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

A method to measure the superconducting (SC) stiffness tensor $$\bar \rho _{\mathrm{s}}$$ ρ ¯ s , without subjecting the sample to external magnetic field, is applied to La1.875Sr0.125CuO4. The method is based on the London equation $${\mathbf{J}} = - {\bar{\mathbf{\rho }}}_{\mathrm{s}}{\mathbf{A}}$$ J = - ρ ¯ s A , 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, $$\bar \rho _{\mathrm{s}}$$ ρ ¯ s at T → Tc 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