Specific Heat of the 1D Spin-1/2 Ising Model with Added Dzyaloshinskii–Moriya Interaction

The 1D spin-1/2 Ising model in a uniform magnetic field with added the Dzyaloshinskii–Moriya (DM) interaction is considered. The energy spectrum is obtained using the fermionization approach and defining some mean field order parameters. Then the specific heat is determined in an infinite chain system. Results show that there is only one peak in the specific heat as a function of the temperature. In the Neel phase, the position of the peak is found almost field-independent, but the maximum value of the specific heat decreases by increasing the magnetic field. Also, in the region of the saturated ferromagnetic phase, by increasing h, the peak becomes wider and goes to higher temperatures, which is a signal for the saturated ferromagnetic phase. In addition, the specific heat at low temperature shows two peaks structure on both sides of the quantum critical point.     

Excitonic Phase Transition in the Extended Three-Dimensional Falicov–Kimball Model

We study the excitonic phase transition in a system of the conduction band electrons and valence band holes described by the three-dimensional (3D) extended Falicov–Kimball (EFKM) model with the tunable Coulomb interaction \(U\) between both species. By lowering the temperature, the electron–hole system may become unstable with respect to the formation of the excitons, i.e, electron–hole pairs at temperature \(T=T_{\Delta }\) , exhibiting a gap \(\Delta \) in the particle excitation spectrum. To this end we implement the functional integral formulation of the EFKM, where the Coulomb interaction term is expressed in terms of U(1) phase variables conjugate to the local particle number, providing a useful representation of strongly correlated system. The effective action formalism allows us to formulate a problem in the phase-only action in the form of the quantum rotor model and to obtain analytical formulas for the critical lines and other quantities of physical interest like charge gap, chemical potential and the correlation length.     

Overcoming the Limits of the Interfacial Dzyaloshinskii–Moriya Interaction by Antiferromagnetic Order in Multiferroic Heterostructures

Topologically protected magnetic states have a variety of potential applications in future spintronics owing to their nanoscale size (<100 nm) and unique dynamics. These fascinating states, however, usually are located at the interfaces or surfaces of ultrathin systems due to the short interaction range of the Dzyaloshinskii–Moriya interaction (DMI). Here, magnetic topological states in a 40-unit cells (16 nm) SrRuO₃ layer are successfully created via an interlayer exchange coupling mechanism and the interfacial DMI. By controlling the thickness of an antiferromagnetic and ferromagnetic layer, interfacial ionic polarization, as well as the transformation between ferromagnetic and magnetic topological states, can be modulated. Using micromagnetic simulations, the formation and stability of robust magnetic skyrmions in SrRuO₃/BiFeO₃ heterostructures are elucidated. Magnetic skyrmions in thick multiferroic heterostructures are promising for the development of topological electronics as well as rendering a practical approach to extend the interfacial topological phenomena to bulk via antiferromagnetic order.     

Metamagnetic Transition in the Quasi-Two-Dimensional Mott Transition System Ca2−xSrxRuO4

Ca _2–x Sr _x RuO ₄ is the new type of quasi-two-dimensional Mott transition system that connects the Mott insulator Ca ₂ RuO ₄ with the spin-triplet superconductor Sr ₂ RuO ₄ . In the metallic region near the metal-insulator boundary (0.2x0.5), we found an unusual magnetic state with a broad peak in the susceptibility at low temperatures. In this region, a clear metamagnetic transition was observed at the field of several tesla.     

Flux Phase and Its Competition with Superconductivity in the t–J Model

The phase diagram of the t–J model is investigated within the X-operator formalism using the Baym–Kadanoff theory and a 1/N expansion. In this way, no auxiliary fields are introduced. For finite Coulomb repulsion, the system shows a strong competition between d-wave superconductivity and d-wave flux phase, leading to a strong suppression of superconductivity in the flux state. The underdoped region is characterized by flux order in the normal state, with a d-wave gap in the excitation spectrum, and by coexistence of both superconductivity and flux phases below the superconducting transition temperature T _c. The balance between the two phases is determined by the short-range Coulomb repulsion, while the long-range part of Coulomb interaction prevents phase separation and leads to incommensurate charge-density-wave state far away from the superconducting region.     

