Showing papers on "Landau theory published in 2004"
TL;DR: In this article, the magnetocaloric effect in ferromagnetic systems with magnetoelastic and magnetoelectronic couplings is described. And the existence of a broad magnetic entropy peak above T c is related to these couplings.
212 citations
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07 Jun 2004
TL;DR: Superconductivity: A brief overview of superconductivity can be found in this paper, where the authors present a diagram of the superconducting phase transition of a supercondensate.
Abstract: Preface.Acknowledgements.I: BASIC TOPICS.1. What is superconductivity? A brief overview.2. Superconducting materials.3. Fermi-liquids and attractive interactions.4.The superconducting state. An electronic condensate.5. Weak Links and Josephson Effects.6. London Approximation to Ginzburg-Landau Theory (constant).7. Applications of Ginzburg- Landau Theory (spatially varying).8. More on the Flux-line System.II: ADVANCED TOPICS.9. Two-dimensional superconductivity. Vortex-paired unbinding.10. Dual description of the superconducting phase transition.III: SELECTED APPLICATIONS.11. Small scale applications.12. Superconducting Wire and Cable Technology.IV: TOPICAL CONTRIBUTIONS.13. Topical Contributions.V: HISTORICAL NOTES.Historical notes on supeconductivity: the Nobel Laureates.References.Author Index.Subject Index.
117 citations
TL;DR: In this paper, a Ginzburg-Landau theory for the elastic properties of shape memory polycrystals is proposed, where a single crystal elastic free energy for a system that undergoes a square-to-rectangle transformation is generalized to a polycrystal by introducing a crystal orientational field that is determined from a continuum phase-field model.
83 citations
TL;DR: In this article, the authors point out a close relation between a family of Godel-type solutions of 3+1 general relativity and the Landau problem in and, in particular, the classical geodesics correspond to Larmor orbits in the Lau problem.
Abstract: We point out a close relation between a family of Godel-type solutions of 3+1 general relativity and the Landau problem in and ; in particular, the classical geodesics correspond to Larmor orbits in the Landau problem. We discuss the extent of this relation, by analysing the solutions of the Klein–Gordon equation in these backgrounds. For the case, this relation was independently noticed in hep-th/0306148. Guided by the analogy with the Landau problem, we speculate on the possible holographic description of a single chronologically safe region.
82 citations
TL;DR: In this article, a new inequality for the Jacobian associated to the Ginzburg-Landau energy in any dimension was proved, which allows to retrieve existing lower bounds on the energy, to extend them to the case of unbounded vorticity, and to get other corollaries.
80 citations
TL;DR: It is shown that critical spin fluctuations are stronger in Ni3Ga, due to weaker q dependence of the susceptibility, and this effect is enough to reverse the trend, and provide evidence for strong, beyond LDA, spin fluctuations associated with the critical point in both materials.
Abstract: Ni3Al and Ni3Ga are closely related materials on opposite sides of a ferromagnetic quantum critical point. The Stoner factor of Ni is virtually the same in both compounds and the density of states is larger in Ni3Ga. Thus in Stoner theory it should be more magnetic, and in local-density approximation (LDA) calculations it is. However, experimentally it is a paramagnet, while Ni3Al is an itinerant ferromagnet. We show that critical spin fluctuations are stronger in Ni3Ga, due to weaker q dependence of the susceptibility, and this effect is enough to reverse the trend. The approach combines LDA calculations with Landau theory and the fluctuation-dissipation theorem using the same momentum cutoff for both compounds. The calculations provide evidence for strong, beyond LDA, spin fluctuations associated with the critical point in both materials, but stronger in Ni3Ga than in Ni3Al.
76 citations
TL;DR: In this article, the authors established the connection between the presence of a glass phase and the appearance of a Coulomb gap in disordered materials with strongly interacting electrons, and showed that in the case of strong disorder, a continuous glass transition takes place whose Landau expansion is identical to that of the Sherrington-Kirkpatrick spin glass.
