Reversible magnetization of high-Tcmaterials in intermediate fields

Abstract

In high-$T_c$ superconductors there exists a broad field domain, in which the reversible magnetization $\mathbf{M}$ is linear in the logarithm of the applied field $H_a$. The dependence $\mathbf{M}\left(\ln H_a\right)$ is obtained taking the strong uniaxial anisotropy into account. It is shown, that for an arbitrary orientation of the single crystal with respect to ${\mathbf{H}}_a$ the magnetization vector has a component normal to the applied field comparable to the usually measured component parallel to ${\mathbf{H}}_a$. A procedure is suggested for extracting the value of the penetration depth from the linear part of $\mathbf{M}\left(\ln H_a\right)$. Being applied to the data available for ${\mathrm{Y}}_1$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, the method yields $\lambda \propto {(T_c-T)}^{\frac{-1\mathrm{}}{2}}$ near $T_c$ up to temperatures $\frac{(T_c-T)}{T_c\sim {10}^{-3\mathrm{}}}$. This puts an upper bound upon the value of the temperature domain, in which the underlying mean-field theory is valid.