Nonlocal electrodynamics and low-temperature magnetization of clean high-κ superconductors

Abstract

We show that magnetic properties of clean superconductors with a large Ginzburg-Landau parameter \ensuremath{\kappa} at low temperatures are affected by the nonlocality of the microscopic current-field relation and can be described by modified London equations. We argue that for clean materials at low temperatures, the standard London formula for the reversible magnetization in intermediate fields, M\ensuremath{\sim}ln(${\mathit{H}}_{\mathit{c}2}$/B), should contain the field ${\mathit{H}}_{0}$\ensuremath{\sim}${\mathrm{\ensuremath{\varphi}}}_{0}$/${\mathrm{\ensuremath{\rho}}}^{2}$ instead of ${\mathit{H}}_{\mathit{c}2}$\ensuremath{\sim}${\mathrm{\ensuremath{\varphi}}}_{0}$/${\ensuremath{\xi}}^{2}$(T), with \ensuremath{\rho} being the nonlocality range on the order of ${\ensuremath{\xi}}_{0}$, the zero-T coherence length. Since \ensuremath{\rho} depends weakly on T, the magnetization should exhibit an approximate scaling M(T,B)=X(T)Y(B) as observed in Bi- and Tl-based compounds in a broad temperature domain well below ${\mathit{T}}_{\mathit{c}}$. Our expression for the magnetization reduces to the standard London result near ${\mathit{T}}_{\mathit{c}}$ and at any temperature for the dirty case. Implications of our results for interpretation of neutron scattering data and for procedures of extracting the penetration depth are discussed. \textcopyright{} 1996 The American Physical Society.