Geometry fluctuations and Casimir effect in a quantum antiferromagnet

We show the presence of a Casimir type force between domain walls in a two dimensional Heisenberg antiferromagnet subject to geometrical fluctuations. The type of fluctuations that we consider, called phason flips, are well known in quasicrystals, but less so in periodic structures. As the classical ground state energy of the antiferromagnet is unaffected by this type of fluctuation, energy changes are purely of quantum origin. We calculate the effective interaction between two parallel domain walls, defining a slab of thickness d, in such an antiferromagnet within linear spin wave theory. The interaction is anisotropic, and for a particular orientation of the slab we find that it decays as 1/d, thus, more slowly than the electromagnetic Casimir effect in the same geometry.Comment: 5 pages, 5 figures, minor modifications, accepted for publication in EPJ

A phason disordered two dimensional quantum antiferromagnet

We examine a novel type of disorder in quantum antiferromagnets. Our model consists of localized spins with antiferromagnetic exchanges on a bipartite quasiperiodic structure, which is geometrically disordered in such a way that no frustration is introduced. In the limit of zero disorder, the structure is the perfect Penrose rhombus tiling. This tiling is progressively disordered by augmenting the number of random "phason flips" or local tile-reshuffling operations. The ground state remains N\'eel ordered, and we have studied its properties as a function of increasing disorder using linear spin wave theory and quantum Monte Carlo. We find that the ground state energy decreases, indicating enhanced quantum fluctuations with increasing disorder. The magnon spectrum is progressively smoothed, and the effective spin wave velocity of low energy magnons increases with disorder. For large disorder, the ground state energy as well as the average staggered magnetization tend towards limiting values characteristic of this type of randomized tilings.Comment: 5 pages, 7 figure

Geometry fluctuations in a two-dimensional quantum antiferromagnet

The paper considers the effects of random fluctuations of the local spin connectivities (fluctuations of the geometry) on ground state properties of a two-dimensional quantum antiferromagnet. We analyse the behavior of spins described by the Heisenberg model as a function of what we call phason flip disorder, following a terminology used for aperiodic systems. The calculations were carried out both within linear spin wave theory and using quantum Monte Carlo simulations. An "order by disorder" phenomenon is observed in this model, wherein antiferromagnetism is found to be enhanced by phason disorder. The value of the staggered order parameter increases with the number of defects, accompanied by an increase in the ground state energy of the system.Comment: 5 pages, 7 figures. Shortened and corrected version (as accepted for publication in Physical Review B

Electronic Structure and Transport in Approximants of the Penrose Tiling

Proceedings of the 12th International Conference on Quasicrystal. 4 pagesInternational audienceWe present numerical calculations of electronic structure and transport in the Penrose approximants. The electronic structure of perfect approximants shows a spiky density of states and a tendency to localization that is more pronounced in the middle of the band. Near the band edges the behavior is more similar to that of free electrons. These calculations of band structure and in particular the band scaling suggest an anomalous quantum diffusion when compared to normal ballistic crystals. This is con firmed by a numerical calculation of quantum diffusion which shows a crossover from normal ballistic propagation at long times to anomalous, possibly insulator-like, behavior at short times. The time scale t∗(E) for this crossover is computed for several approximants and is detailed. The consequences for electronic conductivity are discussed in the context of the relaxation time approximation. The metallic-like or non-metallic-like behavior of the conductivity is dictated by the comparison between the scattering time due to defects and the time scale t∗(E)

Spin waves and local magnetizations on the Penrose tiling

We consider a Heisenberg antiferromagnet on the Penrose tiling, a quasiperiodic system having an inhomogeneous Neel-ordered ground state. Spin wave energies and wavefunctions are studied in the linear spin wave approximation. A linear dispersion law is found at low energies, as in other bipartite antiferromagnets, with an effective spin wave velocity lower than in the square lattice. Spatial properties of eigenmodes are characterized in several different ways. At low energies, eigenstates are relatively extended, and show multifractal scaling. At higher energies, states are more localized, and, depending on the energy, confined to sites of a specified coordination number. The ground state energy of this antiferromagnet, and local staggered magnetizations are calculated. Perpendicular space projections are presented in order to show the underlying simplicity of this "complex" ground state. A simple analytical model, the two-tier Heisenberg star, is presented to explain the staggered magnetization distribution in this antiferromagnetic system.Comment: 14 pages, 21 figure

