Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables H _z and H _y . In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.     

Continuum limit of A Z2 lattice gauge theory

Phase diagrams of lattice gauge theories have in several cases lines of first-order transitions ending at points at which continuous (second-order) transitions take place. In the vicinity of this critical point, a continuum field theory may be defined. We have analyzed here a Z₂ gauge plus matter model (which has no formal continuum limit) and identified the critical point with a usual Ø⁴, globally Z₂ invariant, field theory. The analysis relies on a mean field functional formalism and on a loop-wise expansion around it, which is reviewed.     

Effect of electric field on the dielectric permittivity of betaine phosphite crystals in the paraelectric phase

Temperature dependences of the dielectric permittivity of betaine phosphite crystals are studied both without and under application of an electric bias. It is shown that, in view of the fact that the high-temperature improper ferroelastic (antiferrodistorsive) phase transition at T _c1=355 K is nearly tricritical, the nonlinear temperature dependence of inverse dielectric permittivity in the paraelectric phase and the effect of the field on the dielectric permittivity can be described within a phenomenological model containing two coupled (polar and nonpolar) order parameters with a negative coupling coefficient. An analysis of the model revealed that, in the case where two phase transitions, a nonpolar and a ferroelectric one, can occur in the crystal, all of its dielectric properties, including the polarization response in a field, can be described by one dimensionless parameter a. For the crystal under study, we have a=?2.5. This value of the parameter corresponds to a second-order ferroelectric transition far from the tricritical point, at which a=?1. It is shown that the polarization response in the paraelectric phase in an electric field calculated within this model differs radically from that in the ferroelectric phase-transition model for which the Curie-Weiss law holds in the paraelectric phase.     

Temperature behavior of the order parameter in Pb5Ge3O11

The temperature dependence of the spontaneous polarization in the Pb₅Ge₃O₁₁ lead germanate (PGO) is experimentally investigated using optical, magnetic resonance, and conventional electrical measurements. The deviations from the temperature dependence typical of second-order phase transitions at temperatures below 420 K are explained in terms of incomplete polarization switching and polarization induced by a residual depolarization field. The low-temperature anomalies are interpreted without consideration of additional structural transformations. The internal bias field is determined from the experimental temperature dependence of the perfect polarization of PGO single crystals in an electric field.     

A new type of second-order phase transition derived from Devonshire's theory of ferroelectrics

Including external fields Devonshire's theory of ferroelectric phase transitions leads to a type of second-order transitions for which the order parameter is different from zero below and aboveT _c . Although in a certain limiting case the order parameter becomes zero aboveT _c the resulting theory is nevertheless different from the usual Landau-theory suggesting the existence of different types of systems undergoing second-order phase transitions.     

Magnetic phase transitions and the dynamic electric polarization in the LaMn<Subscript>2</Subscript>O<Subscript>5</Subscript> compound

Possible phase transitions to the ferromagnetic phase in the LaMn₂O₃ compound have been studied in the framework of a phenomenological approach based on a symmetry analysis. The conditions that parameters of the thermodynamic potential must satisfy to realize a second-order transition have been found. The line of the first-order phase transitions in this system and the critical point of the second-order phase transition line have been determined. It was shown that a dynamic electric polarization can form in the antiferromagnetic phase.     

Magnetic phase transitions,soliton lattices,and electric polarization in <Emphasis Type="Italic">R</Emphasis>Mn<Subscript>2</Subscript>O<Subscript>5</Subscript> multiferroics

The magnetic phase transitions in RMn₂O₅ oxides were analyzed. It was shown that the transition from the paramagnetic phase to the incommensurate phase is described by not only the basic magnetic parameter but also an associated order parameter: electric polarization along the y axis of the crystal. It was established that the antiferromagnetic-incommensurate phase transformation is a second-order phase transition, accompanied by a decrease in electric polarization.     

Electron and nuclear magnetic resonances associated with magnetoelectric and antiferroelectric interactions in the exchange-noncollinear (“square”) chiral antiferromagnet Nd<Subscript>2</Subscript>CuO<Subscript>4</Subscript> and their behavior in chiral phase transitions

Experiments with the tetragonal antiferromagnet Nd₂CuO₄ in the temperature range 1.5 K < T < T _N = 245 K show that the magnetic moments of Cu²⁺ possess an exchange-noncollinear magnetic structure of the “square” type, which has the form of an exchange doublet whose components exhibit different chiralities (Γ₄ and Γ₅ phases). Between these phases, consecutive phase transitions Γ₄ ? Γ₅ ? Γ₄ with a change in chirality take place at temperatures T₁ = 30 K and T₂ = 70 K. The electron and nuclear magnetic resonances (natural frequencies and susceptibilities) associated with excitation of magnons (due to the magnetoelectric and antiferroelectric interactions) by an ac electric field E(t), as well as a variable magnetic field H(t) applied in the case of a constant electric field E⁰, are calculated. It is predicted that nuclear magnetic resonance is excited by an ac electric field at frequencies determined by hyperfine fields of the sublattices. The change in the resonance frequencies upon the above chiral phase transitions are analyzed (being first-order phase transitions, these transitions possess a number of features associated with the chirality of the magnetic structures).     

