Neutron studies of the flux-line lattice in high temperature superconductors

Abstract

In a type II superconductor, such as the Nb or the high temperature superconductors, there are two critical magnetic fields, H_C1 and H_C2. When a sample is cooled through the critical temperature for superconductivity, T_C in a magnetic field of less than H_C1 all magnetic flux is expelled from the material-the Meissner-Ochsenfeld effect. H_C2 is the maximum magnetic field which can be applied to the superconductor without driving the sample back into the normal state. At intermediate magnitudes of magnetic field, H_C1<H<H_C2 a superconducting sample is in the mixed state where magnetic flux still exists within the bulk of the material. In this mixed state, the magnetic flux enters as “flux-lines”; each one of these objects has a normal core which is surrounded by a circulating supercurrent flow and contains a total amount of flux equal to h/2e. At low fields, these flux-lines are independent, but in higher fields their magnetic fields and supercurrents overlap. In response to this interaction, the flux-lines rearrange themselves to minimize their free energy. This arrangement is usually in the form of a two-dimensional, hexagonal lattice. A fluxline has a core of radius ζ the coherence length or minimum length scale for variations in the superconducting wavefunction, and is surrounded by a spatially, decaying magnetic induction on the length scale of the penetration depth, λ. In the past, neutron diffraction experiments have played an important role in determining the properties of flux-line lattices in conventional superconductors.