Heisenberg antiferromagnetic model on 2D quasiperiodic tilings

The Penrose tiling is a perfectly ordered two dimensional structure with fivefold symmetry and scale invariance. Quantum spin models on such a system can be expected to differ significantly from more conventional structures as a result of its special symmetries. We considered a Heisenberg antiferromagnet on the Penrose rhombus tiling, and showed it has an inhomogeneous Neel-ordered ground state. Spin wave energies and wavefunctions were studied in the linear spin wave approximation. A linear dispersion law was found at low energies, as in other bipartite antiferromagnets, with an effective spin wave velocity lower than in the square lattice. Spatial properties of eigenmodes were characterized in several different ways. At low energies, eigenstates were found to be relatively extended, and appeared to show multifractal scaling. At higher energies, states were found to be more localized, and, depending on the energy, confined to sites of a specified coordination number. The ground state energy of this antiferromagnet, and local staggered magnetizations were calculated. Perpendicular space projections were shown, showing the underlying simplicity of this “complex" ground state. A simple analytical model, the two-tier Heisenberg star, was presented to explain the staggered magnetization distribution in this antiferromagnetic system. The effects of a novel type of disorder in a two dimensional quantum antiferromagnet is considered. The original bipartite structure is geometrically disordered in such a way that no frustration is introduced, and the system retains a Néel ordered ground state. We show, using a linear spin wave expansion and Quantum Monte Carlo, that the staggered moment decreases exponentially as a function of increasing disorder. The spatial distribution of staggered magnetizations becomes more homogeneous compared to the deterministic tiling, the effective spin wave velocity increases with disorder, and singularities in the magnon spectrum and wavefunctions are partly smoothed. For large disorder, the ground state energy as well as the average staggered magnetization appear to tend to a limiting value characteristic of these randomized tilings. These results are discussed and compared with the behavior found in disordered periodic lattices.Le pavage de Penrose est une structure quasipériodique bidimensionnelle, utilisée dans la description des composés quasicristallins. Cette structure est parfaitement ordonnée, avec une symétrie de rotation cinq et elle est invariante sous un changement d'échelle par un facteur $\tau$ (le nombre d'or). On s'attend à ce que les propriétés d'un modèle d'antiferromagnétisme dans un tel système diffèrent nettement de celles des antiferromagnétiques périodiques. Nous avons étudié les propriétés d'un modèle d'Heisenberg sur le pavage de Penrose construit à partir de losanges, en utilisant une méthode de développement en ondes de spin. Les énergies et fonctions d'ondes des magnons (quantum d'une onde des spins) ont été étudiées dans le cadre d'une théorie linéarisée. A basse énergie, on trouve une loi de dispersion linéaire, comme dans d'autres antiferromagnetiques bipartites, avec une vitesse effective de l'onde de spin inférieure à celle d'un réseau carré équivalent. Les propriétés spatiales des modes propres ont été étudiées en détail. A basse énergie, nous trouvons que les états propres sont relativement étendus. Une analyse multifractale montre qu'ils sont de type “critique”, ayant une distribution d'exposants multifractaux. Aux énergies plus élevées, les états deviennent plus localisés, et, en fonction de l'énergie, l'amplitude de la fonction d'onde est non-nulle autour d'un sous-ensemble de sites d'une valeur de coordinence donnée. L'énergie de l'état fondamental de cette antiferromagnetique, et la distribution des aimantations locales dans cet état ont été calculés. Des projections dans l'espace perpendiculaire montrent la simplicité sous-jacente de ce état "complexe". Un simple modèle analytique, l'étoile de Heisenberg à deux niveaux, a été présenté pour expliquer de la distribution d'aimantation locales dans ce système antiferromagnétique.Dans une dernière partie, les effets de désordre de type “phason” sont considérés. Nous avons progressivement augmenté le désordre géometrique de la structure originale. Nous avons trouvé que l'etat fondamental conserve son ordre de Néel, mais que la forme de la distribution ainsi que la norme des aimantations sont modifiés. Nous montrons, à l'aide d'un développement en ondes des spin ainsi que par Quantum Monte Carlo, que l'aimantation alternée diminue exponentiellement vers une valeur asymptote en fonction du désordre. La distribution spatiale de magnetizations locales devient plus homogène par rapport à pavage parfait. La vitesse des ondes des spin augmente avec le désordre, et les singularités dans le spectre et les functions d'onde sont en partie lissées. Ces résultats sont comparés avec des résultats connus dans des systèmes désordonnés

