Transition order and dynamics of a model with competing exchange and dipolar interactions

We performed Monte Carlo simulation of phase transitions from isotropic stripe phase with short-range order to long-range stripe phase in a model with competing ferromagnetic exchange and antiferromagnetic dipolar interactions on triangular lattice. We calculated phase diagram for different values of exchange and dipolar interaction constants ratio, η. We also determined the order of the transitions to stripe phases AFh of different stripe widths h: first-order phase transition was found to transitions into AF1 and AF2 phases, while transitions to AF3 and AF4 phases were of the second order. In the phase diagram the tricritical point was determined at the AF2 and AF3 phase boundary. We observed the peak of nematic phase at the transition region to the AF1 phase, but found it metastable at low values of η. We have also found that in AF1 phase spin relaxation corresponds to the Ising model dynamics. In phases AF3 and AF4 the dynamics slows down, and stripe domain growth with time is proportional to logt.     

Sound propagation near the tricritical point of FeCl2

The magnetically induced phase transitions, near the tricritical point of FeCl₂ were studied by acoustic velocity measurements. Longitudinal waves propagating along the (100) trigonal axis exhibit a critical shift in the velocity along the second order λ-line and anomalous change at the first order phase transitions. The phase diagram in the plane of temperature and applied magnetic field is constructed near the tricritical point.     

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.7A0.3(Mn1−xbx)O3 (A=Sr; B=Ti and Al; x=0.0 and 0.05) compounds

The critical parameters provide important information concerning the interaction mechanisms near the paramagnetic-to-ferromagnetic transition. In this paper, we present a thorough study for the critical behavior of La_0.7A_0.3(Mn_1−xB_x)O₃ (A=Sr; B=Ti and Al; x=0.0 and 0.05) polycrystalline samples near ferromagnetic-paramagnetic phase transition temperature by analyzing isothermal magnetization data. We have analyzed our dc-magnetization data near the transition temperature with the help of the modified Arrot plot, Kouvel-Fisher method. We have determined the critical temperature T_C and the critical parameters β, γ and δ. With the values of T_C, β and γ, we plot M×(1−T/T_C)^−β vs. H×(1−T/T_C)^−γ. All the data collapse on one of the two curves. This suggests that the data below and above T_C obey scaling, following a single equation of state. Critical parameters for x=0 and x_Ti=0.05 samples are between those predicted for a 3D-Heisenberg model and mean-field theory and for x_Al=0.05 samples the values obtained for the critical parameters are close to those predicted by the mean-field theory.     

Percolation threshold near the second phase transition in diluted system of Gd2−x(La, Y)xIn

In this paper it is demonstrated that the second phase transition of Gd₂In intermetallic compound gets eliminated by diluting Gd_2−x(LaY)_xIn at a critical composition of x=0.5. The exchange coupling for intra-cluster interactions is estimated in the correlation ranges of 3.3 Å<R_C<3.6 Å (anisotropic source) and for inter-cluster interactions in the ranges of R_C>4 Å where the correlation length is defined as . The sign and strength of the exchange coupling are identified by the eigenvalues λ(k) and are obtained from zeros of the 4×4 matrix of J_ij^RR′ along the three directions of the reciprocal lattice for each dilution (x=0.25, 0.5, 0.75, 1). The transition temperature is calculated using the minimum eigenvalue λ_min (k=0, π) which agrees with the experiment. Magnetic field and temperature dependence of the magnetization and electrical resistivity measurements show that: (i) Elimination of the AFM phase is caused by breaking of some FM short-range exchange couplings, and (ii) Conduction electrons order antiferromagnetically at low temperatures and ferromagnetically at high temperatures.     

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.     

Disorder-order phase transition induced by size effect in bulk La2/3Sr1/3MnO3

Bulk La_2/3Sr_1/3MnO₃ ceramic samples prepared by thermal decomposition are investigated using transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM). An abnormal phenomenon, where three kinds of La_2/3Sr_1/3MnO₃ phases with different structures and the same composition coexist in the same grain, has been observed. Besides the stable rhombohedral majority phase, the two other phases are a simple cubic structure with a=0.389 nm and a new hexagonal structure with a=0.544 nm, c=0.668 nm. The simple cubic phase is a residual phase of high-temperature due to the size effect and bondage of twin boundary. Image simulations have suggested that the new hexagonal phase is the La-Sr ordered structure with space group , which is converted from the disordered simple cubic phase. The formation mechanism of the ordered phase is explained from volume energy and interface energy considerations.     