Structural Phase Transition in Nanostructured TiO_2

Using DTA (difFerential thermal analysis) measurement on nanostructured TiO2, we find two endothermic peaks on the DTA curve. From XRD (X-ray diffraction) analysis of the original nanostructured TiO2 and its heat-treated samples, we obtain the following results: the first endothermic peak corresponds to the desorption of physical or chemical absorption, the second one is related to the structural phase transition from brookite to anatase then to rutile, and this structural phase transition is beneficial to the grain growth of nanocrystal     

Metamagnetic Phase Transitions in La1−x Nd x Mn2Si2

Experimental measurements for the magnetization at various temperatures are analyzed using a mean field model for the purely ferromagnetic spin configuration near the metamagnetic phase transitions in La_1?x Nd _x Mn₂Si₂ (x=0.3) at a constant magnetic field (50 mT). By fitting the temperature dependence of the magnetization from the free energy in the mean field model to the experimental data for this compound, the coefficients in the free energy expansion are determined. Our analysis of the magnetization describes a first-order character of the metamagnetic transition in La_1?x Nd _x Mn₂Si₂ (x=0) on the basis of the mean field model studied here.     

Metastable States in Liquid–Gas Phase Transition. Simulation by the Method of Molecular Dynamics

The method of molecular dynamics is used to investigate the p, , T-properties and the structural characteristics of the Lennard–Jones fluid in the stable and metastable states in the liquid–gas phase transition. The calculation results demonstrate the presence of phase separation in molecular models at close-to-spinodal supersaturation. The effect of the cut-off radius of the interparticle potential on the process of phase transformation is analyzed, and the position of spinodal of superheated liquid and supersaturated vapor is estimated.     

Phase Transitions in the Gross–Neveu Model on a Sphere for High-T c Materials

Phase transitions were studied in the 3D Gross–Neveu model on a sphere at T 0. The zeta function of the Dirac operator of the model was represented with a double sum, and its derivative was calculated using recurrent formulas for generalized Epstein–Hurwitz functions. The effective potential Vwas determined as a function of the field, temperature T, and inverse radius of curvature r. Phase transitions first-order in temperature at R= 0 (T _c = 1/2ln2) and second-order in curvature R= 2/r ² at T= 0 (r _c = 1/1.5) were identified. For the general case, T 0 and R 0, the critical phase dependence T _c(r _c) was obtained, and the V(, T, r) surface was constructed. External stimuli such as temperature and curvature were shown to restore the symmetry of the system in the 3DGross–Neveu model.     

Phase Relations in the Cu–Sb–O System

The Cu–Sb–O system was studied by x-ray diffraction and thermal analysis between 700 and 1000°C. The compositions of copper antimonates were refined. Sb₂O₄ was found to exist in two polymorphs above 800°C: -Sb₂O₄ (dominant phase) and -Sb₂O₄. The evolution of phase equilibria with increasing temperature was examined. The isothermal sections of the Cu–Sb–O phase diagram were mapped out using new and earlier reported results.     

Phase Equilibria in the Cd–Ga–As–Te System

Inorganic Materials - An isothermal subsolidus x–y–z phase diagram, a block diagram of invariant phase equilibria, and a model for the p–T projection of the...     

Phase Relations in the SiC–LaB6 System

The T–x phase diagram of the SiC–LaB₆ join in the quaternary system La–B–C–Si is mapped out. The join is shown to be pseudobinary, with simple eutectic phase relations. The eutectic is located at 74 mol % SiC and 26 mol % LaB₆, with a melting point of 2110 ± 20°C.     

Phase transformations in the ternary Ag–Ga–Sb system

Phase diagram of the Ag–Ga–Sb ternary system was extrapolated using calculation of phase diagrams (CALPHAD) method. Phase transition temperatures of the alloys with compositions along three vertical sections with constant molar ratios Ga/Sb = 1, Ag/Ga = 1 and Ag/Sb = 1 were measured using differential scanning calorimetry (DSC). Scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDX) was used for identification of phases in equilibrated samples. Experimental results were compared with thermodynamic prediction.     