Heisenberg antiferromagnétique model sur le pavage quasicrystaux bidimensionnelle

Le pavage de Penrose est une structure quasipériodique bidimensionnelle, utilisée dans la description des composés quasicristallins. Cette structure est parfaitement ordonnée, avec une symétrie de rotation cinq et elle est invariante sous un changement d'échelle par un facteur . Nous avons étudié les propriétés d'un modèle d'Heisenberg sur le pavage de Penrose construit à partir de losanges, en utilisant une méthode de développement en ondes de spin. Les énergies et fonctions d'ondes des magnons (quantum d'une onde des spins) ont été étudiées dans le cadre d'une théorie linéarisée. Les propriétés spatiales des modes propres ont été étudiées en détail. A basse énergie, nous trouvons que les états propres sont relativement étendus. Une analyse multifractale montre qu'ils sont de type critique , ayant une distribution d'exposants multifractaux. L'énergie de l état fondamental de cette antiferromagnetique, et la distribution des aimantations locales dans cet état ont été calculés. Des projections dans l espace perpendiculaire montrent la simplicité sous-jacente de ce état "complexe". Un simple modèle analytique, l étoile de Heisenberg à deux niveaux, a été présenté pour expliquer de la distribution d'aimantation locales dans ce système antiferromagnétique. Dans une dernière partie, les effets de désordre de type phason sont considérés. Nous avons progressivement augmenté le désordre géometrique de la structure originale. Nous montrons, à l'aide d'un développement en ondes des spin ainsi que par QMC, que l'aimantation alternée diminue exponentiellement vers une valeur asymptote en fonction du désordre. La vitesse des ondes des spin augmente avec le désordre.The Penrose tiling is a perfectly ordered two dimensional structure with fivefold symmetry and scale invariance. We considered a Heisenberg antiferromagnet on the Penrose rhombus tiling, and showed it has an inhomogeneous Neel-ordered ground state. Spin wave energies and wavefunctions were studied in the linear spin wave approximation. Spatial properties of eigenmodes were characterized in several different ways. At low energies, eigenstates were found to be relatively extended, and appeared to show multifractal scaling. At higher energies, states were found to be more localized, and, depending on the energy, confined to sites of a specified coordination number. The ground state energy of this antiferromagnet, and local staggered magnetizations were calculated. Perpendicular space projections were shown, showing the underlying simplicity of this complex" ground state. A simple analytical model, the two-tier Heisenberg star, was presented to explain the staggered magnetization distribution in this antiferromagnetic system. The effects of a novel type of disorder in a two dimensional quantum antiferromagnet is considered. The original bipartite structure is geometrically disordered in such a way that no frustration is introduced, and the system retains a Neel ordered ground state. We show, using a linear spin wave expansion and QMC, that the staggered moment decreases exponentially as a function of increasing disorder. The spatial distribution of staggered magnetizations becomes more homogeneous compared to the deterministic tiling, the effective spin wave velocity increases with disorder, and singularities in the magnon spectrum and wavefunctions are partly smoothed.ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF

Phase-field modeling of polycrystalline solidification, from needle crystals to spherulites: a review

Advances in the orientation-field-based phase-field (PF) models made in the past are reviewed. The models applied incorporate homogeneous and heterogeneous nucleation of growth centers and several mechanisms to form new grains at the perimeter of growing crystals, a phenomenon termed growth front nucleation. Examples for PF modeling of such complex polycrystalline structures are shown as impinging symmetric dendrites, polycrystalline growth forms (ranging from disordered dendrites to spherulitic patterns), and various eutectic structures, including spiraling two-phase dendrites. Simulations exploring possible control of solidification patterns in thin films via external fields, confined geometry, particle additives, scratching/piercing the films, etc. are also displayed. Advantages, problems, and possible solutions associated with quantitative PF simulations are discussed briefly