Phase transitions and optical properties in 〈001〉 (1−<Emphasis Type="Italic">x</Emphasis>)PbZn<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>−<Emphasis Type="Italic">x</Emphasis>PbTiO<Subscript>3</Subscript> single crystals

The effect of a constant electric field (0 < E < 5 kV/cm) on the optical properties of PbZn_1/3Nb_2/3O₃?xPbTiO₃ (PZN-xPT) crystals with x = 7 and 9% has been analyzed. It has been shown that, at temperatures close to the temperature of the transition from the rhombohedral [R(X)] phase to the tetragonal (T) phase, two induced phase transitions are observed in the electric field, which are associated with the appearance of new intermediate phases M_a and M_c [R(X)-M_a-M_c-T]. Correlation between these two transitions and the PbTiO₃ content x has been found. The E-T phase diagrams have been obtained. The M_c phase in PZN-9PT crystals is found to remain the ground state after the removal of the electric field, whereas the M_c phase in PZN-7PT crystals is metastable and is transformed into the M_a phase after the removal of the electric field.     

Surface and bulk order-disorder transitions

Interrelation of surface an bulk order-disorder transitions in binary alloys A_xB_1−x is discussed within the framework of the Bragg-Williams approximation, using the fcc (100) and bcc (110) surfaces as an example. In an fcc alloy with a (100) surface, layers parallel to the surface undergo alternately second-order transitions. On the other hand, the bulk fee alloy reveals a first-order transition from the disordered phase to a mixture of the disordered and the AB₃- (or A₃B-) type ordered phases except for X = 0.5. The origin of the bulk first-order transition is discussed by taking into account order-disorder transitions in the surface region. For comparison, the bulk second-order transition in a bcc alloy is also discussed.     

Magnetic catalysis and magnetic oscillations in the Nambu-Jona-Lasinio model

The phase structure of the four-dimensional Nambu-Jona-Lasinio model in the presence of a chemical potential μ and an external magnetic field H is investigated at comparatively small values of the bare coupling constant (G<G _c). It is shown that only for magnetic-field strengths in excess of some critical value H _c(μ) does the magnetic field induce a spontaneous breakdown of chiral symmetry. On the phase portrait of the model, there are infinitely many massless chiral-invariant phases; in addition, there is one massive phase characterized by spontaneously broken chiral invariance. It is because of this phase structure of the system that some physical features of its ground state, including magnetization, pressure, and particle density, oscillate as H → 0. Changes in the vacuum properties of the model are accompanied by first-or second-order phase transitions.     

Thermomodulation experiments at the cubic-to-tetragonal phase transition in SrTiO3

After a brief comment on the important features of strontium titanate and a critical review of recent optical work in this material, thermoabsorption results at the cubic-to-tetragonal second-order phase transition are reported. Use of insulating samples has been possible by means of indirect heating. Optical evidence of the phase change is seen for the momentum-forbidden transitions starting at the indirect gap energy. This is discussed in terms of the relaxation of the momentum condition brought about by structural fluctuations near the transition temperature T₀. Part of the effect may be related to the increasing static distortion of the lattice in the tetragonal state. The results presented also confirm earlier pictures of the absorption threshold as due to LO-phonon-assisted Γ₁₅→X₃ transitions (with phonon energy equal to 52 meV). Furthermore, in the vicinity of T₀, an extra thermomodulation signal, corresponding to a weak absorption threshold ? 20 meV higher than the gap, becomes visible. This critical point is also particularly sensitive to the application of electric fields, as found by electroabsorption results obtained at liquid nitrogen temperature.     

Magnetic properties of Ising metamagnet in both external longitudinal and transverse fields

The phase diagrams of a two-sublattice Ising metamagnet at finite temperature in a mixed longitudinal field and a transverse magnetic field are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented in the phase diagrams, since the Gibbs free energy can be calculated numerically. The results show that there is no fourth-order critical line in the phase diagrams given by using EFT as found by using mean-field theory (MFT). The tricritical lines and their projection in the t−h_x plane obtained by using EFT are also quite different from those by using MFT. Only one type of phase diagram is obtained by using EFT while three kinds of phase diagrams are obtained by using MFT, which indicates that only the first kind of phase diagrams obtained by using MFT is reliable. Furthermore, it is shown that the region of first-order transitions increases as the transverse magnetic field h_x decreases.     

