Small-Angle Neutron Scattering

&

The Superconducting Vortex Lattice

Superconductors: What & Why

• Discovered in 1911 By H. Kammerlingh-Onnes, who observed at complete loss of resistance in mercury below 4.2 K.

• Displays an intriguing response to applied magnetic fields (Meissner effect, mixed state).

• Many aspects still not understood on microscopic level.

• Immense potential for practical applications.36.5 MW ship propulsion motor

(American Superconductor)

Loss free energy transport(physicsweb.org)

Magnetic levitation(Railway Technical Research Institute,Japan)

Magnetic properties

• Superconductors “allergic” to magnetic fields.

• At low fields: Complete flux expulsion (Meissner effect).

• Superconducting screening currents will produce opposing field cancelling applied field.

Superconducting vortices

• For type-II superconductors in the mixed state, the applied magnetic field penetrates in vortices or flux lines.

• Each vortex carries one flux quantum of magnetic flux:

• The vortices forms an ordered array - the vortex-lattice (ignoring pinning, melting, etc….).

University of Oslo, Superconductivity lab.

Small-angle neutron scattering

• Neutrons scattered by periodic magnetic field distribution, allowing imaging of the vortex lattice (VL).

• Typical values: l = 10 Å d = 1000 Å

SANS-I beam line at Paul Scherrer Institute, Villigen (Switzerland).

• Cryomagnet cool sample and contain magnets. Must rotate around two axes to satisfy Bragg condition for VL.

Sample environment

• The diffraction pattern is directly measured on 2D detector.

LuNi2B2C

• Member of RNi2B2C family of SC’s (R = Y, Dy, Ho, Er, Tm, Lu).

• Tc = 16. 6 K, Hc2(2 K) = 7.3 T. Relatively well understood, good case study.

• Intriguing in-plane anisotropy:a) FS anisotropy + non-local electrodynamics → VL symmetry transitions.b) Anisotropic s-wave (s+g?) gap symmetry (nodes along 100).

K. Maki, P. Thalmeier, H. Won,Phys. Rev. B 65, 140502(R) (2002).

V. G. Kogan et al.,Phys. Rev. B 55, R8693 (1997).

N. Nakai et al.,Phys. Rev. Lett. 89, 237004 (2002).

• Absolute VL reflectivity → vortex form factor.

• Form factor can be measured continuously as function of scattering vector, q :

VL reflectivity and form factor

VL field reconstruction

LuNi2B2

C

J. M. Densmore et al., Phys. Rev. B 79, 174522 (2009)