Pinning mediated field penetration and complex susceptibility in inhomogeneous superconductors

The penetration of the magnetic field in a network consisting of the superconducting grains and intergranular region depends not only on the applied external magnetic field but also on the underlying pinning force density and fraction of the superconducting grains in the sample. Considering the underlying pinning force density in the form of the repetitive Gaussian (RG) nature we have solved the critical state model to get the spatial internal field profile at a particular time instant. The internal magnetic field as a function of the position inside the superconductor exhibits nonlinear, step-like nature. The complicated nature of the penetration of the field gets strongly affected by the size of the granular region and the total pinning force density in the superconductors. We have numerically calculated the real and imaginary parts of the complex susceptibility. The variation of the imaginary part with the temperature has a peak at a temperature which shifts towards the higher temperature with the reduction of the superconducting fraction.

Automated summary

The penetration of magnetic field in a network of superconducting grains is influenced by external field, pinning force density, and superconducting grain fraction. The internal magnetic field profile inside the superconductor exhibits nonlinear, step-like nature influenced by the size of granular region and total pinning force density. Numerically calculated real and imaginary parts of complex susceptibility show that the peak of the imaginary part shifts to higher temperature with reduction of superconducting fraction.