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

We show that magnetic properties of clean superconductors with a large Ginzburg-Landau parameter 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 similar to In(H-c2/B), should contain the field H-0 similar to phi(0)/rho(2) instead of H-c2 similar to phi(0)/xi(2)(T), with rho being the nonlocality range on the order of xi(0), the zero-T coherence length. Since 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 T-c. Our expression for the magnetization reduces to the standard London result near T-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.