Vortex-lattice Melting Research Articles

Peak effect and its disappearance in YBCO superconducting crystals

The anomalous temperature dependence of vortex pinning, known as the peak effect, in a YBa2Cu3O6.55 crystal is studied by an AC susceptibility technique. The peak effect is found to appear only at the intermediate field range. The onset of the peak effect in the H-T plane exhibits a reentrant behavior, reminiscent of the Nelson phase diagram for 3D vortex-lattice melting.

Anisotropic Latent Heat of Vortex-Lattice Melting in UntwinnedYBa2Cu3O7−δ

We report a distinct thermal signature of the first-order vortex-lattice melting for the external magnetic field $H$ both parallel and perpendicular to the $c$ axis of an untwinned ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystal. Latent heats and discontinuities in specific heat were observed for each configuration. The entropies of melting and the melting lines ${H}_{\mathrm{m}}(T)$ both scale with an anisotropy parameter $\ensuremath{\gamma}\ensuremath{\approx}8$. The specific heat of the vortex fluid is considerably larger than that of the vortex solid (by up to $2\mathrm{mJ}/\mathrm{mole}{\mathrm{K}}^{2}$), which is not explained by simple arguments based on counting the numbers of thermodynamic degrees of freedom.

Thermally assisted flux flow and melting transition for Mo/Si multilayers

Two-dimensional and three-dimensional vortex-lattice melting is observed for superconducting Mo/Si multilayers. The position of the melting transition on the H-T phase diagram is in reasonable quantitative accordance with the existing theories. Above the melting line another phase transition is found connected with the decoupling in the liquid phase or with transition from hexatic to ordinary liquid. The thermally assisted flux-flow (TAFF) regime of the vortex motion is observed in the fluid phase governed by the plastic barrier characteristic for viscous liquid. The TAFF regime with different activation energy takes place also in a vortex solid phase above the depinning line. {copyright} {ital 1996} {ital The American Physical Society}

Quantum melting of a two-dimensional vortex lattice at zero temperature.

We consider the quantum melting of a two-dimensional flux lattice at temperature $T=0$ in the "superclean limit." In this regime, we find that vortex motion is dominated by the Magnus force. A Lindemann criterion predicts melting when $\frac{{n}_{v}}{{n}_{p}}>~\ensuremath{\beta}$, where ${n}_{v}$ and ${n}_{p}$ are the areal number densities of vortex pancakes and Cooper pairs, and $\ensuremath{\beta}\ensuremath{\approx}0.1$. A second criterion is derived by using Wigner-crystal and Laughlin wave functions for the solid and liquid phases respectively, and setting the two energies equal. This gives a melting value similar to the Lindemann result. We discuss the numerical value of the $T=0$ melting field for thin layers of a low-${T}_{c}$ superconductor, such as $a$-MoGe, and single layers of high-${T}_{c}$ materials.

Comment on "Vortex Glass and Lattice Melting Transitions in a YNi2B2C Single Crystal"

A Comment on the Letter by Mi-Ock Mun, et al., Phys. Rev. Lett. 76, 2790 (1996). The authors of the Letter offer a Reply.Received 25 April 1996DOI:https://doi.org/10.1103/PhysRevLett.77.2145©1996 American Physical Society

Vortex lattice melting and interlayer coupling in Bi2Sr2CaCu2O8+δ crystals

We find that resistive hysteresis accompanies vortex lattice melting in Bi2Sr2CaCu2O8+° single crystals, together with a sharp drop of the resistance with decreasing temperature. The melting transition temperatureT m was current dependent, indicating that current drives the vortex system out of equilibrium. AboveT m , we find a second sharp feature in the data which we interpret to signify the decoupling transition of the vortex line liquid. Our measurements show nonlocal conductivity in the vortex liquid phase, which correlates with the strength of interlayer vortex coupling. Finally, we review existing literature on vortex lattice melting in BSCCO. While the melting curve varies significantly for different samples, the measurements appear to probe the same physical process in all cases.

Vortex lattice melting in 2D superconducting networks

We use Monte Carlo simulations to study the melting of vortex lattices in two-dimensional square superconducting networks, for weak magnetic fields ( f = 1 n ), and for magnetic fields near full frustration ( f = 1 2 − 1 n ). We find distinct pinned vortex lattice, floating vortex lattice, and vortex liquid phases.

Coincidence of vortex-lattice melting and loss of vortex correlation along the c direction in untwinned YBa2 Cu3O7- delta single crystals.

We report on transport measurements using the dc flux transformer configuration in clean and twinned single crystals of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. We show that correlated disorder changes not only the order of the solid-liquid phase transition but also the nature of the vortices in the liquid state. In clean crystals, melting is shown to take place between a solid of vortex lines and a liquid with no correlation in the direction of the magnetic field.

