a larger scale, we find unambiguous signature of an out-of-equilibrium physics. Comparing our findings with numerical simulations, we interpret the efficiency of our thermalization procedure in terms of kinetic pathways that the system follows upon cooling and which drive the arrays into degenerate low-energy manifolds that are hardly accessible otherwise., Comment: 6 pages, 4 figures

Magnetic frustration effects in artificial kagome arrays of nanomagnets with out-of-plane magnetization are investigated using Magnetic Force Microscopy and Monte Carlo simulations. Experimental and theoretical results are compared to those found for the artificial kagome spin ice, in which the nanomagnets have in-plane magnetization. In contrast with what has been recently reported, we demonstrate that long range (i.e. beyond nearest-neighbors) dipolar interactions between the nanomagnets cannot be neglected when describing the magnetic configurations observed after demagnetizing the arrays using a field protocol. As a consequence, there are clear limits to any universality in the behavior of these two artificial frustrated spin systems. We provide arguments to explain why these two systems show striking similarities at first sight in the development of pairwise spin correlations., Comment: 7 pages, 6 figures

We explore the spin dynamics emerging from the N\'eel phase of the chain compound antiferromagnet BaCo2V2O8. Our inelastic neutron scattering study reveals unconventional discrete spin excitations, so called Zeeman ladders, understood in terms of spinon confinement, due to the interchain attractive linear potential. These excitations consist in two interlaced series of modes, respectively with transverse and longitudinal polarization. The latter have no classical counterpart and are related to the zero-point fluctuations that weaken the ordered moment in weakly coupled quantum chains. Our analysis reveals that BaCo2V2O8, with moderate Ising anisotropy and sizable interchain interactions, remarkably fulfills the conditions necessary for the observation of these longitudinal excitations., Comment: 5 pages, 4 figures, 2 additional pages of supplemental material with 2 figures; Journal ref. added; 1 page erratum added at the end with 1 figure

Condensed matter in the low temperature limit reveals much exotic physics associated with unusual orders and excitations, examples ranging from helium superfluidity to magnetic monopoles in spin ice. The far-from-equilibrium physics of such low temperature states may be even more exotic, yet to access it in the laboratory remains a challenge. Here we demonstrate a simple and robust technique, the 'magnetothermal avalanche quench', and its use in the controlled creation of nonequilibrium populations of magnetic monopoles in spin ice at millikelvin temperatures. These populations are found to exhibit spontaneous dynamical effects that typify far-from-equilibrium systems, yet are captured by simple models. Our method thus opens the door to the study of far-from-equilibrium states in spin ice and other exotic magnets., Comment: submitted version + suppl. info

Micromagnetic properties of monopoles in artificial kagome spin ice systems are investigated using numerical simulations. We show that micromagnetics brings additional complexity into the physics of these monopoles that is, by essence, absent in spin models: besides a fractionalized classical magnetic charge, monopoles in the artificial kagome ice are chiral at remanence. Our simulations predict that the chirality of these monopoles can be controlled without altering their charge state. This chirality breaks the vertex symmetry and triggers a directional motion of the monopole under an applied magnetic field. Our results also show that the choice of the geometrical features of the lattice can be used to turn on and off this chirality, thus allowing the investigation of chiral and achiral monopoles., Comment: 10 pages, 4 figures

The accuracy of finite difference methods is related to the mesh choice and cell size. Concerning the micromagnetism of nano-objects, we show here that discretization issues can drastically affect the symmetry of the problem and therefore the resulting computed properties of lattices of interacting curved nanomagnets. In this paper, we detail these effects for the multiaxe kagome lattice. Using the Oommf finite difference method, we propose an alternative way of discretizing the nanomagnet shape via a variable moment per cell scheme. This method is shown to be efficient in reducing discretization effects., Comment: 4 pages, 5 figures

