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Small-Angle Neutron Scattering & T he Superconducting Vortex Lattice

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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

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

- 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.

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).

VL reflectivity and form factor

- Absolute VL reflectivity → vortex form factor.
- Form factor can be measured continuously as function of scattering vector, q :

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