Abstract: We establish the connection between the presence of a glass phase and the appearance of a Coulomb gap in disordered materials with strongly interacting electrons. Treating multiparticle correlations in a systematic way, we show that in the case of strong disorder a continuous glass transition takes place whose Landau expansion is identical to that of the Sherrington-Kirkpatrick spin glass. We show that the marginal stability of the glass phase controls the physics of these systems: it results in slow dynamics and leads to the formation of a Coulomb gap.
67 citations
TL;DR: In this paper, a vibrational mode that breaks half of the interslab silicon dimers and rotates slabs in the monoclinic structure, thus lowering the symmetry from Pnma to P112 1 /a, has been identified using Landau theory.
Abstract: Temperature-dependent single crystal x-ray-diffraction studies revealed a reversible first-order phase transition in Er 5 Si 4 . The high-temperature phase adopts the orthorhombic Gd 5 Si 4 -type structure, and the low-temperature phase has the monoclinic Gd 5 Si 2 Ge 2 -type structure. Unlike the magnetic/martensitic transition in Gd 5 Si 2 Ge 2 , the structural change in Er 5 Si 4 is not coupled with a magnetic transition, and the structural sequence below room temperature is just the reverse. A vibrational mode that breaks half of the interslab silicon dimers and rotates slabs in the monoclinic structure, thus lowering the symmetry from Pnma to P112 1 /a, has been identified using Landau theory. While the monoclinic phase is electronically stabilized at low temperatures, the orthorhombic phase is entropically preferable at high temperatures.
59 citations
TL;DR: In this article, the tip-induced domain switching can be mapped on the Landau theory of phase transitions with the domain size as an order parameter, and the authors proposed that the early stages of the nucleation process when domain size is comparable with the tip radius of curvature requires exact field structure to be taken into account.
Abstract: Nanoscale polarization switching in ferroelectric materials by Piezoresponse Force Microscopy (PFM) in weak and strong indentation limits is analyzed using exact solutions for electrostatic and coupled electroelastic fields below the tip. It is proposed that the tip-induced domain switching can be mapped on the Landau theory of phase transitions with the domain size as an order parameter. For a point charge interacting with a ferroelectric surface, switching of both first and second order is possible depending on the charge-surface separation. For a realistic tip shape, the domain nucleation process is first order in charge magnitude and polarization switching occurs only above a critical tip bias. In pure ferroelectric or ferroelastic switching, the late stages of the switching process can be described using point charge/force model and arbitrarily large domains can be created; however, the description of the early stages of nucleation process when domain size is comparable with the tip radius of curvature requires exact field structure to be taken into account.
55 citations
TL;DR: In this paper, a spin transition is described as an isostructural transition with a totally symmetric order parameter, and the resulting phase diagrams are in good qualitative agreement with experiments.
Abstract: We analyze spin transitions in molecular crystals with the help of Landau theory. Experimental observations show that a pure spin transition may be described as an isostructural transition with a totally symmetric order parameter. For long-range ordering of different spin states, a model is developed in which the spin transition is coupled with a structural transformation. The resulting phase diagrams are in good qualitative agreement with experiments.
55 citations
TL;DR: In this article, an extension to the phenomenological thermodynamic Landau-Devonshire theory was proposed to include the contribution of inhomogeneous strains caused by lattice defects to the Gibbs free energy.
Abstract: We propose an extension to the phenomenological thermodynamic Landau-Devonshire theory to include the contribution of inhomogeneous strains caused by lattice defects to the Gibbs free energy. The model yields correction terms for dielectric and ferroelectric quantities as a function of both elastic misfit strain and defectrelated strain that can be measured by x-ray-diffraction techniques. We compare the correction in Curie-Weiss temperature due to elastic and inhomogeneous strain in pristine, W and Mn 1% doped Ba 0.6Sr0.4TiO3 thin films grown on the LaAlO3 substrate. If the contribution of inhomogeneous strain is included, the agreement with measurements markedly improves.
