Order Melting Transition Research Articles

Vortex dynamics in YBa2Cu3O7−δ with in-plane columnar defects introduced by irradiation

We report on the effects of introducing columnar defects by irradiation in clean single crystals of YBa2Cu3O7−δ in a direction parallel to the ab-plane. The defects were introduced by bombarding the samples with 208Pb56+ ions at an energy of 1.4GeV. We find that the defects suppress the first order melting transition for magnetic fields aligned parallel or at small angles relative to the defects. The columnar defects inhibit vortex motion of vortices parallel to the defects, while the vortices experience less pinning when they are perpendicular to the defects. Our results suggest that the pinning anisotropy is increased, at least for magnetic fields up to the matching field dose of 1T.

Two-step melting of Na41+

The heat capacity of the mass selected Na41+ cluster has been measured using a differential nanocalorimetry method. A two-peak structure appears in the heat capacity curve of Na41+, whereas Schmidt and co-workers [M. Schmidt, J. Donges, Th. Hippler, and H. Haberland, Phys. Rev. Lett. 90, 103401 (2003)] observed, within their experimental accuracy, a smooth caloric curve. They concluded from the absence of any structure that there is a second order melting transition in Na41+ with no particular feature such as premelting. The observed difference with the latter results is attributed to the better accuracy of our method owing to its differential character. The two structures in the heat capacity are ascribed to melting and premelting of Na41+. The peak at lower temperature is likely due to an anti-Mackay to Mackay solid-solid transition.

Melting of a tetrahedral network model of silica

Thermal properties of an idealised tetrahedral network model of silica are investigated by Monte Carlo simulations. The interatomic potential consists of anharmonic stretching and bending terms, plus a short range repulsion. The model includes a bond interchange rule similar to the well known Wooten, Winer and Weaire (WWW) algorithm (see Phys. Rev. Lett., 1985, 54, 1392). Simulations reveal an apparent first order melting transition at T = 2200 K. The computed changes in the local coordination upon melting are consistent with experimental and ab initio data.

Charge order melting and magnetic transition in Nd 0.5(1+ x) Ca 0.5(1− x) Mn (1− x) Cr xO 3 system

The magnetic property of double doped manganite Nd 0.5(1+ x) Ca 0.5(1− x) Mn (1− x) Cr x O 3 with a fixed ratio of Mn 3+:Mn 4+=1:1 has been investigated. For the undoped sample, it undergoes one transition from charge disordering to charge ordering (CO) associated with paramagnetic (PM)-antiferromagnetic (AFM) phase transition at T<250 K. The long range AFM ordering seems to form at 35 K, rather than previously reported 150 K. At low temperature, an asymmetrical M– H hysteresis loop occurs due to weak AFM coupling. For the doped samples, the substitution of Cr 3+ for Mn 3+ ions causes the increase of magnetization and the rise of T c. As the Cr 3+ concentration increases, the CO domain gradually becomes smaller and the CO melting process emerges. At low temperature, the FM superexchange interaction between Mn 3+ and Cr 3+ ions causes a magnetic upturn, namely, the second FM phase transition.

Flux melting inBi2Sr2CaCu2O8+δ: Incorporating both electromagnetic and Josephson couplings

Multilevel Monte Carlo simulations of a BSCCO system are carried out including both Josephson as well as electromagnetic couplings for a range of anisotropies. A first order melting transition of the flux lattice is seen on increasing the temperature and/or the magnetic field. The phase diagram for BSCCO is obtained for different values of the anisotropy parameter $\gamma$. The best fit to the experimental results of D. Majer {\it et al.} [Phys. Rev. Lett. {\bf 75}, 1166 (1995)] is obtained for $\gamma\approx 250$ provided one assumes a temperature dependence $\lambda^2(0)/\lambda^2(T)=1-t$ of the penetration depth with $t=T/T_c$. Assuming a dependence $\lambda^2(0)/\lambda^2(T)=1-t^2$ the best fit is obtained for $ \gamma\approx 450$. For finite anisotropy the data is shown to collapse on a straight line when plotted in dimensionless units which shows that the melting transition can be satisfied with a single Lindemann parameter whose value is about 0.3. A different scaling applies to the $\gamma=\infty$ case. The energy jump is measured across the transition and for large values of $\gamma$ it is found to increase with increasing anisotropy and to decrease with increasing magnetic field. For infinite anisotropy we see a 2D behavior of flux droplets with a transition taking place at a temperature independent of the magnetic field. We also show that for smaller values of anisotropy it is reasonable to replace the electromagnetic coupling with an in-plane interaction represented by a Bessel function of the second kind ($K_0$), thus justifying our claim in a previous paper.