Slowing down of the relaxational dynamics at the ferroelectric phase transition in one-dimensional (TMTTF)2AsF6

We present measurements of the dielectric response of quasi one-dimensional system (TMTTF)₂AsF₆ in a wide temperature and frequency range. We provide a thorough characterization of the relaxational dynamics observed close to the ferroelectric-like transition at T_c=100 K. Our measurements, extending up to 100 MHz, reveal a continuous slowing down of the mean relaxation time when approaching T_c from high as well as from low temperatures. The simultaneous critical rise of the dielectric constant and relaxation time point to an explanation of the transition in terms of a classic ferroelectric scenario.     

Critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.7Pb0.05Na0.25MnO3

Critical behavior in La_0.7Pb_0.05Na_0.25MnO₃ has been investigated by dc magnetization measurements. Magnetic data indicate that the compound exhibits a continuous (second-order) paramagnetic (PM) to ferromagnetic (FM) phase transition. Estimates of critical exponents yield δ=4.80±0.01, γ=1.296±0.002 and β=0.344±0.007 (consistent with both the predictions for the three-dimensional-Heisenberg model and with those reported for materials when the FM transition is ascribed to the double exchange (DE) mechanism as a major origin) with T_C=334.54±0.08. The critical exponent γ is slightly inferior than predicted from the 3D Heisenberg model. Such a difference may be due, within the context of the quenched disorder, to the presence of some alterations of short-range magnetic order of FM clusters in the PM phase. The temperature variation in the effective exponent (γ_eff) is similar to those for disordered ferromagnets.     

Specific heat and critical behavior of Tl0.3MoO3 near the Peierls phase transition

The specific heat of the quasi-one-dimensional charge-density-wave (CDW) compound Tl_0.3MoO₃ has been measured using an adiabatic continuous heating method from 100 to 220 K. A specific heat jump associated with the Peierls phase transition occurs at 172.3 K. A good scaling relation between the excess specific heat and the susceptibility is found between 140 K and 190 K. Further analysis indicates that the width of the critical region of Tl_0.3MoO₃ is about 10 K and the specific-heat critical behavior can be well described by the three-dimensional XY model.     

Magnetic phase transition of Mn1.88Cr0.12Sb

The nature of the first order phase transition in Mn_1.88Cr_0.12Sb crystal is discussed. According to the magnetic susceptibility χ_⊥ and the specific heat measurements, there are two phase transitions, at 280 K and 315 K, respectively. They correspond to the vanishing of the “magnetic soft modes” for FIM and AF phases [4]. No change of the energy level positions was detected using the ESCA method.     

Fine structure of the field-induced magnetic transition in Nd0.1La0.9Fe11.5Al1.5

For the Nd_0.1La_0.9Fe_11.5Al_1.5 compound, the fine structure of the magnetic transition from the ferromagnetic (FM) to the antiferromagnetic (AFM) states has been studied carefully by means of magnetization (M) and heat capacity (C_p) measurements. Although a single phase with the cubic NaZn₁₃-type structure (Fm3c) has been proved by the room temperature X-ray diffraction pattern, the phase transition has been clearly found to be a stepwise process in M(T) and C_p(T) curves under proper fields. Due to the strong competition between the FM order and AFM order, the characteristic is especially evident under low fields, weakens gradually with the increasing applied field and finally vanishes when the field is higher than 2 T. This multi-step magnetic transition results from the inhomogeneity of the sample, probably due to the inhomogeneous distribution of Nd atoms.     