TL;DR: In this paper, a microscopic model based on optical spectroscopy and x-ray diffraction was proposed to explain the displacive phase transition observed in monoclinic zirconia after irradiation.
Abstract: Optical spectroscopy and x-ray diffraction were used to study the behavior of polycrystalline samples of pure monoclinic zirconia irradiated by low energy ions. A microscopic model based on these experiments is proposed to explain the displacive phase transition observed in this material after irradiation. Defects, produced in the oxygen sublattice, induce important strain fields on a nanometric scale. This strain field can be handled as a secondary order parameter within the Landau theory approach, leading to a decrease of the phase transition temperature and thus quenching the high temperature tetragonal phase. The model also explains the consequences of the thermal annealing for restoring the ground state monoclinic structure.
TL;DR: In this paper, the Ginzburg-Landau system was shown to be constant in the case n = M⩾3 and N = M ⩾4.
TL;DR: In this article, the magnetic properties of the weak itinerant ferromagnet were analyzed using Landau theory based on a comparison of density-functional calculations and experimental data as a function of field and pressure.
Abstract: The magnetic properties of the weak itinerant ferromagnet ${\mathrm{ZrZn}}_{2}$ are analyzed using Landau theory based on a comparison of density-functional calculations and experimental data as a function of field and pressure. We find that the magnetic properties are strongly affected by the nearby quantum critical point, even at zero pressure; local-density approximation LDA calculations neglecting quantum critical spin fluctuations overestimate the magnetization by a factor of $\ensuremath{\approx}3.$ Using renormalized Landau theory, we extract pressure dependence of the fluctuation amplitude. It appears that a simple scaling based on the fluctuation-dissipation theorem provides a good description of this pressure dependence.
TL;DR: In this article, the authors developed a substantially modified Landau theory approach for analytically studying phase transitions between different spin arrangements in circular sub-micron magnetic dots subject to an in-plane externally-applied magnetic field.
Abstract: Using the rigid magnetic vortex model, we develop a substantially modified Landau theory approach for analytically studying phase transitions between different spin arrangements in circular sub-micron magnetic dots subject to an in-plane externally-applied magnetic field. We introduce a novel order parameter: the inverse distance between the center of the circular dot and the vortex core. This order parameter is suitable for describing closed spin configurations such as curved or bent-spin structures and magnetic vortices. Depending on the radius and thickness of the dot as well as the exchange coupling, there are five different regimes for the magnetization reversal process when decreasing the in-plane magnetic field. The magnetization-reversal regimes obtained here cover practically all possible magnetization reversal processes. Moreover, we have derived the change of the dynamical response of the spins near the phase transitions and obtained a “critical slowing down” at the second order phase transition from the high-field parallel-spin state to the curved (C-shaped) spin phase. We predict a transition between the vortex and the parallel-spin state by quickly changing the magnetic field --providing the possibility to control the magnetic state of dots by changing either the value of the external magnetic field and/or its sweep rate. We study an illuminating mechanical analog (buckling instability) of the transition between the parallel-spin state and the curved spin state (i.e., a magnetic buckling transition). In analogy to the magnetic-disk case, we also develop a modified Landau theory for studying mechanical buckling instabilities of a compressed elastic rod embedded in an elastic medium. We show that the transition to a buckled state can be either first or second order depending on the ratio of the elasticity of the rod and the elasticity of the external medium. We derive the critical slowing down for the second-order mechanical buckling transition.
TL;DR: In this article, a perturbation expansion method based on the Fourier expansion and the Floquet theorem is proposed for phase diagrams on dynamical symmetry breaking, which is caused by varying the amplitude h or frequency h cos (Ω t ) in systems under the Landau type potentials.
