Abstract
In extremely anisotropic cuprate superconductors a lattice of stacks of pancake vortices nucleates when a magnetic field is applied perpendicular to the copper oxide layers, while an orthogonal lattice of highly elliptical Josephson vortices forms when the applied field is parallel to the layers. Under tilted magnetic fields these sublattices can interact in complex ways to form systems of vortex chains and composite vortex lattices. Here we have used high-resolution scanning Hall microscopy (SHM) to map the rich tilted-field vortex phase diagram in an underdoped Bi2Sr2CaCu2O8+δ single crystal. We find that the Josephson vortex lattice spacing has an unexpected non-monotonic dependence on the pancake vortex density reflecting the delicate balance between attractive and repulsive vortex interactions, and actually undergoes a field-driven structural transformation with increasing out-of-plane fields. We also identify particularly stable composite structures composed of vortex chains separated by an integer number of rows of interstitial pancake vortex stacks and are able to establish the precise evolution of vortex-chain phases as the out-of-plane field is increased at small in-plane fields. Our results are in good semi-quantitative agreement with theoretical models and could enable the development of vortex ratchets and lenses based on the interactions between Josephson and pancake vortices.
Highlights
If the field is instead applied at an arbitrary ‘tilt’ angle away from the crystallographic c-axis, the very high anisotropy in BSCCO-2212 leads to a wide variety of possible groundstates including kinked lattices[3,4,5,6], tilted vortex chains[7,8,9] and coexisting orthogonal PV and JV lattices[4,10]
Previous vortex imaging work[12,13,14,15,16,17] has only experimentally investigated a tiny part of the available phase space, and here we describe an extensive vortex imaging survey in an underdoped BSCCO-2212 single crystal which allows us to develop a detailed vortex-matter phase diagram as a function of in-plane and out-of-plane fields
For very small values of Hc dilute linear arrays of PVs are trapped on JV stacks and the attractive JV-PV interaction is maximised by having the most JV/PV crossing points
Summary
If the field is instead applied at an arbitrary ‘tilt’ angle away from the crystallographic c-axis, the very high anisotropy in BSCCO-2212 leads to a wide variety of possible groundstates including kinked lattices[3,4,5,6], tilted vortex chains[7,8,9] and coexisting orthogonal PV and JV lattices[4,10]. For low out-of-plane fields (Bc ≈ 0–2 G) all pancake vortices interact strongly with stacks of Josephson vortices over a wide range of in-plane fields (Bab ≈ 10–650 G) in so-called vortex-chains phases. This limit has been theoretically investigated both analytically and numerically[11], and the rich lattice structures that can arise due to the combined magnetic and Josephson interactions between pancake vortices in different layers were elucidated. The exact sequence of phases depends on the specific value of Bab, and above a critical in-plane field the crossing pancake-chain state no longer arises and a first-order transition from kinked tilted vortices to tilted straight vortices is predicted. Our work provides important insights into the properties of vortex matter in highly anisotropic cuprate superconductors under tilted magnetic fields and will inform the development of first generation high-temperature superconductor wires based on them
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