Showing papers on "Landau theory published in 2012"

Landau theory of topological defects in multiferroic hexagonal manganites

Abstract: Topological defects in ordered states with spontaneously broken symmetry often have unusual physical properties, such as fractional electric charge or a quantised magnetic field-flux, originating from their non-trivial topology. Coupled topological defects in systems with several coexisting orders give rise to unconventional functionalities, such as the electric-field control of magnetisation in multiferroics resulting from the coupling between the ferroelectric and ferromagnetic domain walls. Hexagonal manganites provide an extra degree of freedom: In these materials, both ferroelectricity and magnetism are coupled to an additional, non-ferroelectric structural order parameter. Here we present a theoretical study of topological defects in hexagonal manganites based on Landau theory with parameters determined from first-principles calculations. We explain the observed flip of electric polarisation at the boundaries of structural domains, the origin of the observed discrete vortices, and the clamping between ferroelectric and antiferromagnetic domain walls. We show that structural vortices induce magnetic ones and that, consistent with a recent experimental report, ferroelectric domain walls can carry a magnetic moment.

Landau Theory of Phase Transitions

Abstract: In this chapter, starting with the classical approach, we define a phase as homogeneous stable matter and classify phase transitions according to the Ehrenfest classification. Then we introduce a concept of an order parameter as a hidden variable responsible for symmetry changes during the transition. We consider different thermodynamic functions and choose the Gibbs free energy as a function of temperature, pressure, and order parameter (the Landau potential) to identify the equilibrium states in open systems. Using the concept of the order parameter, the phase transitions are considered as mathematical catastrophes of the Landau potential. The “catastrophic” approach helps us to classify the phase transitions and see how different forms of the Landau potential are applicable to different cases of phase transitions. We also look at the special lines and points of the phase diagram from the point of view of the “catastrophic” changes of the order parameter. We conclude the chapter with the analysis of the external field on the phase transition, using the properties of conjugation between the field and order parameter.

Influence of Ca-deficiency on the magneto-transport properties in La(0.8)Ca(0.2)MnO(3) perovskite and estimation of magnetic entropy change

Abstract: La0.8Ca0.2 − x□xMnO3 (x = 0.00, 0.10, and 0.20) perovskite was prepared by the conventional solid-state reaction and annealed at 1473 K. X-ray diffraction and scanning electron microscopy shown the existence of a secondary phase attributed to the unreacted Mn3O4 oxide. The magneto transport properties have been investigated based on the temperature dependence of the resistivity ρ(T) measurements under several applied magnetic fields. We note that the La0.8Ca0.2MnO3 (x = 0.00) sample has a classical metal-insulator transition at Tρ. But we have observed that the lacunars samples (x = 0.10 and 0.20) include a metallic and insulator behavior simultaneously below Tρ and the resistivity is dominated by tunneling through the barriers associated with the insulating phase. In other words, the calcium deficiency favors the enhancement of the insulator behavior. The electrical resistivity is fitted with the phenomenological percolation model, which is based on the phase segregation of ferromagnetic metallic clusters and paramagnetic insulating regions. Furthermore, we found that the estimated results are in good agreement with experimental data. Above all, the resistivity dependence on the temperature and magnetic field data is used to deduce the magnetic entropy change. We have found that these magnetic entropy change values are similar to those calculated in our previous work from the magnetic measurements. Finally, we have found an excellent estimation of the magnetic entropy change based on the Landau theory.

Above room temperature magnetic transition and magnetocaloric effect in La0.66Sr0.34MnO3

Abstract: In this study, the magnetic and the magnetocaloric properties of the La0.66Sr0.34MnO3 (LSMO) compound were investigated. The X-ray diffraction result indicates that the LSMO sample has a single phase of rhombohedral symmetry without any impurity phase. The magnetic study reveals that the specimen La0.66Sr0.34MnO3 exhibits a ferromagnetic-paramagnetic transition at T C ∼ 376 K. Using Arrott plots, the phase transition from ferromagnetic to paramagnetic is found to be of second order. A maximum magnetic entropy change of 1.25 J/kgK has been observed for a low applied magnetic field of 1T. The relative cooling power values exhibit a nearly linear dependence on the applied magnetic field. Moreover, the analysis of the magnetocaloric effect (MCE) using the Landau theory o f phase transitions shows good agreement with the experimental results, confirming the importance of magnetoelastic coupling and electron interactions in the magnetocaloric properties of perovskite manganites. This investigation suggests that La0.66Sr0.34MnO3 can be used as a potential magnetic refrigeration material.

