Ordered Vortex Lattice Research Articles

Direct evidence for an intrinsic square vortex lattice in the overdoped high- T(c) superconductor La(1.83)Sr(0.17)CuO(4+delta).

We report here the first direct observations of a well ordered vortex lattice in the bulk of a La(2-x)Sr(x)CuO(4+delta) single crystal (slightly overdoped, x = 0.17). Our small angle neutron scattering investigation of the mixed phase reveals a crossover from triangular to square coordination with increasing magnetic field. The existence of an intrinsic square vortex lattice has never been observed in high-temperature superconductors and is indicative of the coupling of the vortex lattice to a source of anisotropy, such as those provided by a d-wave order parameter or the presence of stripes.

First-order disorder-driven transition and inverse melting of the vortex lattice

Vortex matter phase transitions in the high-temperature superconductor Bi 2Sr 2CaCu 2O 8 were studied using local magnetization measurements combined with a vortex `shaking' technique. The measurements revealed thermodynamic evidence of a first-order transition (FOT) along the second magnetization peak line, at temperatures below the apparent critical point T cp. We found that the FOT line does not terminate at T cp, but continues down to at least 30 K. This observation suggests that the ordered vortex lattice phase is destroyed through a unified FOT that changes its character from thermally induced melting at high temperatures to a disorder-induced transition at low temperatures. At intermediate temperatures the transition line shows an upturn, which implies that the vortex matter displays `inverse' melting behavior.

Superconducting fluctuation effect on the de Haas–van Alphen oscillations in the vortex liquid state of quasi-2D superconductors

The damping of the de Haas–van Alphen (dHvA) oscillations in the mixed state of a 2D superconductor is studied within a new analytical approach to the problem of vortex-lattice fluctuations at high magnetic fields. It is shown that in the ‘liquid’ state around mean field H c2( T), averaging over phase fluctuations leads to damping of the dHvA osillations, which can be well described by the random vortex lattice model. The calculated damping rate is in a good quantitative agreement with recent experiments carried out on a quasi-2D organic superconductor. It is predicted that deep in the mixed state, the freezing into an ordered vortex lattice is accompanied by a sharp upward turn in the slope of the ‘Dingle plot’.

Crystallization of the ordered vortex phase in high-temperature superconductors

The Landau-Khalatnikov time-dependent equation is applied to describe the crystallization process of the ordered vortex lattice in high temperature superconductors after a sudden application of a magnetic field. Dynamic coexistence of a stable ordered phase and an unstable disordered phase, with a sharp interface between them, is demonstrated. The transformation to the equilibrium ordered state proceeds by movement of this interface from the sample center toward its edge. The theoretical analysis dictates specific conditions for the creation of a propagating interface, and provides the time scale for this process.

Current driven organization of magnetic vortices

We report on a novel form of organization of magnetic vortices in a superconductor driven by a current. By following the vortex motion with fast transport measurements we show that the current enables the system to escape out of metastable states and explore its energy landscape. At low fields and temperatures the system relaxes into an ordered vortex lattice while just below H 2 it is in a disordered state. In the intermediate region the vortex state can be controlled by an extemal driving current. In this regime the critical current can be either increased or decreased with an appropriate driving current.

Avalanchelike magnetic relaxation in the peak-effect regime of a Nb-O solid solution

An increase of the pinning of vortices near the upper critical field boundary, the peak effect (PE), is studied in a Nb-O solid solution by means of the magnetization measurements. The PE onset is understood as a disorder-induced transition between a relatively ordered vortex lattice and an entangled vortex state. It is found that a characteristic feature of the vortex state in the PE region is a relaxation occurring via a large size magnetization jump or avalanche. It is also found that the temperature and field-dependent time ${t}_{j}(H,T),$ at which the jump occurs, quasi diverges at the peak field ${H}_{p}(T).$

Manifestation of history-dependent critical currents via dc and ac magnetization measurements in single crystals ofCeRu2and2H−NbSe2

A study of path dependent effects in single crystals of ${\mathrm{CeRu}}_{2}$ and $2H\ensuremath{-}{\mathrm{NbSe}}_{2}$ shows that critical current density ${J}_{c}$ of the vortex state depends on its thermomagnetic history over a very large part of $(H,T)$ parameter space. The path dependence in ${J}_{c}$ is absent above the peak position (i.e., $H>{H}_{p})$ of the peak effect region, which we believe identifies the complete loss of order in the vortex structure. The highly disordered field cooled (FC) state can be healed into a relatively ordered vortex lattice by subjecting it to a large enough change in dc field (few tens of Oe) or by shaking the field cooled state with sufficient ac field (few Oe).

