The nature of the phase transition in the cuprates as revealed by a magnetic field free stiffness meter

A new method to measure the superconducting stiffness tensor ρ_s, without subjecting the sample to magnetic field, is applied to La_1.875Sr_0.125CuO_4 (LSCO). The method is based on the London equation J=-ρ_s A, where J is the current density and A is the vector potential. Using rotor free A and measuring J via the magnetic moment of superconducting rings, we extract ρ_s at T→ T_c. The technique, named Stiffnessometer, is sensitive to very small stiffness, which translates to penetration depth on the order of a few millimeters. We apply this method to two different LSCO rings: one with the current running only in the CuO_2 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. The Stiffnessometer results are accompanied by Low Energy μSR measurements on the same sample to determine the stiffness anisotropy at T < T_c.