We report on the magnetic properties of four isomorphous compounds of a family of quinternary oxalates down to 60 mK. In all these materials, the magnetic FeII ions with a strong magneto-crystalline anisotropy form a distorted kagome lattice, topologically equivalent to a perfect kagome one if nearest-neighbor interactions only are considered. All the compounds order at low temperature in an antiferromagnetic arrangement with magnetic moments at 120{\deg}. A remarkable magnetic behavior emerges below the N\'eel temperature in three compounds (with inter-kagome-layer Zr, Sn, Fe but not with Al): the spin anisotropy combined with a low exchange path network connectivity lead to domain walls intersecting the kagome planes through strings of free spins. These produce an unfamiliar slow spin dynamics in the ordered phase observed by AC susceptibility, evolving from exchange-released spin-flips towards a cooperative behavior on decreasing the temperature., Comment: 9 pages, 13 figures

The hole-doped kagome lattice of Cu2+ ions in LaCuO2.66 was investigated by nuclear quadrupole resonance (NQR), electron spin resonance (ESR), electrical resistivity, bulk magnetization and specific heat measurements. For temperatures above ~180 K, the spin and charge properties show an activated behavior suggestive of a narrow-gap semiconductor. At lower temperatures, the results indicate an insulating ground state which may or may not be charge ordered. While the frustrated spins in remaining patches of the original kagome lattice might not be directly detected here, the observation of coexisting non-magnetic sites, free spins and frozen moments reveals an intrinsically inhomogeneous magnetism. Numerical simulations of a 1/3-diluted kagome lattice rationalize this magnetic state in terms of a heterogeneous distribution of cluster sizes and morphologies near the site-percolation threshold.

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., Comment: 17 pages, 14 fig

We report magnetization and neutron scattering measurements down to 60 mK on a new family of Fe based kagome antiferromagnets, in which a strong local spin anisotropy combined with a low exchange path network connectivity lead to domain walls intersecting the kagome planes through strings of free spins. These produce unfamiliar slow spin dynamics in the ordered phase, evolving from exchange-released spin-flips towards a cooperative behavior on decreasing the temperature, probably due to the onset of long-range dipolar interaction. A domain structure of independent magnetic grains is obtained that could be generic to other frustrated magnets., Comment: 5 pages, 4 figures

We study the energy spectrum and electronic properties of graphene in a periodic magnetic field of zero average with a symmetry of triangular lattice. The periodic field leads to formation of a set of minibands separated by gaps, which can be manipulated by external field. The Berry phase, related to the motion of electrons in $k$ space, and the corresponding Chern numbers characterizing topology of the energy bands are calculated analytically and numerically. In this connection, we discuss the anomalous Hall effect in the insulating state, when the Fermi level is located in the minigap. The results of calculations show that in the model of gapless Dirac spectrum of graphene the anomalous Hall effect can be treated as a sum of fractional quantum numbers, related to the nonequivalent Dirac points., Comment: 6 pages, 5 figures

Magnetic frustration effects in artificial kagome arrays of nanomagnets are investigated using x-ray photoemission electron microscopy and Monte Carlo simulations. Spin configurations of demagnetized networks reveal unambiguous signatures of long range, dipolar interaction between the nanomagnets. As soon as the system enters the spin ice manifold, the kagome dipolar spin ice model captures the observed physics, while the short range kagome spin ice model fails., Comment: 4 pages, 4 figures, 1 table

Noncollinear frustrated magnets are proposed as a new class of spintronic materials with high magnetoresistance which can be controlled with relatively small applied voltages. It is demonstrated that their magnetic configuration strongly depends on position of the Fermi energy and applied voltage. The voltage induced control of noncollinear frustrated materials (VCFM) can be seen as a way to intrinsic control of colossal magnetoresistance (CMR) and is the bulk material counterpart of spin transfer torque concept used to control giant magnetoresistance in layered spin-valve structures., Comment: 4 pages, 4 figures