d-wave holographic superconductors with backreaction in external magnetic fields

Abstract: We study the d-wave holographic superconductors (the d-wave model proposed in (arXiv:1003.2991(hep-th))) immersed in constant external magnetic fields by using the analytic matching method and numerical computation. In the probe limit, we calculate the spatially dependent condensate solution in the presence of the magnetism and find that the expression for the upper critical magnetic field satisfies the relation given in the Ginzburg- Landau theory. The result shows that the upper critical field gradually increases to its maximum value Bc2 at absolute zero temperature T = 0, while vanishing at the critical temperature T = Tc. Moving away from the probe limit, we investigate the effect of spacetime backreaction on the critical temperature and the upper critical magnetic field. The magnetic fields as well as the electric fields acting as gravitational sources reduce the critical temperature of the superconductor and actually result in a dyonic black hole solution to the leading order. We obtain the expression for the upper critical magnetic field up to O(κ 2 ) order. The analytic result is consistent with the numerical findings.

Molecular-field-theory approach to the Landau theory of liquid crystals: uniaxial and biaxial nematics.

Abstract: Nematic liquid crystal phase diagrams in temperature-biaxiality space are usually complex. We construct a Landau theory based on the analogous molecular-field theory for orthorhombic biaxial nematic fluids. A formal procedure yields coefficients (some of which, unusually, can be tensorial) in this Landau expansion, correctly predicts the complete set of invariants formed from the ordering tensors, and avoids ad hoc parametrization of the molecular biaxiality. By regularizing the Landau expansion to avoid unwanted order parameter divergences at low temperatures, we predict phase behavior over the whole range of biaxiality. The resulting phase diagrams have the same topology as those of molecular-field theory.

The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals

Abstract: We study the radial-hedgehog solution in a three-dimensional spherical droplet, with homeotropic boundary conditions, within the Landau–de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a global Landau–de Gennes minimiser in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. The static properties of the radial-hedgehog solution are governed by a non-linear singular ordinary differential equation. We study the analogies between Ginzburg–Landau vortices and the radial-hedgehog solution and demonstrate a Ginzburg–Landau limit for the Landau–de Gennes theory. We prove that the radial-hedgehog solution is not the global Landau–de Gennes minimiser for droplets of finite radius and sufficiently low temperatures and prove the stability of the radial-hedgehog solution in other parameter regimes. These results contain quantitative information about the effect of geometry and temperature on the properties of the radial-hedgehog solution and the associated biaxial instabilities.

Magnetocaloric effect of an Fe-based metallic glass compared to benchmark gadolinium

Abstract: We report on the magnetocaloric effect in an Fe-based metallic glass (Fe80B12Nb8) as compared to the benchmark material gadolinium. From temperature-dependent magnetization measurements, the magnetic entropy change was calculated using the thermodynamic Maxwell relations. The adiabatic temperature change was directly measured for both materials using a dedicated setup. An analysis of the magnetic transition in amorphous Fe80B12Nb8 and crystalline gadolinium using a mean field and a phenomenological model was carried out. It was shown that both materials, in particular crystalline gadolinium, which does not possess structural disorder but merely a fluctuation of the exchange integral, can be described using the Handrich model for the magnetic transition of disordered materials. Furthermore, the Landau theory of second-order phase transitions quantitatively describes the magnetic entropy change and its dependence on the applied field very well for both materials with different definitions of disorder.