Structural phase transitions and sodium ordering in Na0.5CoO2: a combined electron diffraction and Raman spectroscopy study

The nonstoichiometric Na_xCoO₂ system exhibits extraordinary physical properties that correlate with temperature and Na concentration in its layered lattice without evident long-range structure modification when conventional crystallographic techniques are applied. For instance, Na_0.7CoO₂, a thermodynamically stable phase, shows large thermoelectric power; water-intercalated Na_0.33CoO₂·1.3H₂O is a newly discovered superconductor with T_c∼4 K, and Na_0.5CoO₂ exhibits an unexpected charge ordering transition at around T_co∼55 K. Recent studies suggest that the transport and magnetic properties in the Na_xCoO₂ system strongly depend on the charge carrier density and local structural properties. Here we report a combined variable temperature transmission electron microscopy and Raman scattering investigation on structural transformations in Na_0.5CoO₂ single crystals. A series of structural phase transitions in the temperature range from 80 to 1000 K are directly identified and the observed superstructures and modulated phases can be interpreted by Na-ordering. The Raman scattering measurements reveal phase separation and a systematic evolution of active modes along with phase transitions. Our work demonstrates that the high mobility and ordering of sodium cations among the CoO₂ layers are a key factor for the presence of complex structural properties in Na_xCoO₂ materials, and also demonstrate that the combination of electron diffraction and Raman spectroscopy measurements is an efficient way for studying the cation ordering and phase transitions in related systems.     

Angular dependence of vortex matter phase transition in MgB2 single crystal

The vortex matter phase transitions and intrinsic pinning effect were investigated in an MgB₂ single crystal using the torque magnetometry. For the field directions apart from the ab plane, we succeed in the observation of the vortex lattice melting transitions, which are transformed from the order-disorder transitions at low temperatures. Both transition fields with field directions can be describe by the GL effective mass model. For the field direction along the ab plane, these transitions become unobservable. Instead, the sudden increase in the hysteresis of magnetization curve occurs, indicating the existence of the intrinsic pinning coming from the layer structure.     

Nature of the quantum spin correlations through the superconducting-normal phase transition in electron-doped superconducting Pr0.88LaCe0.12CuO4

We use neutron scattering and specific heat measurements to relate the response of the spin fluctuations and static antiferromagnetic (AF) order to the superconductivity in the electron-doped high-transition-temperature superconductor, Pr_.88LaCe_.12CuO_4−δ (PLCCO) (T_c=24 K), as the system is tuned via a magnetic field applied beyond the upper critical field (H_c2) and driven into the normal state. The strength of the collective magnetic excitation commonly termed “resonance” decreases smoothly with increasing field and vanishes in the normal state, paralleling the behavior of the superconducting condensation energy. The suppression of superconductivity is accompanied by a smooth reduction in the very low energy spin fluctuations, and the concomitant emergence of static AF order. Our results suggest an intimate connection between the resonance and the superconducting condensation energy.     

Magnetic fluids in an external field

Within mean field approximation we investigate the phase diagrams of magnetic fluids in presence of a magnetic field. In a finite field the magnetic phase transition is absent, but instead a line of first order liquid-liquid transitions ending in a critical point occurs for a magnetic interaction, which is sufficiently strong. Varying the magnetic field these critical points extend from the tricritical point at H=0 to a critical endpoint. For a fluid with Ising spins we calculate the critical lines and several tricritical exponents analytically. For Heisenberg fluids we obtain the phase diagrams from a numerical solution of the mean field equations of state. Received 20 March 1998     

Crystallographic study of the phase transition in (Me4P)2ZnBr4

The compound (Me₄P)₂ZnBr₄, a member of the β-K₂SO₄ structure class, undergoes a phase transition at 84°C from the room temperature space group P12₁/c1 to the parent Pmcn structure. The room temperature structure corresponds to a ferrodistortive transition of B_1g symmetry at the zone center. At room temperature, the compound has lattice constants a=9.501(1), b=16.055(2), c=13.127(2) Å and β=90.43(1)°. For the high temperature phase, the orthorhombic cell has dimensions a=9.466(2), b=16.351(3) and c=13.284(2) Å. The structures consist of two crystallographically independent Me₄P⁺ cations and the ZnBr₄²⁻ anions. In the room temperature phase, all three ionic species show substantial displacement from the mirror plane perpendicular to the a-axis that exists in the high temperature phase, as well as rotations out of that plane. The thermal parameters of the cations are indicative of substantial librational motion. Measurements of lattice parameters have been made at 2-5°C intervals over the temperature range 40-140°C. The changes in the lattice constants appear continuous at T_c (within experimental limits) indicating that the phase transition is likely second-order. The a lattice constant shows an anomalous shortening as T_c is approached. Thermal expansion coefficients are calculated from this data. An application of Landau theory is used to derive the temperature dependencies of spontaneous shear strain and corresponding elastic stiffness constants associated with the primary order parameter.     

