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Small-Angle Neutron Scattering & T he 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.

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superconductors what why
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


Magnetic levitation

(Railway Technical Research Institute,


magnetic properties
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
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
Small-angle neutron scattering

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

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

l = 10 Å

d = 1000 Å

sample environment
Sample environment
  • The diffraction pattern is directly measured on 2D detector.
  • Cryomagnet cool sample and contain magnets. Must rotate around two axes to satisfy Bragg condition for VL.
luni 2 b 2 c
  • 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).

vl reflectivity and form factor
VL reflectivity and form factor
  • Absolute VL reflectivity → vortex form factor.
  • Form factor can be measured continuously as function of scattering vector, q :
vl field reconstruction
VL field reconstruction


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