Excitation spectrum of a type-II superconductor in a very high magnetic field with randomly pinned vortices.

Superconductivity of a two-dimensional electron gas under a very high magnetic field is studied by using the Bogoliubov--nde Gennes equations. It is shown that in the quantum limit, where all of the carriers are confined into the lowest Landau level, the excitation spectrum is gapless for any distribution of zeros of the order parameter. Therefore, it is concluded that the presence of gapless excitations, which has been first demonstrated for ordered vortex lattice, is in fact a topological property of the system. The model describes the physics of type-II superconductors where the vortices are pinned by lattice imperfections.

Observation of vortex-lattice melting by NMR spin-lattice relaxation in the mixed state

For anisotropic layered superconductors a NMR technique is proposed to study the structure of the moving vortex state in the presence of transport current flowing in the layers. The internal field in an anisotropic superconductor will have a component perpendicular to an applied field which is tilted away from the c axis. The moving ordered vortex lattice produces an alternating magnetic field which causes nutation of nuclear spins and contributes to the decay of the spin-echo amplitude. This decay rate will display an array of peaks as a function of frequency. In the liquid phase this alternating field contributes to the longitudinal relaxation rate ${\mathit{W}}_{1}$ which has a single peak.

Electromagnetic properties of stacks of superconducting layers.

A system of superconducting layers, coupled solely by the electromagnetic field, is analyzed. Thermal fluctuations induce isolated vortices in individual layers, whose mutual interaction increases logarithmically with separation. In an applied field, the penetration depth is increased over that of individual layers by a factor proportional to the volume fraction of the superconductor. The stiffness of a vortex line under an inhomogeneous displacement in adjacent layers is analyzed. The interaction between vortex lines is enhanced near a free surface, making possible the existence of an ordered vortex lattice at the surface, while it may not exist in the bulk of the sample.

Magnetic field distribution in superconducting niobium by nuclear magnetic resonance fourier spectroscopy

Nuclear magnetic resonance measurements of the superconducting mixed-state field distribution in niobium metal are reported. It is demonstrated that pulsed NMR Fourier spectroscopy (defined in the text) can resolve considerable detail in the field distribution functionf(h). A simple analytic model forf(h) was used for numerical calculation of the expected spectrum shape. An ordered vortex lattice was always observed. Far from the transition the spectra were most consistent with triangular lattice symmetry. The temperature variation of the Maki parameterℵ 2 was measured. The shift of spectrum position is compatible with appreciable reduction of spin susceptibility in the superconducting state.

Local-Field Mapping in Mixed-State Superconducting Vanadium by Nuclear Magnetic Resonance

A 10-kG field was applied to polarize the spins; it was then quickly reduced below ${H}_{c2}$, and remained there for about 0.1 sec, during which time a transverse ac probe field of frequency ${\ensuremath{\nu}}_{p}$ was applied. Then the large dc field was reapplied and a rapid-passage resonance signal observed in order to measure the effect of the probe field, the decrease in this subsequent signal reflecting the NMR absorption. Except near ${H}_{c2}$ the probe field only burns a small hole in the nuclear magnetization, and it was also necessary to move the vortex structure about by applying a 100-Hz field of a few gauss during the time that the sample was in the mixed state. Detailed studies are reported for a multiple foil sample of vanadium with main field perpendicular to the surface; aluminum foil was interleaved, and the flux density $B$ was measured using the ${\mathrm{Al}}^{27}$ NMR by exactly the same field-cycling resonance as applied to the vanadium. The magnetization was measured ballistically in the same magnet and field cycle. For flux density around $\frac{1}{2}{H}_{c2}$ the line shape almost uniquely implies a triangular vortex lattice. At high probe power, the effect of the probe field is still confined to the same definite frequency range as at low power, as would be the case for a completely ordered vortex lattice; this implies order over several vortex-lattice spacings. Accurate measurements are presented of the field at a vortex center and at the saddle point halfway between two vortices, and of the average flux density $B$, as a function of $H$, in a fairly clean sample at 1.4\ifmmode^\circ\else\textdegree\fi{}K. These parameters determine an accurate field map. Near ${H}_{c2}$ the field at a vortex center equals $H$, with a deviation of second (or greater) order in $H\ensuremath{-}{H}_{c2}$. The linewidth is greater, for a given magnetization, than would be expected from solutions of the Ginsburg-Landau equations. By extrapolation to zero $B$, it is concluded that the field at the center of a vortex is 1.2\ifmmode\pm\else\textpm\fi{}0.2 times ${\mathrm{H}}_{c1}$. The data are consistent, at low $B$, with a superposition model of independent vortices.