Phase Transitions in Spin-1/2 Falicov–Kimball Model on a Two-dimensional Triangular Lattice

Phase transitions from low-temperature (ordered) phases to high-temperature (disordered/homogeneous) phases for different fillings are studied on a triangular lattice using the spin-dependent Falicov–Kimball model. Numerical diagonalization and Monte Carlo simulation methods are used to study thermodynamic properties of the system. It has been observed that low-temperature ordered phases persist up to a finite temperature and after reaching a critical temperature (\(T_c\)), homogeneous phases are observed for all parameter space. We have also calculated the temperature dependence of specific heat and observed a sharp jump at \(T_c\) indicating the phase transition, and this \(T_c\) increases with increase in on-site Coulomb correlation U and electron fillings.     

Phase Relations in the Reduction of Solid Solutions in the Co–Mn–Ti–O System

The hydrogen reduction of spinel solid solutions in the Co–Mn–Ti–O system was investigated by a static method. Six phase regions were identified in which the gas phase is in equilibrium with various combinations of -Co, TiO₂ (rutile), and solid solutions of variable composition: Co _A Mn _B Ti_{3 – A – B} O₄ (spinel), Co _m Mn_{2 – m} TiO₄ (spinel), Co _N Mn_{1 – N} TiO₃ (ilmenite), and Co _n Mn_{1 – n} O (NaCl). The equilibrium compositions of the solid solutions and the corresponding oxygen partial pressures were determined, and the general trends of the reduction of spinel solid solutions in the Co–Mn–Ti–O system were established.     

Momentum Distribution of Liquid $$^{}$$He Across the Normal–Superfluid Phase Transition

We have carried out a study of the momentum distribution and of the spectrum of elementary excitations of liquid \(^4\)He across the normal–superfluid transition temperature, using the path integral Monte Carlo method. Our results for the momentum distribution in the superfluid regime show that a kink is present in the range of momenta corresponding to the roton excitation. This effect disappears when crossing the transition temperature to the normal fluid, in a behavior currently unexplained by theory.     

Phase equilibria and transformation in the Ti–Al–Ta system

Journal of Materials Science - TiAl- or Ti3Al-based alloys have gained industrial applications in recent years. The incorporation of β-stabilizing element Ta has demonstrated to better adjust...     

Phase transitions in alloys of the Ni–Mo system

The structure of Ni–20 at.% Mo and Ni–25 at.% Mo alloys heat treated at different temperatures was studied by the method of transmission electron microscopy. X-ray photoelectron spectroscopy was used to detect the sign of the chemical interaction between Ni and Mo atoms at different temperatures. It is shown that at high temperatures the tendency toward phase separation takes place. The system of additional reflections at positions {1 ½ 0} on the electron diffraction patterns testifies that the precipitation of crystalline bcc Mo particles begins in the liquid solution. At 900 °C and below, the tendency toward ordering leads to the precipitation of the particles of the chemical compounds. A body-centered tetragonal phase Ni₄Mo (D1_a) is formed in the Ni–20 at.% Mo alloy. In the Ni–25 at.% Mo alloy, the formation of the Ni₃Mo (D0₂₂) chemical compound from the A1 solid solution has gone through the intervening stage of the Ni₄Mo (D1_a) and Ni₂Mo (Pt₂Mo) formation.     

p–T–x Phase Equilibria in the Cd–Zn–Te System

The p–T–x–y phase equilibria in the Cd–Zn–Te system are analyzed. The p–T and T–x–yprojections of the p–T–x–y phase diagram and a T–x–y isobar (for pressures at which Cd_1–x Zn _x Te_{1 ±} solid solutions sublime congruently in terms of Te) are mapped out. The key features of the sublimation behavior of the solid solution are examined. The p–T projection is studied by static vapor pressure measurements at temperatures from 700 to 1300 K and pressures of up to 101.3 kPa. The p–T sections of the phase diagram are constructed for x = 0.05, 0.10, 0.15, 0.25, 0.50, 0.75, 0.90, and 1. The solid solution containing 35 mol % ZnTe is found to phase-separate at 473 K.