Showing papers on "Landau theory published in 1999"
124 citations
TL;DR: In this article, the authors study the effects of an applied magnetic field on a superconductor and estimate the value of the upper critical magnetic field HC3 at which superconductivity can nucleate.
119 citations
TL;DR: In this paper, the eigenvalue problems for the Ginzburg-Landau operator with a large parameter in bounded domains in R2 under gauge invariant boundary conditions are studied.
Abstract: In this paper we study the eigenvalue problems for the Ginzburg–Landau operator with a large parameter in bounded domains in R2 under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunctions is discussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity.
104 citations
TL;DR: In this paper, the antiferroelastic phase transition in strontium titanate was analyzed using a Landau free energy of the form ΔG = 1/2Aθs (cothθ s/Tc-colb.θ/T)Q2 + 1/4BQ 4 + 1 /6CQ 6, with A = 0·6472 J K−1mol−1, B = 29·12 Jmol− 1, C = 39·27 Jmol, T c= 105·6 K, �
Abstract: Existing experimental data for the antiferroelastic phase transition in strontium titanate are reviewed and analysed using a Landau free energy of the form ΔG = 1/2Aθs (cothθs/ Tc-colb.θ/T)Q2 + 1/4BQ 4 + 1/6CQ 6, with A = 0·6472 J K−1mol−1, B = 29·12 Jmol−1, C = 39·27 Jmol, T c= 105·6 K, θ S = 60·8 K. The temperature dependence of the critical exponent is found to be due to the delicate balance between the Q 4 and Q 6 terms in the free energy expansion, and the saturation of the order parameter at low temperatures. The spontaneous strains observed in this phase transition are not consistent with simple rotation of the TiO6 octahedra around [001], An alternative model is proposed, where these octahedra expand in order to preserve the volume of the twelve-fold co-ordinated Sr site and the spacing between SrO3 pseudo-closepacked layers.
103 citations
91 citations
60 citations
TL;DR: In this paper, the authors discuss the Mott transition in a fully frustrated lattice with a semicircular density of states in the limit of infinite dimensions from the point of view of a Landau free energy functional.
Abstract: We discuss the solution of the Mott transition problem in a fully frustrated lattice with a semicircular density of states in the limit of infinite dimensions from the point of view of a Landau free energy functional. This approach provides a simple relation between the free energy of the lattice model and that of its local description in terms of an impurity model. The character of the Mott transition in infinite dimensions, (as reviewed by Georges, Kotliar, Krauth and Rozenberg, Rev. Mod. Phys. 68, 13 (1996)) follows simply from the form of the free energy functional and the physics of quantum impurity models. At zero temperature, below a critical value of the interaction U, a Mott insulator with a finite gap in the one particle spectrum, becomes unstable to the formation of a narrow band near the Fermi energy. Using the insights provided by the Landau approach we answer questions raised about the dynamical mean field solution of the Mott transition problem, and comment on its applicability to three dimensional transition metal oxides.
57 citations
TL;DR: In this paper, a moving screw dislocation theory in a conventional crystal was extended to a one-dimensional hexagonal quasicrystal in the framework of the Landau theory.
Abstract: This paper extends a moving screw dislocation theory in a conventional crystal to a one-dimensional hexagonal quasicrystal in the framework of the Landau theory. By introducing two functions and ψ which satisfy wave equations, respectively, a general solution is suggested in terms of and ψ. The analytical expressions for displacement and stress fields induced by a moving screw dislocation as well as the energy are found. The results obtained here when imposing the condition that the phason fields is absent reduce to those for a moving screw dislocation in a crystal.
47 citations
TL;DR: In this article, the first-order transition from P4/ncc to Pnma at 980 K to 1200 K hides the transition from the higher-temperature phase P 4/nmm (via Cmca) to pnma, and at 623(24) K, Pnema transforms via octahedral rotations in a tricritical transition to P21/n.
Abstract: Neutron powder diffraction results on the tetragonal-orthorhombic and orthorhombic-monoclinic structural phase transitions of tungsten oxide are reported. The observed first-order transition from P4/ncc to Pnma at 980 K to 1200 K hides the transition from the higher-temperature phase P4/nmm (via Cmca) to Pnma. At 623(24) K, Pnma transforms via octahedral rotations in a tricritical transition to P21/n. The structural characteristics and thermodynamic properties of the order parameters are described in detail. The evolution of the WO6 octahedra and the atomic positions is documented using such parameters as the octahedral elongation, octahedral variance and the off-centre displacement vectors for the tungsten atoms. It is shown that the phase transitions can be adequately described within the framework of a decoupled mean-field Landau theory.
