Phase transition in the cuprates from a magnetic-field-free stiffness meter viewpoint

A method to measure the superconducting (SC) stiffness tensor ρ_s, without subjecting the sample to external magnetic field, is applied to La_1.875Sr_0.125CuO₄. The method is based on the London equation J = -ρ_sA, where J is the current density and A is the vector potential which is applied in the SC state. Using rotor free A and measuring J via the magnetic moment of superconducting rings, at T →T_c is extracted. The technique is sensitive to very small stiffnesses (penetration depths on the order of a few millimeters). The method is applied to two different rings: one with the current running only in the CuO₂ planes, and another where the current must cross planes. We find different transition temperatures for the two rings, namely, there is a temperature range with two-dimensional stiffness. Additional low energy muon spin rotation measurements on the same sample determine the stiffness anisotropy at T < T_c.