Evidence for a Square-Square Vortex Lattice Transition in a High-T_{c} Cuprate Superconductor

Using sound velocity and attenuation measurements in high magnetic fields, we identify a new transition in the vortex lattice state of La_{2-x}Sr_{x}CuO_{4}. The transition, observed in magnetic fields exceeding 35 T and temperatures far below zero field T_{c}, is detected in the compression modulus of the vortex lattice, at a doping level of x=p=0.17. Our theoretical analysis based on Eilenberger's theory of the vortex lattice shows that the transition corresponds to the long-sought 45° rotation of the square vortex lattice, predicted to occur in d-wave superconductors near a van Hove singularity.