41 citations
TL;DR: In this article, the authors study the propagation of the normal-superfluid interface under inhomogeneous cooling and establish the conditions for creating topological defects for both slow and fast superfluid transitions using the time-dependent Ginzburg-Landau theory.
Abstract: We study the propagation of the normal-superfluid interface under inhomogeneous cooling. Assuming a uniform temperature gradient we establish the conditions for creating topological defects for both slow and fast superfluid transitions using the time-dependent Ginzburg-Landau theory. For fast transitions, we find agreement with the Kibble-Zurek scenario. Experiments where the temperature change is generated by absorption of a neutron in ${}^{3}\mathrm{He}$ are discussed.
35 citations
TL;DR: In this paper, the Ginzburg Landau functional in a multiply connected planar domain with enclosed magnetic flux is considered and a special attention is given to the zero set of the order parameter.
Abstract: We consider the Ginzburg Landau functional in a multiply connected planar domain with enclosed magnetic flux Particular attention is given to the zero set of the order parameter We show that there exist applied fields for which the zero set is of codimension 1
TL;DR: In this paper, the phase transition of SrTiO3 at 105 K has been examined by studying the temperature dependence of the Young's modulus of the crystals along various directions.
Abstract: The phase transition of SrTiO3 at 105 K has been examined by studying the temperature dependence of the Young's modulus of SrTiO3 crystals along various directions. Dynamic Mechanical Analysis (DMA) at 10–140K. and 10–45Hz has been used for the experiments. The elastic behaviour is interpreted in terms of Landau theory and the DMA results are compared with ultrasonic experiments. The striking differences between the two types of data are attributed to the occurrence of domain wall motions at low frequencies. These motions are suppressed at high frequencies (ultrasonics). We have studied the temperature behaviour of the low-frequency elastic constants of SrTiO3 as function of external stress. The data analysis shows that the domain wall contribution to the elastic constants is essentially suppressed with increasing of uniaxial compression.
01 Jan 1999
TL;DR: Two new elementary proofs are given of Landau's Theorem on necessary and sufficient conditions for a sequence of integers to be the score sequence for some tournament, and both proofs are constructive, so they each provide an algorithm for obtaining a tournament realizing a sequence satisfyingLandau's conditions.
Abstract: Two new elementary proofs are given of Landau's Theorem on necessary and sufficient conditions for a sequence of integers to be the score sequence for some tournament. The first is related to existing proofs by majorization, but it avoids depending on any facts about majorization. The second is natural and direct. Both proofs are constructive, so they each provide an algorithm for obtaining a tournament realizing a sequence satisfying Landau's conditions.
TL;DR: In this paper, a comparative study of grain-size influence on the ferro-para phase transition and its thermal hysteresis was performed by recording the temperature dependence of the dielectric constant, heat capacity and pyrocharge.
Abstract: Ferroelectric barium titanate ceramics with grain sizes in the range (0.5, 20) µm were used for a comparative study of grain-size influence on the ferro-para phase transition and its thermal hysteresis. The investigations were performed by recording the temperature dependence of the dielectric constant, heat capacity and pyrocharge. The experimental results have been analysed in the framework of Landau-Devonshire theory. The grain-size dependent Landau coefficients of the free energy have been derived from our experimental data and used to compute the grain-size dependence of the theoretical transition interval related to the thermal hysteresis. The good qualitative agreement between theory and experiment recommends the size dependent Landau coefficients as a way to improve the modelling of the size dependent ferro-para phase transition in ceramics.
TL;DR: In this article, the coexistence of the displacive and the order-disorder features of the ferroelectric phase transition in crystals is explained, and the height of the potential barrier hindering the order parameter fluctuations is estimated from experimental data.
Abstract: This paper explains the coexistence of the displacive and the order-disorder features of the ferroelectric phase transition in crystals. Both have been observed in experiments. The height of the potential barrier hindering the order parameter fluctuations, estimated from experimental data, shows that the phase transition in is actually very close to the theoretical case of the order-disorder versus displacive crossover. Moreover, previously performed model calculations can be used for the analysis of the temperature dependence of dielectric susceptibility and other physical properties which do not obey the predictions of standard Landau theory.
15 Dec 1999-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, a rigorous symmetry-based Landau theory of the two martensitic transformations from the cubic B2 (β2) austenite parent phase to the rhombohedral R (ζ′2) product phase of P3 symmetry was presented.
