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

method to measure the superconducting (SC) stiffness tensor ρ̅_s , without subjecting the sample to external magnetic field, is applied to La 1.875 Sr 0.125 CuO 4 . The method is based on the London equation 𝐉 = - ρ̅_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, ρ̅_s 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 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. Additional low energy muon spin rotation measurements on the same sample determine the stiffness anisotropy at T < T c .