First-order dislocation-magnetic fluxoid interactions

Abstract

The force exerted on a fluxoid in the mixed state of a type II superconductor by a dislocation has been determined by considering the (first-order) interaction between the stress field of the fluxoid and the strain field of the dislocation. The fluxoid is characterized by a disorder parameter exp (-r²/ζ²), where r is the magnitude of a radial vector r extending from the axis of the fluxoid and ζ is the coherence length, and the stress field is determined by analogy with the thermal stress caused by a symmetric temperature gradient in an infinite, isotropic cylinder. The interaction force then is computed by means of the Peach-Koehler formula. A stable separation exists between an edge dislocation characterized by Burgers vector b and a parallel fluxoid when r is perpendicular to b and equal in magnitude to 1·1ζ. The minimum depinning force per unit length is given by 0·24Ab, where A =ε _u μ(1+v)/3(1-v), ε _u denotes the relative volume change between the superconducting and normal states, μ is the shear modulus, and v is Poisson's ratio. Moreover, when r≳2ζ, the interaction energy per unit length reduces to Aζ²(b/r) sin θ, where θ denotes the angle between r and -b (0 < θ < π designates tension). A screw dislocation, however, does not interact with a parallel fluxoid. The net interaction force between any dislocation and a perpendicular fluxoid is vanishing small, although local forces generate local torques. Consideration of the shorter range (second-order) modulus interaction does not affect the conclusions appreciably.