Abstract: We present a rigorous symmetry-based Landau theory of the two martensitic transformations from the cubic B2 (β2) austenite parent phase to the rhombohedral R (ζ′2) product phase of P3 symmetry and to the orthorhombic B19 (γ′2) product phase of Pmma symmetry. Both are improper ferroelastic transformations; their primary order parameters are expressed in terms of the shuffle displacements that correspond to the two ζζ0 TA2 modes for ζ=1/3 and ζ=1/2, respectively. Numerical agreement with experimental data is exact for the B2–B19 transformation and good/fair for the B2–R transformation in AuCd/TiNi, respectively.
TL;DR: In this paper, the authors considered a generalization of the random quantum rotor model in which each rotor is characterized by an M-component vector spin and showed that the Gabay-Toulouse line exists for $M>1 when the distribution of exchange interactions has non-zero mean.
Abstract: We consider here a generalization of the random quantum rotor model in which each rotor is characterized by an M-component vector spin. We focus entirely on the case not considered previously, namely when the distribution of exchange interactions has non-zero mean. Inclusion of non-zero mean permits ferromagnetic and superconducting phases for M=1 and M=2, respectively. We find that quite generally, the Landau theory for this system can be recast as a zero-mean problem in the presence of a magnetic field. Naturally then, we find that a Gabay-Toulouse line exists for $M>1$ when the distribution of exchange interactions has non-zero mean. The solution to the saddle point equations is presented in the vicinity of the bi-critical point characterized by the intersection of the ferromagnetic (M=1) or superconducting (M=2) phase with the paramagnetic and spin glass phases. All transitions are observed to be second order. At zero temperature, we find that the ferromagnetic order parameter is non-analytic in the parameter that controls the paramagnet/ferromagnet transition in the absence of disorder. Also for M=1, we find that replica symmetry breaking is present but vanishes at low temperatures. In addition, at finite temperature, we find that the qualitative features of the phase diagram, for M=1, are {\it identical} to what is observed experimentally in the random magnetic alloy $LiHo_xY_{1-x}F_4$.
TL;DR: In this article, an expression for the free energy of a superconductor near the critical temperature, taking account of the terms of next highest order in the parameter 1−T/Tc, is derived.
Abstract: An expression is derived for the free energy of a superconductor near the critical temperature, taking account of the terms of next highest order in the parameter 1−T/Tc. These terms become important for Ginzburg-Landau parameter values |κ−1|≪1, and in this case, in an external magnetic field H0 close to Hc2, the structure of the order parameter is determined by the relative values of the three small parameters |κ−1|, 1−T/Tc, and (Hc2−H0)/Hc2. Three types of lattices are investigated: triangular with one and two flux quanta per cell and square with one flux quantum per cell.
TL;DR: In this paper, the authors used Ginzburg - Landau equations approach to calculate the contribution of higher Landau levels to magnetization and specific heat of superconductors, and found that the excitation spectrum around solution of these equations (treated perturbatively) is softer than that of usual acoustic phonons.
Abstract: Higher than the lowest Landau level contributions to magnetization and specific heat of superconductors are calculated using Ginzburg - Landau equations approach. Corrections to the excitation spectrum around solution of these equations (treated perturbatively) are found. Due to symmetries of the problem leading to numerous cancellations the range of validity of the LLL approximation in mean field is much wider then a naive range and extends all the way down to $H = {H_{c2}(T)}/13$. Moreover the contribution of higher Landau levels is significantly smaller compared to LLL than expected naively. We show that like the LLL part the lattice excitation spectrum at small quasimomenta is softer than that of usual acoustic phonons. This enhanses the effect of fluctuations. The mean field calculation extends to third order, while the fluctuation contribution due to HLL is to one loop. This complements the earlier calculation of the LLL part to two loop order.
TL;DR: In this paper, the bifurcation of symmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg-Landau equations by the methods of formal asymptotics.
Abstract: The bifurcation of symmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg–Landau equations by the methods of formal asymptotics. The behaviour of the bifurcating branch depends upon the parameters d, the size of the superconducting slab, and κ, the Ginzburg–Landau parameter. It was found numerically by Aftalion & Troy [1] that there are three distinct regions of the (κ, d) plane, labelled S1, S2 and S3, in which there are at most one, two and three symmetric solutions of the Ginzburg–Landau system, respectively. The curve in the (κ, d) plane across which the bifurcation switches from being subcritical to supercritical is identified, which is the boundary between S2 and S1∪S3, and the bifurcation diagram is analysed in its vicinity. The triple point, corresponding to the point at which S1, S2 and S3 meet, is determined, and the bifurcation diagram and the boundaries of S1, S2 and S3 are analysed in its vicinity. The results provide formal evidence for the resolution of some of the conjectures of Aftalion & Troy [1].
TL;DR: In this paper, the authors describe the generalization of spherical field theory to other modal expansion methods and apply the method to φ 4 theory in two dimensions and compute the critical coupling and critical exponents, and compare with lattice results and predictions via universality and the two-dimensional Ising model.