Irreversibility line and second peak in the magnetization curves of Pb 2Sr 2Y 1− xCa xCu 3O 8 single crystals

The irreversibility field H irr and the anomalous second peak in the magnetization curves have been studied from the magnetization measurements ( H || c-axis) for Pb 2Sr 2Y 1− x Ca x Cu 3O 8 single crystals with 0 ≦ x ≦ 0.5 and with the anisotropic parameter γ ≡ (m c ∗/m ab ∗) 1 2 of 24 ≧ γ ≧ 5 . The temperature dependence of H irr is discussed in terms of flux creep and 2D or 3D vortex-lattice melting. The anomalous second peak is observed for all x values. The peak shape is similar to that of YBa 2Cu 3O 7−δ. The peak field H p is dependent on temperature and proportional to ( 1 − T/T c ) 3 2 near T c. Both H irr and H p at each reduced temperature are proportional to γ −2 the origin of the second peak is discussed in terms of dimensional crossover of the vortices from 3D to 2D and collective pinning.

Vortex glass and lattice melting transitions in a YNi2B2C single crystal.

The mixed state of the weakly disordered superconductor ${\mathrm{YNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ is found to be similar to that of high- ${T}_{c}$ materials due to its large fluctuations. The very sharp resistive transition with a kink and the S-shaped $I\ensuremath{-}V$ curve appear below $H\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}$ 1 T indicating a lattice melting transition. The scaling behavior of the vortex glass transition in $R\ensuremath{-}T$ and $I\ensuremath{-}V$ curves for $H\ensuremath{\ge}2$ T is observed with critical exponents $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.23\ifmmode\pm\else\textpm\fi{}0.02$ and $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5.46\ifmmode\pm\else\textpm\fi{}0.32$, which are field independent. The vortex solid state changes from the vortex lattice at low fields to the vortex glass at high fields due to a field-enhanced pinning effect. The type of multicriticality is not yet conclusive.

Dimensional crossover on a vortex-lattice melting line in superlattices and high-T c superconductors

It is well known that upper critical field, Hc2, in superlattices (SL) and layered superconductors (LS) is a nonlinear function of temperature,T, due to the so-called dimensional crossover. This nonlinearity manifests itself as well (via dependence of the vortex-lattice elastic moduli onH c2) at theH-T phase diagram for vortex-lattice melting. We calculated the shape of a melting (irreversibility) line,H m (T), in SL and LS taking into account thermal and quantum fluctuations as well as equation forH c2 (T) in these systems in various regimes. In particular, the squareroot crossover ofH c2 (T) results in a crossover from the power branchH m ∝(T c −T) a (a≤2) nearT c to the linear oneH m ∝(T *−T) below someT * in agreement with the data on vortex melting in YBaCuO.

Vortex-lattice melting transition in La1.85Sr0.15CuO4 single crystal

We have measured the magnetization of La1.85Sr0.15CuO4 single crystal as a function of the temperatureT and the magnetic fieldH. Above the irreversibility fieldHirr, the magnetization shows small anomaly at the magnetic fieldHm. This anomaly is attributed to the first-order vortex-lattice melting transition. The temperature dependence ofHm is described asHmα (1−T/Tc)n withn=1.8, which agree with the vortex-lattice melting theory. The Lindemann criterioncL is estimated to be 0.12 which is as large as the reported values for YBa2Cu3O7−δ or Bi2Sr2CaCu2O8+δ system.

Irreversibility line and reversible magnetization for the in-plane magnetic field in Bi2Sr2CaCu2O8+δ single crystals

The irreversibility lineHirr(T) and reversible magnetizationM(H) for magnetic field applied along thea-axis of Bi2Sr2CaCu2O8+δ were determined in the vicinity ofTc. TheHirr(T) was found to be located at higher fields than those predicted by an anisotropic vortex-lattice melting scaling approach. Obtained results can be explained by the discrepancy between the fields of the appearance of the irreversibilityHirr and those of the vortex-lattice melting and/or by higher value of the effective mass anisotropy than the values commonly accepted for the Bi2Sr2CaCu2O8+δ.

Observation of resistivity drops and the vortex phase diagram in Bi 2Sr 2CaCu 2O y

The in-plane resistivity of a Bi 2Sr 2CaCu 2O y single crystal under various magnetic fields applied along the crystalline c-axis direction was measured. A carefully prepared overdoped crystal ( T c = 78.3 K) was used for the measurement. Employing an AC resistance bridge, the noise level was reduced to about 10 −9 Ω cm. A clear resistivity drop was observed in the resistivity region of 10 −7–10 −9 Ω cm when a magnetic field lower than 900 Oe was applied. The temperature of this resistive drop coincided well with that of the magnetization step observed on the same sample using SQUID magnetometry. The results are discussed in the context of the vortex-lattice melting transition.

