The Stiffnessometer a magnetic field free superconducting stiffness meter and the nature of the phase transition in cuprates

A new method to measure the superconducting stiffness tensor bar rho s without subjecting the sample to magnetic field is presented and applied to La 1 875 Sr 0 125 CuO 4 LSCO The method is based on the London equation J bar rho sA 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 bar rho s 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 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 The Stiffnessometer results are accompanied by Low Energy mSR measurements on the same sample to determine the stiffness anisotropy at favorable temperatures