Stripe Domains and First-Order Phase Transition in the Vortex Matter of Anisotropic High-Temperature Superconductors

Abstract

We report the direct imaging of a novel modulated flux striped domain phase in a nearly twin-free YBCO crystal. These domains arise from instabilities in the vortex structure within a narrow region of tilted magnetic fields at small angles from the in-plane direction. By comparing the experimental and theoretically derived vortex phase diagrams we infer that the stripe domains emerge from a first order phase transition of the vortex structure. The size of domains containing vortices of certain orientations is controlled by the balance between the vortex stray field energy and the positive energy of the domain boundaries. Our results confirm the existence of the kinked vortex chain phase in an anisotropic high temperature superconductor and reveal a sharp transition in the state of this phase resulting in regular vortex domains.In type II superconductors (SC) the magnetic field penetrates in the form of vortices -magnetic flux tubes each carrying a single flux quantum [1]. Interactions between vortices and their coupling to crystal defects result in a rich variety of vortex structures. They include a triangular or square vortex lattice that can subsequently melt at high temperatures to a vortex liquid, a pinned vortex glassy state that can sustain high current carrying capacity, and in highly anisotropic superconductors, 2D pancake vortices that can interact with in-plane Josephson vortices to create 1D vortex chain states. These states of vortex matter define all transport and magnetic properties of applied superconductors.Here we report on an unusual vortex domain structure that arises following a first order phase transition in the vortex state in nearly untwined YBCO crystal under tilted magnetic fields. Typically, vortices repulse each other when the distance between them is much smaller than the penetration depth λ, the scale over which the magnetic field of the vortices decays. In this case, the vortices can arrange into a uniformly spaced lattice or form smooth density gradients defined by the critical current, the maximum current that the superconductor can sustain before reverting to the normal state. In contrast, at larger distances the interactions between vortices can be attractive, resulting in the formation of vortex chains and bundles (see review [2]). For example, periodic stripe domains and circular bundles of vortices interspersed with flux free Meissner regions occur in thin niobium disks with a low Ginzburg-Landau parameter κ = λ/ξ ∼ 1, where ξ is the coherence length setting the size of the vortex core. These vortex domains are similar to the alternating normal (N) and superconducting Meissner (M) domains found in the intermediate state of type I SCs with a nonzero demagnetizing factor. In the latter, the lamellae M/N domains are known to minimize the magnetostatic energy of the normal regions at the expense of the positive energy of the boundaries between the normal and SC phases.Vortex attraction can also appear in large κ, anisotropic type II SCs when an applied magnetic field is tilted f...

Flux cutting in high-Tcsuperconductors

“…At some small value of the remaining B ⊥ we observe the appearance of flux stripes carrying vortices with different tilt angles. They remain after switching off H || (Fig.6e) and are similar to vortex domains observed after cooling in tilted fields [32]. The stripes disappear upon subsequent increase of H || .…”

Anisotropic superconductors in tilted magnetic fields

“…The advance motion of BZ along the in--plane field component means that the average current density across the in--plane field component Ha || is smaller than along Ha || , and the stripe BZ structure corresponds to the oscillations of the transverse current lines as illustrated in Fig.4e. The stripes inside the bowtie are very similar to the vortex domains reported in [37].…”

“…They carry trapped positive BZ , which produces negative normal stray fields (darker contrast) around the sample. The stripe structure represents vortex domains, where vortices are tilted at different angles from the sample plane as described in [37]. In addition to the stripes, we observe bright and dark contrast at the long edges due to the in-- Obviously, the effect of shape modifies the details of the patterns and conditions of their occurrence depending on the orientation of the tilted fields.…”

“…These currents support the superconductors [13,18--24,7 ]. Recently we found that after cooling in a tilted field and slowly reducing the field such an instability results in the formation of stripe domains containing vortices with different orientations [37]. We assume that the BZ stripes observed during magnetization of the YBCO crystal at small θ is a precursor of the vortex domains caused by the same angular vortex instability.…”

“…When decreasing the field from a maximum of Ha =2.1 kOe, the sharp front spreads and merges with zones of weak BZ expanding from the short edges (Fig.3b). After reducing the field to zero, the BZ pattern transforms into bright longitudinal stripes ( Fig.3c) reminiscent of vortex domains with different tilt angles [37]. Also, dark and bright contrast due to the trapped in--plane flux appears at the short edges and alternating contrast similar to that in Tilting the applied field up--to θ~3 0 results in magnetization patterns similar to those observed for θ~1.5 0 in the increasing field (Fig.4a, note that for the in--plane component of…”