We investigate the classical spin dynamics of the kagome antiferromagnet by combining Monte Carlo and spin dynamics simulations. We show that this model has two distinct low temperature dynamical regimes, both sustaining propagative modes. The expected gauge invariance type of the low energy low temperature out of plane excitations is also evidenced in the non linear regime. A detailed analysis of the excitations allows to identify ghosts in the dynamical structure factor, i.e propagating excitations with a strongly reduced spectral weight. We argue that these dynamical extinction rules are of geometrical origin., Comment: 4+ pages, 4 figures. Accepted for publication in the Physical Review Letters

The macroscopic magnetic characterization of the Mn(II) - nitronyl nitroxide free radical chain (Mn(hfac)2(R)-3MLNN) evidenced its transition from a 1-dimensional behavior of ferrimagnetic chains to a 3-dimensional ferromagnetic long range order below 3 K. Neutron diffraction experiments, performed on a single crystal around the transition temperature, led to a different conclusion : the magnetic Bragg reflections detected below 3 K correspond to a canted antiferromagnet where the magnetic moments are mainly oriented along the chain axis. Surprisingly in the context of other compounds in this family of magnets, the interchain coupling is antiferromagnetic. This state is shown to be very fragile since a ferromagnetic interchain arrangement is recovered in a weak magnetic field. This peculiar behavior might be explained by the competition between dipolar interaction, shown to be responsible for the antiferromagnetic long range order below 3 K, and exchange interaction, the balance between these interactions being driven by the strong intrachain spin correlations. More generally, this study underlines the need, in this kind of molecular compounds, to go beyond macroscopic magnetization measurements., Comment: 12 pages, 10 figures, submitted to Phys. Rev. B

Low-temperature powder neutron diffraction measurements are performed in the ordered magnetic state of the pyrochlore antiferromagnet Gd2Sn2O7. Symmetry analysis of the diffraction data indicates that this compound has the ground state predicted theoretically for a Heisenberg pyrochlore antiferromagnet with dipolar interactions. The difference in magnetic structures of Gd2Sn2O7 and of nominally analogous Gd2Ti2O7 is found to be determined by a specific type of third-neighbor superexchange interaction on the pyrochlore lattice between spins across empty hexagons., Comment: 6 pages

In the R$\_{3}$Ga$\_{5}$SiO$\_{14}$ compounds, the network R of rare earth cations form well separated planes of corner sharing triangles topologically equivalent to a kagom\'e lattice. Powder samples and single crystals with R = Nd and Pr were prepared and magnetostatic measurements were performed under magnetic field up to 10 T in the temperature range from 1.6 K to 400 K. Analysis of the magnetic susceptibility at the high temperatures where only the quadrupolar term of the crystal electric field prevails, suggests that the Nd and Pr magnetic moments can be modeled as coplanar elliptic rotators perpendicular to the three fold axis of the crystal structure that interact antiferromagnetically. Nonetheless, a disordered phase that can be ascribed to geometric frustration persists down to the lowest temperature which is about 25 times smaller than the energy scale for the exchange interactions., Comment: 9 pages. 1 table, 5 figures. Accepted for publication in Journal of Physics : Condensed Matter. 2006

We study the energy spectrum of magnons in a ferromagnet with topologically nontrivial magnetization profile. In the case of inhomogeneous magnetization corresponding to a metastable state of ferromagnet, the spin-wave equation of motion acquires a gauge potential leading to a Berry phase for the magnons propagating along a closed contour. The effect of magnetic anisotropy is crucial for the Berry phase: we show that the anisotropy suppresses its magnitude, which makes the Berry phase observable in some cases, similar to the Aharonov-Bohm effect for electrons. For example, it can be observed in the interference of spin waves propagating in mesoscopic rings. We discuss the effect of domain walls on the interference in ferromagnetic rings, and propose some experiments with a certain geometry of magnetization. We also show that the nonvanishing average topological field acts on the magnons like a uniform magnetic field on electrons. It leads to the quantization of the magnon spectrum in the topological field., Comment: 8 pages, 5 figures