Persistence of the intrinsic transition in the vortex matter of disordered BSCCO:2212 crystals

The first order melting transition (FOT) in vortex matter of clean Bi 2Sr 2CaCu 2O 8 crystals, is identified by a discontinuity in the reversible magnetization, which extends to the low temperature (irreversible) regime in the form of a jump in the energy barrier vs. current, U( J), variation. Heavy ion irradiation disorders the vortex lattice, enhances flux pinning, and is believed to suppress the FOT. However, in underdoped samples, detailed measurements of magnetic relaxation by the Hall-array technique reveal the existence of a discontinuous jump in the U( J) curve precisely at the location of FOT of pristine crystals.

Strong vortex liquid correlation from multiterminal measurements on untwinned YBa2Cu3O(7-delta) single crystals.

Multiterminal transport measurements indicating a strongly correlated vortex liquid above the first order melting transition in untwinned YBa2Cu3O(7--delta) single crystals are presented. The correlation is found to be surprisingly stable for different weak variations of point disorder. We investigate the differences between intervortex and intravortex correlations in different contact geometries. The results are in agreement with the local conductivity model, with zero resistivity along straight vortex line segments.

Scaling behaviour of magneto-resistance in clean YBa 2Cu 3O 7− δ single crystals in the vortex liquid state

We present temperature and angular studies of the ohmic magneto-resistivity of clean twinned and detwinned YBa 2Cu 3O 7− δ single crystals. The scaling behaviour of thermodynamic and dynamic properties of the vortex liquid phase, in the region H c1≪ H< H c2, was analysed. Using the melting field B m, as en example, we demonstrate that when the applied field is tilted an angle θ away from the crystalline c-axis, the thermodynamic properties of the vortex system are controlled by the effective field B eff= Bε θ , where ε θ =(cos 2 θ+ ε 2sin 2 θ) 0.5 is the angular dependent anisotropy parameter (with ε=0.134) and B= μ 0 H. We observe a suppression of the `melting kink' (which is a fingerprint of the first order melting transition) when the applied field is larger than the multicritical field B mc. However, this transition recovers when the sample is tilted at an angle θ such that Bε θ < B mc. We find that this `effective field' model can also describe phenomena associated with vortex dynamics, but only for sufficiently low angles ( θ<60°). From ρ( T)/ B scaling of resistivity for different magnetic fields (at θ=0°), we show that the free flux-flow model applies for a considerable part of the resistive transition.

Thermally Assisted Flux Creep of a Driven Vortex Lattice in Untwinned YBa 2 Cu 3 O 7-δ Single Crystals.

The authors have studied the driven vortex lattice in untwinned, clean YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} single crystals, showing the first order (melting) transition T{sub m}. At high enough driving currents (j {approximately} 10{sup 3} A/cm{sup 2}, j {approx{underscore}gt} j{sub c}) and temperatures T < T{sub m}, a clear distinction is found between two different behaviors of the moving vortex lattice. The onset of dissipation is characterized by a noisy flux creep with a temperature independent activation energy U(j). At higher temperatures, the creep regime crosses over into a flux flow regime with linear resistivity. Apart from the dip in resistivity at T{sub m}, associated with the peak effect and usually assigned to a softening of the shear modulus, the resistivity of the flowing flux lattice continuously extends into the vortex-liquid.