Abstract: We propose a systematic perturbation expansion method for getting phase diagrams on dynamical symmetry breaking which is caused by varying the amplitude h or frequency Ω of the periodic external force h cos (Ω t ) in systems under the Landau type potentials. The method is based on the Fourier expansion and the Floquet theorem. We formulate the method by utilizing an introductory example, bistable system driven by the periodic external force. An order estimation criterion based on the magnitude of the Fourier coefficient for the fundamental frequency Ω plays an essential role in order to construct the systematic expansion method. According to the criterion, analytical expressions for the transition point and weak nonlinear expansions (Landau type expansions) near the transition point are derived in desired orders of approximation. We also show two applications of the method: the dynamical symmetry breaking in the XY-spin system with uniaxial anisotropy and tristable system at the presence of the forcing. T...
TL;DR: The cubic to tetragonal phase transition in the solid solution K(Mn,Ca)F3 has been investigated by conduction calorimetry and x-ray diffraction as discussed by the authors.
Abstract: The cubic to tetragonal phase transition in the solid solution K(Mn,Ca)F3 has been investigated by conduction calorimetry and x-ray diffraction. The behaviour of the excess specific heat, latent heat and spontaneous strain has been explained in terms of a 2–4–6 Landau potential. The coefficients A and C, prefactors of Q2 and Q6 in the free energy expansion, are practically constant with composition, but B (the prefactor of Q4) and TC are functions of composition. The tricritical point occurs when the sign of B changes from negative (in pure KMnF3) to positive (in Ca rich samples). However, the variation of the parameters B and TC with dopant concentration x is non-linear. The dependence of TC with composition is explained in terms of an internal stress due to the doping ion of Ca and is compared with the effect of external uniaxial stress on pure KMnF3.
TL;DR: In this article, the second-order phase transition for coupled soft modes of Ca1−xPbxTiO3 solid solutions is investigated in the frequency range ν=7-1000 cm−1 at temperatures from 5 to 300 K using IR Fourier spectroscopy and submillimeter-range techniques.
Abstract: Dielectric spectra ɛ′(ν) and ɛ″(ν) of Ca1−xPbxTiO3 ceramic samples (x=0, 0.15, 0.2, 0.4) have been studied in the frequency range ν=7–1000 cm−1 at temperatures from 5 to 300 K using IR Fourier spectroscopy and submillimeter-range techniques. In the low-frequency range, polar phonons were established to undergo temperature-induced evolution. The results obtained are discussed in terms of the Landau theory of second-order phase transitions for coupled soft modes. The existence of one (or several) phase state(s) in the intermediate concentration region of Ca1−xPbxTiO3 solid solutions is tentatively assumed.
TL;DR: In this paper, a simplifying criterion based on singularity theory is proposed for phase transitions in the Lie-Poincare theory of phase transitions. But when one considers a range of values, in particular near a phase transition, the criterion has to be accordingly partially modified, as we discuss.
TL;DR: The problem of nonlinear transport near a quantum phase transition is solved within the Landau theory for the dissipative insulator-superconductor phase transition in two dimensions using the nonequilibrium Schwinger round-trip Green function formalism and the scaling function for the nonlinear conductivity in the quantum-disordered regime is obtained.
Abstract: The problem of nonlinear transport near a quantum phase transition is solved within the Landau theory for the dissipative insulator-superconductor phase transition in two dimensions. Using the nonequilibrium Schwinger round-trip Green function formalism, we obtain the scaling function for the nonlinear conductivity in the quantum-disordered regime. We find that the conductivity scales as E2 at low fields but crosses over at large fields to a universal constant on the order of e(2)/h. The crossover between these two regimes obtains when the length scale for the quantum fluctuations becomes comparable to that of the electric field within logarithmic accuracy.
TL;DR: A Landau theory for surface enhanced ordering in free-standing smectic-A films is described, based on a generalization of de Gennes's "presmectic" model to systems which undergo a first-order smectics-isotropic transition in bulk.
