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A method to measure the superconducting (SC) stiffness tensor , 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 , 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 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 .

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We developed a new method to measure superconducting stiffness ρs, critical current density J c , and coherence length ξ without subjecting the sample to magnetic field or attaching leads. The method is based on the London equation J = −ρsA, where J is the current density and A is the vector potential. Using a rotor free A and a measurement of J via the magnetic moment of a superconducting ring, we determine ρs. By increasing A until the London equation does not hold anymore we determine J c and ξ. The method is sensitive to very small stiffness, which translates to penetration depth λ 3 mm. It is also sensitive to extremely low critical current density J c ∼ 1 Acm −2 or long coherence length ξ ∼ 1 µm. Naturally, the method does not suffer from demagnetization factor complications, the presence of vortices, or out-of-equilibrium conditions. Therefore, the absolute values of the different parameters can be determined. We demonstrate the application of this method to La2−

We investigate whether the spin or charge degrees of freedom are responsible for the nodal gap in underdoped cuprates by performing inelastic neutron scattering and x-ray diffraction measurements on La 2−x Sr x CuO 4 , which is on the edge of the antiferromagnetic phase. We found that a fluctuating incommensurate spin-density wave (SDW) with a bottom part of an hourglass dispersion exists even in this magnetic sample. The strongest component of these fluctuations diminishes at the same temperature where the nodal gap opens. X-ray scattering measurements on the same crystal show no signature of a charge-density wave (CDW). Therefore, we suggest that the nodal gap in the electronic band of this cuprate opens due to fluctuating SDW with no contribution from CDW.