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Using sound velocity and attenuation measurements in high magnetic fields, weidentify a new transition in the vortex lattice state ofLa$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO). The transition, observed in magnetic fieldsexceeding 35 T and temperatures far below zero field $T_c$, is detected in thecompression modulus of the vortex lattice, at a doping level $x=p=0.17$. Ourtheoretical analysis based on Eilenberger theory of vortex lattice shows thatthe transition corresponds to the long-sought 45 degrees rotation of the squarevortex lattice, predicted to occur in $d$-wave superconductors near a van Hovesingularity.

Evidence for a square-square vortex lattice transition in a high-$T_\textrm{c}$ cuprate superconductor