Theory of small-angle neutron scattering from the imperfect vortex lattice in type-II superconductors

A theory of the neutron scattering intensity from an imperfect vortex lattice in type-II superconductors is developed, which predicts that flux pinning leads not only to a broadening of the Bragg reflections, but also to a finite scattering intensity for wave vectors within the first Brillouin zone. At sufficiently high fields, the small-angle scattering intensity is predicted to exceed that of the Bragg reflections. According to this theory, if the incident beam is chosen parallel to the applied field, shear and tilt strains in the vortex lattice, and thus the most important intrinsic defects, give no contribution to small-angle scattering, and the measured intensity is due almost entirely to the strains caused by pinning forces. Small-angle neutron scattering experiments are thus capable of yielding insight into elementary pinning interactions beyond that obtainable from volume pinning force measurements, which must be interpreted by means of still unsatisfactory statistical summation theories.