Abstract: A Landau theory for surface enhanced ordering in free-standing smectic-$A$ films is described, based on a generalization of de Gennes's ``presmectic'' model to systems which undergo a first-order smectic-isotropic transition in bulk. As found in related work on phase transitions in thin films, the system exhibits three phases, an isotropic liquid, a bulk-like ordered (smectic-$A$) phase, and a surface-ordered (``quasismectic'') phase. Over much of its range, the temperature-thickness boundary between the bulk-ordered and surface-ordered phases is effectively characterized by a power-law relation similar to those observed for layer-thinning transitions in overheated free-standing smectic-$A$ films.
TL;DR: In this article, the spin-glass-to-paramagnet transition of the transverse degrees of freedom in the presence of a finite longitudinal field is investigated, and two complementary techniques, the Landau theory close to the T=0 transition and the exact diagonalization method for finite systems, are used to estimate the size of the critical region.
Abstract: The quantum critical behavior of the Ising glass in a magnetic field is investigated. We focus on the spin-glass-to-paramagnet transition of the transverse degrees of freedom in the presence of a finite longitudinal field. We use two complementary techniques, the Landau theory close to the T=0 transition and the exact diagonalization method for finite systems. This allows us to estimate the size of the critical region and characterize various crossover regimes. An unexpectedly small energy scale on the disordered side of the critical line is found, and its possible relevance to experiments on metallic glasses is briefly discussed.
TL;DR: In this article, a survey of existing phenomenological approaches in interpreting first and second-order thermodynamic phase transitions is given, including Ehrenfest's classification, the Justi-von Laue approach, and Landau's order parameter theory.
Abstract: An attempt is made to apply to the glass transition the formalism, developed by Landau to describe thermodynamic phase transitions. The results obtained show that this classical approach opens a new way of understanding and describing vitrification. The glass transition is compared with the thermodynamics and kinetics of ‘normal’, i.e. thermodynamic phase transitions. A survey is given of existing phenomenological approaches in interpreting first and second-order thermodynamic phase transitions: Ehrenfest’s classification, the Justi–von Laue approach, Landau’s order parameter theory. The principal differences between thermodynamic phase transitions and the glass transition (as a thermodynamic/non-thermodynamic or as an ergodic/non-ergodic change) are pointed out, using Landau’s phenomenological approach. In this way a new, generalized possibility is found in analyzing glass transitions using appropriately chosen Taylor expansions of the thermodynamic potentials. A previously employed generic thermodynamic formalism to describe the kinetics of glass transitions, derived in the framework of the Bragg–Williams equation, is also applied, using Landau’s approach.
TL;DR: In this paper, a Landau expansion in the local rotation, non-order-parameter strains and the local energy density of tetragonal-orthorhombic ferroelastic structures is studied.
Abstract: Domain patterns in several classes of ferroelastics are studied using a Landau expansion in the strains and their derivatives. Examination of the local rotation, the non-order-parameter strains and the local energy density reveals the wedge and other disclinations responsible for the complexity of the patterns in (1) tetragonal-orthorhombic materials, and (2) hexagonal-orthorhombic and related materials. At temperatures where the parent phase is unstable and so has negative stiffness, simulations of hexagonal-orthorhombic systems yield pockets where the order parameter is much reduced; if the parent phase exists experimentally under these conditions, it might give rise to extreme damping. For cubic-tetragonal materials, perturbing the parent phase at a temperature well below its stability limit gives an inhomogeneous noncompact product.
TL;DR: The phase transition is nonconvergent, ferroelastic, pure and proper in hexacelsianLTA and FAU zeolites, as described in this paper, where Gibbs free energy (G), entropy (S) and enthalpy (H) are obtained through the Landau theory of phase transition.
