Ginzburg–Landau Theory for Magneto‐Elastic Interaction and Magnetization in Type‐II Superconductors

Abstract

The interaction between vortex and crystal lattice (periodic arrays of flux quantum and atoms) in type-II superconductors is evaluated through Ginzburg-Landau theory. It is found that, in an isotropic crystal, the magneto-elastic coupling energy counteracts the elasticity-driven intervortex interaction energy. Thus, the elastic response is induced entirely by individual vortices taken separately. Furthermore, the strain in a vortex-lattice cell decays quadratically with the distance from the vortex core, which allows a cutoff at the cell boundary. Finally, it could be concluded that if the jump in the elastic constant at H c2 is comparable to unity, the elasticity energy dominates the competition between the vortex lattice and crystal elasticity. This effect likely results in the second magnetization peak in the reversible magnetization.

Critical states of a superconducting slab subjected to tension and bending

“…When we say macroscopic magneto-elastic coupling effect, we mean electromagnetic responses of a superconductor exhibit strong nonlinearity in low temperature and high magnetic fields and are coupled with its structural deformation. In addition to using Ginzburg-Landau's theory to solve the problem of magnetomechanical coupling at the micro level (see [1][2][3][4] and references therein), the critical-state theory is more likely taken as a macroscopic solution. It is known that the correlation between flux pinning (or cutting) mechanism and macro (experimental) phenomenon brings about the superconducting electromagnetic constitutive relation, which is known as the critical-state theory [5].…”

“…It is thus natural to consider the effect of mechanical deformation on the critical state. Some researchers have studied the relationship between superconducting properties and strain, with GL approaches or experiments (see [1,2,11] and review article [12]), other than by the critical-state model. It is noted that the mechanical deformation was previously related to the critical states [13][14][15], with only Bean model.…”