Dynamic off-centering of Cr3+ ions and short-range magneto-electric clusters in CdCr2S4

Abstract: The cubic spinel CdCr2S4 gained recently a vivid interest, given the relevance of relaxor-like dielectric behavior in its paramagnetic phase. By a singular combination of local probe techniques, namely, pair distribution function and perturbed angular correlation, we firmly establish that the Cr ion plays the central key role on this exotic phenomenon, namely, through a dynamic off-centering displacement of its coordination sphere. We further show that this off-centering of the magnetic Cr ion gives rise to a peculiar entanglement between the polar and magnetic degrees of freedom, stabilizing, in the paramagnetic phase, short-range magnetic clusters, clearly seen in ultralow-field susceptibility measurements. Moreover, the Landau theory is here used to demonstrate that a linear coupling between the magnetic and polar order parameters is sufficient to justify the appearance of magnetic cluster in the paramagnetic phase of this compound. These results open insights on the hotly debated magnetic and polar interaction, setting a step forward in the reinterpretation of the coupling of different physical degrees of freedom.

Gauge theory of topological phases of matter

Abstract: We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our analysis leads to a "gauge theory of states of matter" complementary to the well known Landau theory of order parameters. We illustrate the power of our approach by deriving and interpreting the gauge-invariant effective actions of (topological) superconductors, 2D electron gases exhibiting the quantized Hall- and spin-Hall effect, 3D topological insulators, as well as axion electrodynamics. We also use the theory to elucidate the structure of surface modes in these systems.

Elastic phase transitions in metals at high pressures

Abstract: The elastic phase transitions of cubic metals at high pressures are investigated within the framework of Landau theory. It is shown that at pressures comparable with the magnitude of the bulk modulus the phase transition is connected with the loss of stability relative to uniform deformation of the crystalline lattice. Discontinuity of the order parameter at the transition point and its equilibrium value are expressed through the second- to fourth-order elastic constants. The second-,third- and fourth-order elastic constants and phonon dispersion curves of vanadium under hydrostatic pressure are obtained by first-principles calculations. Structural transformation in vanadium under pressure is studied using the obtained results. It is shown that the experimentally observed at P ≈ 69 GPa phase transition in vanadium is the first-order phase transition close to a second-order phase transition.

Ensemble inequivalence: Landau theory and the ABC model

Abstract: It is well known that systems with long-range interactions may exhibit different phase diagrams when studied within two different ensembles. In many of the previously studied examples of ensemble inequivalence, the phase diagrams differ only when the transition in one of the ensembles is first order. By contrast, in a recent study of a generalized ABC model, the canonical and grand-canonical ensembles of the model were shown to differ even when they both exhibit a continuous transition. Here we show that the order of the transition where ensemble inequivalence may occur is related to the symmetry properties of the order parameter associated with the transition. This is done by analyzing the Landau expansion of a generic model with long-range interactions. The conclusions drawn from the generic analysis are demonstrated for the ABC model by explicit calculation of its Landau expansion.

Chiral spin waves in Fermi liquids with spin-orbit coupling.

Abstract: We predict the existence of chiral spin waves-collective modes in a two-dimensional Fermi liquid with the Rashba or Dresselhaus spin-orbit coupling. Starting from the phenomenological Landau theory, we show that the long-wavelength dynamics of magnetization is governed by the Klein-Gordon equations. The standing-wave solutions of these equations describe ''particles" with effective masses, whose magnitudes and signs depend on the strength of the electron-electron interaction. The spectrum of the spin-chiral modes for arbitrary wavelengths is determined from the Dyson equation for the interaction vertex. We propose to observe spin-chiral modes via microwave absorption by standing waves confined by an in-plane profile of the spin-orbit splitting.

Stability of Abrikosov lattices under gauge-periodic perturbations

Abstract: We consider Abrikosov-type vortex lattice solutions of the Ginzburg–Landau equations of superconductivity, consisting of single vortices, for magnetic fields close to the second critical magnetic field Hc2 = κ2 and for superconductors filling the entire . Here κ is the Ginzburg–Landau parameter. The lattice shape, parametrized by τ, is allowed to be arbitrary (not just triangular or rectangular). Within the context of the time-dependent Ginzburg–Landau equations, called the Gorkov–Eliashberg–Schmid equations, we prove that such lattices are asymptotically stable under gauge-periodic perturbations for and unstable for , where β(τ) is the Abrikosov constant depending on the lattice shape τ. This result goes against the common belief among physicists and mathematicians that Abrikosov-type vortex lattice solutions are stable only for triangular lattices and . (There is no real contradiction though as we consider very special perturbations.)