Phase diagram of optimally dopedYBa2Cu3O7−δ: Effect of oxygen stoichiometry

Influence of the oxygen stoichiometry on the phase diagram of clean ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystals has been studied in the region of optimal doping $(0.05&lt;\ensuremath{\delta}&lt;0.09).$ Temperature and angular dependencies of magnetoresistance were analyzed for fields of up to 23 T. At low fields a sharp resistivity kink, which is a signature of the first order melting transition, was observed in all the samples studied. This kink, however, disappears when B exceeds the multicritical field ${B}_{\mathrm{mc}}.$ It was found that ${B}_{\mathrm{mc}}$ strongly increases with decreasing \ensuremath{\delta}. We have demonstrated that variations in the oxygen stoichiometry in the range of $0.05&lt;\ensuremath{\delta}&lt;0.09$ do not have a significant effect on intrinsic parameters (such as anisotropy, coherence length, and penetration depth) but lead to a strong increase in entanglement of the vortex lines. We relate the dependence of ${B}_{\mathrm{mc}}$ on \ensuremath{\delta} with entanglement of the vortex lines, which is promoted by their interaction with oxygen vacancies.

Grain-boundary component in W-Ga composites: A way towards skeleton structures

Nanostructured materials consist of crystalline and grain boundary components. In the simplest case, both components are chemically identical. Here, we present the results of a study of a system consisting of a crystalline component built by A atoms (tungsten) and a grain boundary component of B atoms (gallium). Within this system, component B is in a disordered state. Most likely it exhibits an 'amorphous-like' structure, and coats the tungsten crystals uniformily with a constant thickness, thus forming a Ga skeleton structure. The non-crystalline gallium seems to undergo no first order structural phase transitions, e.g., no first order melting transition was noted when the composit was below, at or above the equilibrium melting point of Ga. The properties of gallium as grain boundary component differ significantly from those of crystalline and amorphous bulk gallium.

Can there be a second kind of entropy catastrophe in the melting of metastable solids?

We explore here the thermodynamic possibility of the superheating of alloys and the existence of a second order melting transition in metastable alloys subject to concentration fluctuations. Toward the purpose, a novel approach has been adopted which involves simultaneous consideration of the free energy and entropy changes associated with the melting of the fluctuated region. Similar to the well-known Kauzmann paradox in freezing, in principle, there exists an entropy catastrophe in the nucleation of melting in metastable solids, too. However, it would be experimentally difficult to realize the melting of metastable solids because of the tendency to equilibrate at elevated temperatures.

Simulations of two-dimensional melting on the surface of a sphere

We have simulated a system of classical particles confined on the surface of a sphere interacting with a repulsive $r^{-12}$ potential. The same system simulated on a plane with periodic boundary conditions has van der Waals loops in pressure-density plots which are usually interpreted as evidence for a first order melting transition, but on the sphere such loops are absent. We also investigated the structure factor and from the width of the first peak as a function of density we can show that the growth of the correlation length is consistent with KTHNY theory. This suggests that simulations of two dimensional melting phenomena are best performed on the surface of a sphere.

Phase coherence and the boson analogy of vortex liquids

The statistical mechanics of the flux-line lattice in extreme type-II super- conductors is studied within the framework of the uniformly frustrated anisotropic 3D XY-model. A finite-field counterpart of an Onsager vortex-loop transition in extreme type-II superconductors renders the vortex liquid phase- incoherent when the Abrikosov vortex lattice undergoes a first order melting transition. For the filling fractions considered in this paper $f$ given by $1/f=12,14,16,20,25,32,48,64,72,84,96,112$, and 128, the vortex liquid phase is not describable as a liquid of well-defined field induced vortex lines. This is due to the proliferation of thermally induced closed vortex-loops with dia- meters of order the magnetic length in the problem, resulting in a "percolation transition" driven by non-field induced vortices also transverse to the direc- tion of the applied magnetic field. This immediately triggers flux-line lattice melting and loss of phase-coherence in all direction. In a non-relativistic 2D boson-analogy picture, this latter feature would correspond to a vanishing mass of the bosons. Scaling functions for the specific heat are calculated in zero and finite magnetic field. From this we conclude that the critical region is of order 10% of $T_c$ for a mass anisotropy $\sqrt{M_z/M}=3$, and increases with increasing mass anisotropy. The entropy jump at the melting transition is cal- culated as a function of magnetic field for a mass-ansitropy slightly lower than that in $YBCO$, and found to be $\Delta S=0.1k_B$ per vortex panncake, independent of the magnetic field for the filling fractions considered here. This is slightly lower than experimental values of $\Delta S \approx 0.4k_B$ found experimentally for $YBCO$. We attribute this to the slightly lower mass anisotropy used in our simulations.