TL;DR: In this paper, the free energy of the Ginzburg-landau theory can be represented in terms of two observable quantities, the magnetic field and the superconducting charge density.
TL;DR: In this article, the quantum-classical transitions of the escape rates in a uniaxial spin model relevant to the molecular magnet Mn12Ac and an anisotropic ferromagnetic particle are investigated by applying the periodic instanton method.
TL;DR: In this paper, a first order phase transition Landau model is modified by making the nonlinear dielectric stiffness, α11 temperature, T 3 dependent and retaining the non linear c ijk, elastic stiffnesses.
Abstract: Ferroelectric material properties strongly depend on the external and internal stress and electric fields. This strong dependency is due to the coupling of the nonlinear switching polarization to the nonlinear switching strain of the BO6 octahedra of the ABO3 perovskite structure. Therefore any changes imparted to this atomic octahedral configuration either by external or internal mechanisms would lead in an average sense to changes in the material properties. In the current paper, a first order phase transition Landau model is modified by making the nonlinear dielectric stiffness, α11 temperature, T 3 dependent and retaining the nonlinear c ijk, elastic stiffnesses. Due to these modifications, stress induced phase transition shift is observed as well as shifting of the first order transition to second order transition under the applied stress which agrees well with the experimental observations. The model can also predict critical points where multiple phases coexist, the phase stability, thin f...
TL;DR: In this paper, the authors measured the d.c. electric field dependence of the birefringence and conoscopic images for the smectic C* phase of a partially racemized ferroelectric chiral liquid crystal CE-8.
Abstract: We have measured the d.c. electric field dependence of the birefringence and conoscopic images for the smectic C* phase of a partially racemized ferroelectric chiral smectic liquid crystal CE-8. The experiments were performed using 50mu m thick homeotropic cells with lateral electrodes which created a d.c. electric field parallel to the smectic layers. The observed field induced birefringence shows a characteristic step-like behaviour which is due to the stepby-step unwinding of the helical structure in a sample with finite dimensions along the helical axis. In conoscopic observations we observe that these steps are associated with moving disclination lines that traverse the sample in the direction of the smectic layers. The observed electric field dependence of the birefringence is discussed in terms of the soliton-like unwinding of helical smectic structures and compared with the predictions of the Landau theory. A qualitatively good agreement is obtained.
TL;DR: In this article, the symmetry changes of the paramagnetic to the A-type antiferromagnetic and to the ferromagnetic phase transitions in undoped and moderately doped LaMnO$_3$ were analyzed.
Abstract: We analyze the symmetry changes of the paramagnetic to the A-type antiferromagnetic and to the ferromagnetic phase transitions in undoped and moderately doped LaMnO$_3$, respectively. We show that in the orthorhombic-distorted perovskite manganites the phase separation at low doping is associated with the noncollinear nature of the magnetic orders permitted by symmetry. A simple model for the competition between the two phase transitions is put forward within the framework of Landau theory of phase transitions.
TL;DR: In this paper, the authors investigated the quantum-classical transitions of the escape rates in a uniaxial spin model relevant to the molecular magnet Mn$12$Ac and anisotropic ferromagnetic particle by applying the periodic instanton method.
Abstract: The quantum-classical transitions of the escape rates in a uniaxial spin model relevant to the molecular magnet Mn$_{12}$Ac and a biaxial anisotropic ferromagnetic particle are investigated by applying the periodic instanton method. The effective free energies are expanded around the top of the potential barrier in analogy to Landau theory of phase transitions. We show that the first-order transitions occur below the critical external magnetic field $h_x = 1/4$ for the uniaxial spin model and beyond the critical anisotropy constant ratio $\lambda = 1/2$ for the biaxial ferromagnetic grains, which are in good agreement with earlier works.
TL;DR: In this article, the damping of electron states in crystals is investigated beyond the phase transition point related to a rearrangement of the Fermi surface, and the alteration of the standard Landau theory due to the emergence of a flat portion in the spectrum ξ(p) of single-particle excitations as a result of the rearrange is discussed.
Abstract: The damping γ(e) of electron states in crystals is investigated beyond the phase transition point related to a rearrangement of the Fermi surface. Attention is focused on the alteration of the standard Landau theory due to the emergence of a flat portion in the spectrum ξ(p) of single-particle excitations as a result of the rearrangement. In the limit e →0, the width γ(e) of the states in the region of the Brillouin zone where the dispersion of ξ(p) is of an ordinary order of magnitude is found to depend on e almost linearly, in contrast to the Fermi-liquid-theory result γ(e)∼e2.