Glassiness in Uniformly Frustrated Systems

Abstract: We review several models of glassy systems where the randomness is self generated, i.e. already an infinitesimal amount of disorder is sufficient to cause a transition to a non-ergodic, glassy state. We discuss the application of the replica formalism developed for the spin glass systems to study the glass transition in uniformly frustrated many-body systems. Here a localization in configuration space emerges leading to an entropy crisis of the system. Using a combination of density functional theory and Landau theory of the glassy state, we first analyze the mean field glass transition within the saddle point approximation. We go beyond the saddle point approximation by considering the energy fluctuations around the saddle point and evaluate the barrier height distribution.

Ensemble inequivalence : Landau theory and the ABC model

Abstract: It is well known that systems with long-range interactions may exhibit different phase diagrams when studied within two different ensembles. In many of the previously studied examples of ensemble inequivalence, the phase diagrams differ only when the transition in one of the ensembles is first order. By contrast, in a recent study of a generalized ABC model, the canonical and grand-canonical ensembles of the model were shown to differ even when they both exhibit a continuous transition. Here we show that the order of the transition where ensemble inequivalence may occur is related to the symmetry properties of the order parameter associated with the transition. This is done by analyzing the Landau expansion of a generic model with long-range interactions. The conclusions drawn from the generic analysis are demonstrated for the ABC model by explicit calculation of its Landau expansion.

Self-consistent Ginzburg–Landau theory for transport currents in superconductors

Abstract: We elaborate on boundary conditions for Ginzburg–Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in principle also be used for general geometries in three-dimensional superconductors.

Global strong solutions of the time-dependent ginzburg-landau model for superconductivity with a new gauge

Abstract: We consider the initial boundary value problem of the time-dependent Ginzburg-Landau equations in superconductivity. We introduce a new gauge, which has been used by Tao [13] to study wave maps. We prove the global existence of strong solutions of the problem with this new gauge. Mathematics Subject Classifications: 35K55

Theory of the magnetoeletric effect in a lightly doped high- T c cuprate

Abstract: In a recent study, Viskadourakis et al. (arXiv:1111.0050) discovered that extremely underdoped La${}_{2}$CuO${}_{4+x}$ is a relaxor ferroelectric and a magnetoelectric material at low temperatures. It is further observed that the magnetoelectric response is anisotropic for different directions of electric polarization and applied magnetic field. By constructing an appropriate Landau theory, we show that a biquadratic magnetoelectric coupling can explain the experimentally observed polarization dependence on magnetic field. This coupling leads to several interesting low-temperature effects, including a feedback enhancement of the magnetization within the ferroelectric phase, and a predicted magnetocapacitive effect.

Quantum effects of magnetization of an easy-axis ferromagnet with S = 1

Abstract: We analyze the influence of quantum effects on magnetic properties of a strongly anisotropic easy-axis ferromagnet with single-ion anisotropy comparable to the exchange interaction of spins with S = 1. We show that in this case, despite the quantum approach, we can apply a description inspired by the Landau theory of phase transitions. We consider two magnetization cases: by a longitudinal and by a transverse external magnetic field. We determine the critical values of the fields and find quantum corrections manifested in the so-called “shortening” of the mean spin modulus. We find that for a sufficiently large single-ion anisotropy, the angular dependence of the critical field differs from the Stoner-Wohlfarth astroid.

