Sebastian Mühlbauer¹, Peter Böni¹, Christian Pfleiderer¹, Robert Georgii^1,2, E. M. Forgan³, M. Laver³, E. Bauer^4, M.B. Maple^5
1 Technische Universität München, Physics Department E21, D-85747 Garching, Germany
² ZWE FRM-II, Technische Universität München, D-85747 Garching, Germany
³ School of Physics and Astronomy, Condensed Matter Group, Birmingham, UK
⁴ Institut für Festkörperphysik, Technische Universität Wien, Austria
⁵ Physics/IPAPS – 0319, University of California, USA

Small angle neutron scattering (SANS) directly maps the vortex lattice (VL) of a superconductor, revealing both individual sample properties as i.e. pinning potentials and purity - but also reflecting the symmetry of the underlying Fermi-surface as well as the symmetry of the superconducting wavefunction. Especially in high-Tc and heavy-fermion superconductors, the symmetry of is of great interest to figure out recent questions on the pairing mechanism in these compounds, which might be of so called unconventional nature. As the symmetry of the VL is influenced by possible anisotropies of the underlying Fermi-surface, possible non-local corrections to the free energy and itself, classical superconductors are recently reinvestigated as model systems, where certain parameters can be tuned precisely.

Vortex structures in Niobium

Niobium (Nb) is a classical type-II superconductor, characterized with a Ginzburg-Landau parameter = 0.8. With the magnetic field applied along the four-fold (100) direction, a variety of VL symmetries is observed, namely a high-field and low-field square, a scalene and isosceles phase, all breaking the crystal symmetry [1]. These symmetries may be explained by non local corrections to the Eilenberger [2] equations in the form of cos(4Φ) [3], leading to two separated square phases and additionally cos(8Φ) , allowing the VL symmetry breaking the crystal symmetry. Measurements on a pure Nb sample have also been performed on the diffractometer MIRA, an example is shown in Fig. 1.

Polarised small angle neutron scattering on Niobium

Polarised neutron scattering on a VL is restrained by the sample environment magnetic field, forcing the neutron spin parallel to the VL direction. This leads to a spin independent scattering intensity and no signal in the spin-flip channels. Due to the height of the magnetic potential of a single vortex, no Zeemann splitting is observed. But measurements, performed on the instrument SANS 2 at GKSS and on MIRA show a clear polarisation dependency in the VL Bragg peaks. The signal is clearly related to the onset of superconductivity, as shown in Fig. 2. As expected, no spin-flip signal is observed, ruling out strange VL spaghetti structures causing the polarisation dependence. Further measurements by E. M. Forgan [4] show a major purity dependence of the observed polarisation dependent signal, leading to the assumption that this effect may be caused by interference between nuclear scattering from impurities, which is spin independent, and magnetic scattering from the VL, which is spin dependent. As the VL is pinned by impurities and therefore distorted, a spatial correlation between some impurities and the VL positions may exist.

References

[1] M. Laver et al. Spontanueous symmetry breaking vortex lattice transitions in pure niobium. Phys. Rev. Lett, 96, 2006.
[2] G. Eilenberger. Z. Phys, 214:195, 1968.
[3] N. Nakai et al. 2002.
[4] E. M. Forgan. Investigation of flux line lattices by SANS with unpolarized and polarized neutrons. PNCMI conference proceedings, in press 2007.