The Heisenberg nearest neighbour antiferromagnet on the pyrochlore (3D) lattice is highly frustrated and does not order at low temperature where spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions (DMI) may be present in pyrochlore compounds as is shown, and the consequences of such interactions on the magnetic properties are investigated through mean field approximation and monte carlo simulations. It is found that DMI (if present) tremendously change the low temperature behaviour of the system. At a temperature of the order of the DMI a phase transition to a long range ordered state takes place. The ordered magnetic structures are explicited for the different possible DMI which are introduced on the basis of symmetry arguments. The relevance of such a scenario for pyrochlore compounds in which an ordered magnetic structure is observed experimentally is dicussed.

We discuss the mechanism of anomalous Hall effect related to the contribution of electron states below the Fermi surface (induced by the Berry phase in momentum space). Our main calculations are made within a model of two-dimensional electron gas with spin-orbit interaction of the Rashba type, taking into account the scattering from impurities. We demonstrate that such an "intrinsic" mechanism can dominate but there is a competition with the impurity-scattering mechanism, related to the contribution of states in the vicinity of Fermi surface. We also show that the contribution to the Hall conductivity from electron states close to the Fermi surface has the intrinsic properties as well., Comment: 9 pages, 6 figures

Ordering by thermal fluctuations is studied for the classical XY antiferromagnet on a checkerboard lattice in zero and finite magnetic fields by means of analytical and Monte Carlo methods. The model exhibits a variety of novel broken symmetries including states with nematic ordering in zero field and with triatic order parameter at high fields., Comment: 6 pages

The $S=1/2$ Heisenberg antiferromagnet is studied on the kagom\'e lattice by using a Green's function method based on an appropriate decoupling of the equations of motion. Thermodynamic properties as well as spin-spin correlation functions are obtained and characterize this system as a two-dimensional quantum spin liquid. Spin-spin correlation functions decay exponentially with distance down to low temperature and the calculated missing entropy at T=0 is found to be $0.46\ln{2}$. Within the present scheme, the specific heat exhibits a single peak structure and a $T^2$ dependence at low temperature., Comment: 6 (two-column revtex4) pages, 5 ps figures. Submitted to Phys. Rev. B

The stability of the disordered ground state of the classical Heisenberg pyrochlore antiferromagnet is studied within extensive Monte Carlo simulations by introducing an additional exchange interaction $J'$ that interpolates between the pyrochlore lattice ($J'=0$) and the face-centered cubic lattice ($J'=J$). It is found that for $J'/J$ as low as $J'/J\ge 0.01$, the system is long range ordered : the disordered ground state of the pyrochlore antiferromagnet is unstable when introducing very small deviations from the pure $J'=0$ limit. Furthermore, it is found that the selected phase is a collinear state energetically greater than the incommensurate phase suggested by a mean field analysis. To our knowledge this is the first example where entropic selection prevails over the energetic one., Comment: 5 (two-column revtex4) pages, 1 table, 7 ps/eps figures. Submitted to Phys. Rev. B

Due to the particular geometry of the kagom\'e lattice, it is shown that antisymmetric Dzyaloshinsky-Moriya interactions are allowed and induce magnetic ordering. The symmetry of the obtained low temperature magnetic phases are studied through mean field approximation and classical Mont\'e Carlo simulations. A phase diagram relating the geometry of the interaction and the ordering temperature has been derived. The order of magnitude of the anisotropies due to Dzyaloshinsky-Moriya interactions are more important than in non-frustrated magnets, which enhances its appearance in real systems. Application to the jarosites compounds is proposed. In particular, the low temperature behaviors of the Fe and Cr-based jarosites are correctly described by this model., Comment: 6 (revtex4) twocolumn pages, 6 .eps figures. Submitted to Phys. Rev. B