High-Field Vortex Dynamics inYBa2Cu3O7fromO17Nuclear Magnetic Resonance

The magnetic field--temperature phase diagram for vortex dynamics in $\mathrm{Y}\mathrm{Ba}{}_{2}\mathrm{Cu}{}_{3}{\mathrm{O}}_{7}$ has been extended up to 24 T based on $^{17}O$ NMR experiments on aligned powders. Both spectrum analysis and spin-spin relaxation experiments indicate that vortices are pinned below a temperature ${T}_{p}$, which for low fields is consistent with ${T}_{m}$, the first order melting transition for clean, untwinned crystals. At high fields 10--24 T, ${T}_{p}$ is 80 K and field independent. Pinned vortices have a Lorentzian spectral density of field fluctuations with a sharp onset.

Comparative AC susceptibility and resistivity studies of the vortex lattice melting transition in detwinned YBa 2Cu 3O 7− δ single crystals

We have studied the transition from the vortex liquid to the vortex solid state in clean, detwinned YBa 2Cu 3O 7− δ single crystals in fields up to 12 T using AC susceptibility and resistivity measurements. For μ 0 H<7 T a sharp drop in the resistivity at a temperature T m (which has been shown to be a signature of a first order phase transition [1, 2]) was found to be accompanied by an AC field independent abrupt onset of both χ′ and χ″ components. The AC susceptibility data suggest that just below T m there is a transition region where the liquid and solid phases coexist. The width of the transition region was found to be sample dependent and can be related to structural inhomogeneity. Above the multicritical field μ 0 H mc=7 T simultaneous broadening of both the ρ( T) drop and the χ″( T) onset show that the first order melting transition is suppressed.

Denaturation of Heterogeneous DNA

The effect of heterogeneous sequence composition on the denaturation of double stranded DNA is investigated. The resulting pair-binding energy variation is found to have a negligible effect on the critical properties of the smooth second order melting transition in the simplest (Peyrard-Bishop) model. However, sequence heterogeneity is dramatically amplified upon adopting a more realistic treatment of the backbone stiffness. The model yields features of ``multi-step melting'' similar to those observed in experiments.

Effect of Disorder on the Vortex-Lattice Melting Transition.

We use a three dimensional stacked triangular network of Josephson junctions as a model for the study of vortex structure in the mixed state of high Tc superconductors. We show that the addition of disorder destroys the first order melting transition occurring for clean samples. The melting transition splits in two different (continuous) transitions, ocurring at temperatures Ti and Tp (>Ti). At Ti the perpendicular-to-field superconductivity is lost, and at Tp the parallel-to-field superconductivity is lost. These results agree well with recent experiments in YBaCuO.

Path integral monte carlo simulation of vortices

One of the most fascinating properties of high-Tc superconductors is the existence of a thermodynamic phase-transition located well below the mean field transition lineHc2. This transition is a first order melting transition of the Abrikosov vortex lattice into a entangled vortex liquid, and is signalled by a discontinuity in the magnetization. On the London level, the vortex system can be mapped onto interacting bosons in two dimensions. We use this mapping to simulate the vortex system with Path Integral Monte Carlo methods. This approach does not introduce an underlying lattice and allows for the simultaneous investigation of crystalline and longitudinal long-range order. We find a first-order transition as the system passes from a lattice to an entangled liquid. The jump in the magnetization is in agreement with experiments. The phase diagrams of bosons and of vortices are discussed.

Suppression of the first order vortex melting transition by intrinsic pinning in YBa2Cu3O7- delta.

The first order vortex melting transition in single crystal ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ is investigated for magnetic field direction close to H\ensuremath{\parallel}ab. For exact field alignment H\ensuremath{\parallel}ab, the ``kink'' in \ensuremath{\rho}(T) associated with the first order melting transition is replaced with a continuous resistive transition in the presence of intrinsic pinning, indicative of a second order transition with dynamic scaling exponent s=1.4. In addition, we demonstrate the abatement of the ``kink'' in the temperature dependence of the magnetoresistivity, associated with the first order melting transition for H\ensuremath{\parallel}c in the presence of only six twin boundaries.