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Pinning and elastic properties of vortex matter in highly strained Nb$_{75}$Zr$_{25}$: Analogy with viscous flow of disordered solids

We present the results of magnetization and magneto-transport measurements in the superconducting state of an as-cast Nb$_{75}$Zr$_{25}$ alloy. We also report the careful investigation of the microstructure of our sample at various length scales by using optical, scanning electron and transmission electron microscopies. The information of microstructure is used to understand the flux pinning properties in the superconducting state within the framework of collective pinning. The magneto-transport measurements show a non-Arrhenius behaviour of the temperature and field dependent resistivity in the flux flow region. This non-Arrhenius behaviour is understood in terms of a model, which was originally proposed for viscous flow of disordered solids and is popularly known in the literature as the `shoving' model. The activation energy for flux flow is obtained from magneto-transport measurements and is assumed to be mainly the elastic energy stored in the flux-line lattice. The scaling of pinning force density with respect to reduced field indicates the presence of two pinning mechanisms of different origins. The elastic constants of the flux-line lattice are estimated from magnetization measurements and are used to estimate the length scale of vortex lattice movement, or the volume displaced by the flux-line lattice, during flux flow. It appears that the vortex lattice displacement estimated from elastic energy considerations is of the same order of magnitude as that of the flux-bundle hopping length when a finite resistance appears during flux flow. Our results could provide possible directions for establishing a framework where vortex matter and glass forming liquids or amorphous solids can be treated in a similar manner for understanding the phenomenon of viscous flow in disordered solids or more generally the pinning and depinning properties of elastic manifolds in random media.