Pressure-induced structural phase transition in ReO3

We have investigated the pressure-induced structural phase transition in ReO₃ by neutron diffraction on a single crystal. We collected neutron diffraction intensities from the ambient and high pressure phases at P=7 kbar and refined the crystal structures. We have determined the stability of the high pressure phase as a function temperature down to T=2 K and have constructed the (P-T) phase diagram. The critical pressure is P_c=5.2 kbar at T=300 K and decreases almost linearly with decreasing temperature to become P_c=2.5 kbar at T=50 K. The phase transition is driven by the softening of the M₃ phonon mode. The high pressure phase is formed by the rigid rotation of almost undistorted ReO₆ octahedra and the Re-O-Re angle deviates from 180°. We do not see any evidence for the existence of the tetragonal (P4/mbm) intermediate pressure phase reported earlier.     

Effects of the phase transition in Hg2(Br,I)2 crystals

The effects of the phase transition in Hg₂(Br,I)₂ crystals have been investigated over a wide range of temperatures by the Raman scattering spectroscopy and X-ray diffraction analysis. The overtones (at the X point of the Brillouin zone boundary) and the fundamental tones (at the center of Brillouin zone) of soft modes are found in the Raman spectra of these crystals and studied in detail. The density of one-phonon states of the soft TA branch manifests itself in the Raman spectra of mixed crystals. The potentialities of the soft-mode spectroscopy are realized in full measure. Analysis of the ratio between intensities of overtones and fundamental tones of the soft modes has demonstrated the applicability of the Landau phenomenological theory of phase transitions. The orthorhombic splitting of the reflections corresponding to the basal plane is revealed in the X-ray diffraction patterns and thoroughly explored. The temperature dependences of the isotropic and shear spontaneous strains are obtained. It is shown that the shear spontaneous strain plays a decisive role. The critical indices are determined and the model of the improper ferroelastic phase transition D _4h ¹⁷ → D _2h ¹⁷ in the vicinity of the tricritical point is corroborated.     

Detailed infrared spectroscopic study of thermal transitions in new hybrid [(CH3)2CHNH3]4Cd3Cl10 crystal

Phase transitions of tetra(isopropylammonium)decachlorotricadmate(II) [(CH₃)₂CHNH₃]₄Cd₃Cl₁₀ crystal have been studied by infrared, far infrared and Raman measurements in wide temperature range, between 11 K and 388 K. The temperature changes of wavenumber, center of gravity, width and intensity of the bands were analyzed to clarify cationic and anionic contributions to the phase transitions mechanism. The results of investigation showed earlier by differential scanning calorimetry (DSC), thermal expansion and dielectric measurements clearly confirmed the sequence of phase transitions at T₁=353 K, T₂=294 K and T₃=260 K. The current results derived from DSC and infrared measurements revealed additional phase transition at T₄=120 K.     

An apparent Landau-type second order transition in the spinel CdIn2S4

Experimental evidence is given of a second order transition in the spinel CdIn₂S₄. The specific heatc _p shows a step at the transition temperature (T _c=403°K), the thermal expansion coefficientα remains unaffected. An analysis yields a critical region of this transition considerably narrower (5°K) than expected from the critical regions of transitions of a similar type (quartz: 160°K,β-brass: 250°K) and therefore the critical region has not been observed experimentally, i.e. the transition appears to follow Landau’s theory. Landau’s group theoretical analysis of second order transitions in crystals leads to a model for the transition in CdIn₂S₄ on the atomic scale. If the temperature is decreased below the critical temperature a 1:1 ordering occurs between Cd and In on the tetrahedral sites. With this model the gross features of this transition can be qualitatively understood: The unaffected thermal expansion and the long relaxation times for the establishment of equilibrium approachingT _c. Also the narrow critical region can be explained in terms of a large correlation length in CdIn₂S₄. Finally it is shown that a generalized formulation of the thermodynamic part of Landau’s theory correlates thermodynamic quantities far above and far below the critical temperature, as illustrated for CdIn₂S₄. This generalization allows also a more satisfactory determination of the critical region.