Landau theory for the phase diagram of multiferroic Mn 1 − x (Fe,Zn,Mg) x WO 4

Abstract: We present a theoretical analysis of the temperature magnetic field concentration phase diagram of the multiferroic Mn${}_{1\ensuremath{-}x}^{}$$M$${}_{x}^{}$WO${}_{4}^{}$ ($M=$ Fe, Zn, Mg), which exhibits three ordered phases, with collinear and noncollinear incommensurate and with a commensurate magnetic order. The middle phase is also ferroelectric. The analysis uses a semiphenomenological Landau theory based on a Heisenberg Hamiltonian with a single-ion anisotropy. With a small number of adjustable parameters, the Landau theory gives an excellent fit to all three transition lines as well as the magnetic and the ferroelectric order parameters. The fit of the magnetic and ferroelectric order parameters is further improved by including the effect of fluctuations near the transitions. We demonstrate the highly frustrated nature of these materials and suggest a simple explanation for the dramatic effects of doping with different magnetic ions at the Mn sites. The model enables an examination of different sets of exchange couplings that were proposed by a number of groups. Small discrepancies are probably a consequence of small errors in the experimental magnetic parameters. In addition, using the Ginzburg criterion, we estimate the temperature range in which fluctuations of the order parameters become important.

To the landau theory of relaxation phenomena in plasma

Abstract: Landau in his well known work [1] has derived a kinetic equation for completely ionized plasma and solved a problem about temperature relaxation of electron and ion components. According to Landau equilibrium is established in the electron and ion subsystems at first (over periods of time τm and τM respectively), then temperature relaxation of the components is observed over a period of time τT . The last process is the slowest one because of a small electron and ion masses ratio σ ≡ (m/M). Analogously a problem about velocity relaxation of the components over a period of time τu has been solved (see, for example, [2]). The Landau theory is based on an assumption that quasi-equilibrium state of the plasma can be described by the Maxwell distribution:

Field-induced transitions between multilayer phases of polar smectic liquid crystals.

Abstract: Recently Wang et al. [Phys. Rev. Lett. 104, 027801 (2010)] reported the discovery of a novel multilayer phase in polar liquid crystals. The phase was unambiguously assigned to a six-layer antiferroelectric structure (Sm-C(d6)(*)) by resonant x-ray diffraction. This discovery lead to essential progress in understanding the nature of polar phases. However, more recently, Chandani et al. [Liq. Cryst. 38, 663 (2011)] in the same material clearly identified the novel phase as a ferrielectric five-layer structure (Sm-C(d5)(*)) by the electric-field-induced birefringence. This contradiction seemed to be a mystery. In this paper we show that the two experiments are in agreement. Phenomenological Landau theory of the phase transitions shows that both phases (Sm-C(d6)(*) and Sm-C(d5)(*)) exist and transform into each other in a relatively low electric field.

On the parameters of intermediate state structure in high pure type I superconductors at external magnetic field

Abstract: The geometric structure of an intermediate state in the high pure Gallium single crys-tal at the external magnetic field Hext at the temperature T=0.4 K is researched, using the longi-tudinal ultrasonic signal attenuation method at the ultrasonic signal frequency of 30 MHz. It is experimentally shown that the edge inhomogeneities of the magnetic field distribution have an influence on the structure of an intermediate state in the cylindrical superconductor samples at the transverse orientation of external magnetic field Hext. It is shown that the use of the super-conducting plane screens of NbZr permits an approach to the equilibrium intermediate state structure of an infinite cylinder as confirmed by an experimental dependence of the normal metal layer thickness aN on the magnitude of external magnetic field aN(Hext) in the high pure Ga single crystal at an application of the longitudinal ultrasonic signal with the frequency of 30 MHz at the temperature T=0.4 K. The experimentally obtained characteristic parameters of an intermediate state structure in the high pure type I superconductor at the external magnetic field Hext have a partial qualitative agreement with the Landau theory results.

Extensions and some recent applications of the Landau theory of phase transitions

Abstract: The basic concepts of the Landau theory of phase transitions are introduced through working examples. A number of rules governing the application of the theory to second and first-order transitions are given. The approach to magnetostructural transitions in magnetic mulltiferroic materials is detailed. Examples of transitions induced by replica of the same order-parameter in superconducting and liquid crystal systems, are described. The theory of reconstructive transitions is outlined and illustrated by the examples of the graphite-diamond transition and by the phase diagram of iron. An extention of the phenomenological approach to incommensurate structures to the crystal-amorphous transition is proposed (see also the chapter by Perez-Mato et al . for further discussion and applications).