Phase diagram of the system of solid solutions Pb1−X(Li½La½)X(Zr1-YTiY)O3 in the vicinity of the FE-AFE phase stability boundary. II. phase transitions and induced states

Results of the study of phase transitions in the system of solid solutions Pb_1-X(Li_½La_½)_X(Zr_1-YTi_Y)O₃ (PLLZT) at x = 0, 1 under the effect of an electric field are presented. It is shown that there are three regions of Ti-concentration on the “;composition-temperature”; phase diagram. The region of Ti-content from ～ 12 to ～ 19% is the most interesting. In this region the succession of phase transitions depends on the prehistory of the specimens: in the absence of an external electric field only the AFE-PE transition takes place, but after the action of the field, the succession of phase transitions FE-AFE-PE arises. Full “;temperature-field”; phase diagrams are constructed.     

Anomalies in the Magnetic Susceptibility in the Second-Order Phase Transitions beyond the Curie Point

Taking into account the inexhaustible interest in studying the peculiarities of physical properties in the neighborhood of phase transitions and the growth of experimental investigations of cobalt fluoride, we have studied the peculiarities of magnetic susceptibility in the vicinity of the critical field H_C at which cobalt fluoride performs the second-order phase transition from the antiferromagnetic phase to the angular phase. It is discovered that in the magnetic field H ‖ C₄, the magnetic susceptibility becomes infinite at H → H_C. It is shown that as the magnetic field direction deviates from the C₄ axis, the magnetic susceptibility in the critical field H_C proves to be finite. It is also shown that the change in the magnetic susceptibility with the change in the magnetic field considerably decreases at extremely insignificant deviations of the field H from the C₄ axis. Since the calculations are performed in terms of the Landau theory of phase transitions, we pay attention to the similarity and difference between the obtained results and those in the vicinity of the Curie point obtained by using the Landau theory of phase transitions.     

Measurement of the dipole moment of CF3CN

The Stark effect was observed for K = 0 and K = 1, J = 1 → 2 transitions in CF₃CN. Measurements were made in a Stark modulated microwave spectrometer. The dipole moment obtained was μ = 1.262 ± 0.010 D. An analysis of the effects of electric field inhomogeneities on the observed Stark shifts for K = 0 and K = 1 states is included. Appropriate corrections are given for measuring linear Stark effects in a standard waveguide cell calibrated using a molecule with second-order Stark effect.     

Phase states and dielectric properties of sodium-potassium niobate solid solutions

The temperature dependence of dielectric constant ? for single crystals of Na_1?xK_xNbO₃ (0.04?x?0.15) is studied for the first time. From the shape of the ?(T) anomalies corresponding to rotational phase transitions, the type of interaction between the order parameters and the polarization is determined. A phenomenological model is developed which adequately describes the experimentally observed sequence of high-temperature (T>300°C) phase transitions, the dielectric anomalies associated with these transitions, and the changes in the phase states under the action of external factors (pressure, electric field).     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

Step-by-step first order antiferroelectric-paraelectric transition induced by frustration and electric field

We show analytically that even not too strong frustrating next neighbor interaction strongly affects first order antiferroelectric-paraelectric transition in an external electric field. We apply mean-field Landau theory. In the electric field a single phase transition at T ₀ splits into a step-by-step staircase with a series of intermediate phases. Unexpectedly enough we found that the equilibrium structures of the phases differ substantially from structures formed at low temperature both without field and in field. Polarization of intermediate structures decreases with temperature in a stepwise manner. Similar step-by-step transitions can occur also in magnetic materials with frustrating interaction.     

Nonequilibrium phase transition in the kinetic Ising model on a two-layer square lattice under the presence of an oscillating field

The nonequilibrium or dynamic phase transitions are studied, within a mean-field approach, in the kinetic Ising model on a two-layer square lattice consisting of spin- 1/2 ions in the presence of a time varying (sinusoidal) magnetic field has been studied by using Glauber-type stochastic dynamics. The dynamic equations of motion are obtained in terms of the intralayer coupling constants J₁ and J₂ for the first and second layer, respectively, and interlayer coupling constant J₃ between these two layers. The nature (first- or second-order) of the transitions is characterized by investigating the behavior of the thermal variations of the dynamic order parameters. The dynamic phase transitions are obtained and the dynamic phase diagrams are constructed in the plane of the reduced temperature versus the amplitude of the magnetic field and found fourteen fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points for various values of J₂/|J₁| and J₃/|J₁|. Besides the paramagnetic (p), ferromagnetic (f) and compensated (c) phases, there were the f+c,f+sf,c+sf,af+p,m+p,f+m and c+af, where the af, sf and m are the antiferromagnetic, surface ferromagnetic and mixed phases respectively. Coexistence phase regions also exist in the system.