Resistivity onset at the first-order vortex-lattice phase transition in Bi2Sr2CaCu2O8

Simultaneous measurements of resistivity and local magnetization using microscopic Hall sensors were carried out on Bi2Sr2CaCu2O8 (BSCCO) crystals as a function of applied field and temperature. The resistivity onset is found to occur concurrently with the first-order vortex-lattice phase transition, determined by the equilibrium magnetization step. This behavior is indicative of a vortex-lattice melting transition. The resistivity vanishes below the transition although the magnetization remains reversible.

3D–2D crossover in melting transition on superconducting Mo/Si multilayers

Two-dimensional and three-dimensional vortex-lattice melting is observed on superconducting Mo/Si multilayers. Quasi-2D melting takes place in the range of high magnetic fields. The position of the melting transition on H-T phase diagram is in a reasonable quantitative accordance with the existing theories. Above melting line another phase transition is found connected with the decoupling in the liquid phase or with transition from hexatic to ordinary liquid. TAFF regime of the vortex motion is observed in the fluid phase governed by the plastic barrier charateristic for viscous liquid. TAFF regime with different activation energy takes place also in a vortex solid phase above the depinning line.

Crossover from the first-order vortex phase transition to the peak effect in Bi 2Sr 2CaCu 2O y having different oxygen contents

We have measured the magnetization and the heat capacity of over-doped (OVD) and optimally doped (OPD) Bi 2Sr 2CaCu 2O y single crystals in the mixed state under magnetic fields applied along the c-axis. In both samples, a distinct magnetization step is observed in the magnetization curve at high temperatures and is found to change to a kink at low temperatures. At still lower temperatures, the peak effect dominates the magnetization curve and the kink vanishes. The origin of the step and the kink in the magnetization curve is considered to be the first-order phase transition in a quasi-three-dimensional vortex system although the heat capacity shows little anomalies at the transition because the latent heat is small. The first-order phase transition line of each sample is drawn on the H- T plane and it is found that the slope of the line of the OVD sample is steeper than that of the OPD sample. The entropy jump at the transition of the OVD sample is estimated to be larger than that of the OPD one at all temperatures and magnetic fields studied. This behavior is contradictory to the simple vortex-lattice melting picture.

Carrier dependences of anisotropy and irreversibility field in Pb 2Sr 2Y 1−xCa xCu 3O 8 single crystals

Anisotropic properties of the electrical resistivity and the resistive superconducting transition under magnetic fields have been investigated for the single-crystal Pb 2Sr 2Y 1− x Ca x Cu 3O 8 with 0 ≦ x ≦ 0.5 in the so-called underdoped region. The anisotropic parameter γ ≡ (m ∗ c/m ∗ ab) 1 2 is found to increase from ∼5 to 25 with decreasing x, namely, with decreasing hole concentration. The irreversibility field H irr has been studied from the magnetization measurements for H ⋎ c- axis . In the high-temperature regime near T c, H irr is found to be proportional to 1−T/T c ) 3 2 for x∼0.5 and to (1−T/T c ) 3 2 or (1− T/ T c) 2 for smaller x values. In this regime, H irr is also found to be proportional to γ −2. In the low-temperature regime, on the other hand, H irr grows exponentially as approximately expressed as e − T / T o, and shows a still stronger growth as e T o/ T at much lower temperatures for smaller x values. These behaviors are discussed in terms of flux creep, vortex-lattice melting and vortex-glass melting.

First-order melting of vortex lattice in strongly type-II three-dimensional superconductors

We calculate the transition line of the first-order melting of the vortex lattice in a three-dimensional type-II superconductor in fields of several T, using the results from the density-functional theory of vortex melting in two dimensions and a self-consistent Hartree treatment of correlations along the field. The result is in quantitative agreement with experiment. The temperature width of the hysteresis, the latent heat, the Debye-Waller factor and the magnetization at the transition are discussed.

Vortex dynamics below the flux-lattice melting transition in YBa2Cu3O7- delta.

We report measurements of the critical current, differential resistance, and voltage noise below the vortex-lattice melting transition in clean, untwinned ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ crystals. The differential resistance at dc current bias much greater than ${\mathit{J}}_{\mathit{c}}$ shows a sharp feature at the melting transition accompanied by a rapid drop in the voltage noise, demonstrating that the melting transition is insensitive to the static pinning potential. In the solid phase, the measurements all show a marked change from the low-field, pinned lattice to the high-field vortex-glass contiguous with the tricritical point in this sample.