Abstract: Temperature-induced structure and microstructure changes in hexacelsians (BaAl2Si2O8) that have been synthesised from the Ba-exchanged LTA and FAU zeolites (hexacelsianLTA and hexacelsianFAU) show that the phase transition near 580 K exists only in hexacelsianLTA. The X-ray powder diffraction method has been used to follow the evolution of the structure during the phase transition, as described here. The excess thermodynamic quantities Gibbs free energy (G), entropy (S) and enthalpy (H) are obtained through the Landau theory of phase transition. The constants of proportionality between the G and ordering parameter (Q) are: h = −170345 J mol−1, a = −66.6 J mol−1 K−1 and b = −410534 J mol−1. The abrupt change in the trigonal distortion of the single six-member tetrahedral [SiO4]4− and [AlO4]5− ring near 580 K is responsible for the phase transition. The phase transition is non-convergent, ferroelastic, pure and proper.
TL;DR: In this article, the magnetocaloric properties of manganites with ferromagnetic and charge-ordering states are studied. And the physical mechanisms that contribute to the magnetic entropy and its temperature dependence are discussed in terms of the Landau theory for phase transitions.
Abstract: A study of the magnetocaloric properties of manganites with ferromagnetic and chargeordering states is presented. Under the application of a magnetic field in the vicinity of the paramagnetic-ferromagnetic and paramagnetic-charge order transitions large changes of the magnetic entropy are found, negative or positive, respectively. The physical mechanisms that contribute to the magnetic entropy and its temperature dependence are described and in the ferromagnetic case, discussed in terms of the Landau theory for phase transitions.
TL;DR: In this article, the shape fluctuations due to thermal effects in the giant dipole resonance (GDR) observables are calculated using the exact free energies evaluated at fixed spin and temperature.
Abstract: The shape fluctuations due to thermal effects in the giant dipole resonance (GDR) observables are calculated using the exact free energies evaluated at fixed spin and temperature. The results obtained are compared with Landau theory calculations done by parameterizing the free energy. The Landau theory is found to be insufficient when the shell effects are dominating.
TL;DR: In this paper, the authors make a step forward in the direction of incorporating superconductivity and study the mutual effects of this phase and antiferromagnetism in the phase diagram of heavy-fermion metals.
Abstract: The competition between magnetism and Kondo effect is the main effect determining the phase diagram of heavy-fermion systems. It gives rise to a quantum critical point which governs the low temperature properties of these materials. However, experimental results made it clear that a fundamental ingredient is missing in this description, namely superconductivity. In this paper we make a step forward in the direction of incorporating superconductivity and study the mutual effects of this phase and antiferromagnetism in the phase diagram of heavy-fermion metals. Our approach is based on a Ginzburg\char21{}Landau theory describing superconductivity and antiferromagnetism in a metal with quantum corrections taken into account through an effective potential. The proximity of an antiferromagnetic instability extends the region of superconductivity in the phase diagram and drives this transition into a first order one. On the other hand superconducting quantum fluctuations near a metallic antiferromagnetic quantum critical point give rise to a first order transition from a low moment to a high moment state in the antiferromagnet. Antiferromagnetism and superconductivity may both collapse at a quantum bicritical point whose properties we calculate.
TL;DR: In this article, an exact formalism for the relativistic version of Landau theory of Fermi liquid in presence of strong quantizing magnetic field is developed, both direct and exchange type interactions with scalar and vector coupling cases are considered.
TL;DR: In this paper, a two-dimensional Ginzburg-Landau model for superconductors with ferromagnetic ordering in the superconducting phase is considered, where the magnetic field is directly coupled to a vector-valued order parameter in the energy functional.
Abstract: We consider a two-dimensional Ginzburg–Landau model for superconductors which exhibit ferromagnetic ordering in the superconducting phase, introduced by physicists to describe unconventional p-wave superconductors. In this model the magnetic field is directly coupled to a vector-valued order parameter in the energy functional. We show that one effect of spin coupling is to increase the second critical field Hc2, the value of the applied magnetic field at which superconductivity is lost in the bulk. Indeed, when the spin coupling is strong we show that the upper critical field is no longer present, confirming predictions in the physics literature. We treat the energy density as a measure, and show that the order parameter converges (as the Ginzburg–Landau parameter κ→∞) in an average sense to a constant determined by the average energy.