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

We show that magnetic properties of clean superconductors with a large Ginzburg-Landau parameter κ 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∼ln(${\mathit{H}}_{\mathit{c}2}$/B), should contain the field ${\mathit{H}}_0$∼${\mathrm{\phi }}_0$/${\mathrm{\rho }}^2$ instead of ${\mathit{H}}_{\mathit{c}2}$∼${\mathrm{\phi }}_0$/${\xi }^2$(T), with ρ being the nonlocality range on the order of ${\xi }_0$, the zero-T coherence length. Since ρ 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. © 1996 The American Physical Society.