New scaling laws for pinning force density in superconductors

TL;DR

This paper investigates the scaling laws of pinning force density in superconductors, proposing new models that incorporate the critical current density and applying them to various superconducting materials.

Contribution

It introduces new scaling laws for pinning force density based on the full $|F_p(B,J_c)|$ function, extending previous models to include critical current density effects.

Findings

Identified three characteristic ranges of $(B/B_{c2}, J_c/(J_c(sf)))$

Proposed several new scaling laws for $|F_p(J_c)|$

Successfully applied models to multiple superconducting materials

Abstract

Since the report by Fietz and Webb (1968 Phys. Rev. 178 657), who considered the pinning force density, $|F_p| = |J_c \times B|$ (where $J_c$ is the critical current density and $B$ is applied magnetic field), in isotropic superconductors as a unique function of the reduced applied field, $B/B_{c2}$ (where $B_c2$ is the upper critical field), $|F_p|$ has been scaled based on B/B_c2 ratio, for which there is widely used scaling law of $|F_p(B)|=F_{p,max}((B/B_{c2})^p)((1-B/B_{c2})^q)$, where $F_{p,max}$, $B_{c2}$, $p$, and $q$ are free-fitting parameters, proposed by Kramer (1973 J. Appl. Phys. 44 1360) and Dew-Hughes (1974 Phil. Mag. 30 293). To describe $|F_p(B)|$ in high-temperature superconductors, Kramer-Dew-Hughes scaling law was modified by (a) an assumption of the angular dependence of all free-fitting parameters on the rotation angle and (b) by the replacement of the upper critical field, $B_{c2}$, by the irreversibility field, $B_{irr}$. Here we note that the pinning force density is also a function of critical current density and, thus, $|F_p(J_c)|$ scaling law should exist. In an attempt to reveal this law, we considered the full $|F_p(B,J_c)|$ function and reported that there are three distinctive characteristic ranges of $(B/B_{c2}, J_c/(J_c(sf)))$ (where $J_c(sf)$ is the self-field critical current density) on which $|F_p(B,J_c)|$ can be splatted. Several new scaling laws for $|F_p(J_c)|$ were proposed, discussed, and applied to scale $|F_p(J_c)|$ in MgB2, NdFeAs(O,F), REBCO, and near-room temperature superconducting super hydrides (La,Y)H10 and YH6. We pointed out that the general scaling law for the pinning force density is on the quest.