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

LuNi2B2C

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