Small-angle neutron scattering (SANS) studies of the vortex lattice in type-II superconductors

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Introduction

SANS instruments

Research

The small-angle neutron scattering (SANS) sub-group is headed by Professor E.M. Forgan. Its current members are Elizabeth Blackburn, Alex Holmes (post-doctoral research fellow), and Louis Lemberger, Lingjia Shen and Randeep Riyat (research students). Our research in this field has resulted in numerous high-profile publications. Click here to read about the latest Science publication (2008).

Introduction

SANS is a technique for studying by neutron scattering large-scale structures, which can range from a few nanometers to several hundred nanometers in size. This range of sizes encompasses a variety of systems of great interest including large biological molecules, polymers, clusters in alloys and the system we study: vortices in type-II superconductors. Vortices are lines of quantised magnetic flux that penetrate a so-called type-II superconductor when a magnetic field exceeding the first critical field is applied. These vortices repel each other and in many cases arrange themselves into a well-ordered magnetic lattice. (An example of such a lattice, where the vortices assume a triangular co-ordination, is shown in the diagram on the right.) We exploit the magnetic moment of the neutron to study the vortex lattice by diffraction: a neutron passing through the vortex lattice will experience a spatially-varying magnetic potential energy and therefore may be diffracted, albeit by very small angles - typically a few tenths of a degree. This necessitates a neutron scattering instrument adapted to measuring very small momentum transfers.

 

SANS instruments

SANS instruments are ideally suited to studying large-scale systems like the vortex lattice. This is accomplished using cold neutrons, which have wavelengths of the order of ten Angstroms, and a large sample-detector distance to cope with the small angle of scatter. In the figure below is shown a schematic of a typical SANS instrument. It consists of a source of cold neutrons (either reactor- or spallation-based); a mechanical velocity selector, which defines the wavelength and its spread; a variable length of collimation (typically from just a few meters to more than ten metres); the sample, which resides inside a cryomagnet (or a cryostat and electromagnet); and a multi-detector placed at a distance of up to forty meters on some very low momentum transfer instruments. The SANS instruments we employ are based at the ILL in Grenoble, France (instruments D11 and D22) and at PSI in Villigen, Switzerland (instrument SANS-I).

A schematic diagram of the SANS apparatus


Many of our studies of the vortex lattice are performed at large fields (see e.g. YBCO, below). For this purpose we have commissioned a 11T cryomagnet in partnership with PSI, the University of Warwick and the University of Zurich. This cryomagnet, based at PSI, has been specifically designed for SANS and it is possible to tip the entire cryomagnet to rock about the horizontal axis. A horizontal field is produced by a Helmholtz pair and has a field-uniformity of 0.2% over a 1cm sphere. More recently, we have acquired our own world-beating 17 T cryomagnet, which we are using at a variety of European neutron sources.

 

Left: The PSI-based cryomagnet tilted while at 11 T
Right: the new 17 T cryomagnet being filled with liquid helium at ILL before use

Research

Our diverse research portfolio covers many of the current hot topics in vortex physics. These include: the observation of unconventional vortex lattice structures in the cuprate superconductors YBCO and the iron-based "pnictide" superconductor KFe2As2; the study of the interplay between the vortex lattice and disorder; and the discovery of an unexpectedly rich phase diagram in the s-wave superconductor niobium. Our group has a very good pedigree in vortex physics: amongst our previous work is the first observation of the vortex lattice in strontium-ruthenate-214; the measurement of transverse field components in anisotropic superconductors and pioneering work in flux-flow.

YBCO

During the past three years we have made significant progress in understanding the effect on the vortex lattice of the unconventional d-wave order parameter in YBCO. This work is part of a broader programme of research into vortex lattice phase transitions in the cuprate superconductors involving collaborations with The University of St. Andrews, Scotland; PSI, Switzerland and the Max Planck Institute, Stuttgart.

Using the high-field SANS facility on SANS-I at PSI, Switzerland we have observed vortex lattice phase transitions as a function of field in a fully-oxygenated sample of YBCO-123 (see Physical Review Letters 102, 097001 (2009)). These experiments were performed at 4 K with the field applied parallel to the crystal c-axis. Shown in the figure below are: (left) the low field (1.5 T) diffraction pattern, which shows a triangular vortex lattice distorted by the ab-plane band-mass anisotropy; (middle) the mid-field pattern - a hexagon of lower distortion and in a different orientation; (right) the high-field (10.8 T) diffraction pattern, showing an (almost) perfect square vortex lattice. The crystal a direction is vertical, and the diagonal arrows are the crystal {110} directions, which are close to the nodal directions expected for the nearly d-wave superconducting order parameter in this material.


Images of the diffraction of neutrons from YBCO at different magnetic field strengths



Our observations corroborate theoretical calculations (see, e.g., M. Ichioka et al, Phys. Rev. B 59, 8902 (1999).), which predict the formation of a square vortex lattice in a d-wave superconductor at high fields. Essentially, this is a consequence of the four-fold anisotropy of the vortex core induced by the four-fold symmetry of the order parameter. This anisotropy is more pronounced near the vortex cores, therefore one expects a field-driven transition to a square vortex lattice as the vortex cores come into closer proximity to each other. We are currently extending these results to higher fields using our new 17 T cryomagnet.


A "pnictide" superconductor KFe2As2

There has been great interest in a new class of iron-based pnictide superconductors, with Tc's up to 55 K. In collaboration with Hazuki Kawano-Furukawa of Ochanomizu University, Tokyo, we have made the only successful measurements of an ordered vortex lattice in any pnictide material (H. Kawano-Furukawa et al., arXiv:1005.4468v2). With the field applied parallel to the c-axis of the tetragonal crystal, we see 12 spots because two equivalent orientations of hexagonal vortex lattice have the same energy in the fourfold environment of the crystal. It will be noted that the vortex lattices are slightly distorted from the regular hexagonal shape, but unlike YBCO, no vortex lattice phase transitions are observed on increasing the field. We deduce that the superconducting order parameter does not have d-wave nodes like YBCO. However, when we measure the variation of the signal with temperature, we find that there is a strong temperature-dependence down to a very small fraction of Tc. (Optimally-doped pnictide materials have a larger Tc but badly-disordered vortex lattices; our material is "over-doped" with a much lower Tc ~ 3.6 K, but a stoichiometric formula and is "clean"). The temperature-dependence of the signal strongly suggests that the order parameter does have nodes. See our paper for a possible explanation of this apparent paradox...

 

Left: SANS diffraction image from the flux lines in KFe2As2 at 0.2 T and 1.5 K; right: temperature dependence of the diffracted intensity at 0.1 T