Magnetization and resistivity measurements of the first-order vortex phase transition in $({\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{)}_2{\mathrm{CuO}}_4$

We report magnetization and resistivity measurements of the first-order vortex lattice phase transition (FOT) in single crystals of $({\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{)}_2{\mathrm{CuO}}_4$ $(0.046\mathrm{}<~x<~0.077).$ Through the comparison of the present results with ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ and ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_y,$ we show that the key parameters for the FOT are the anisotropy factor, the distance between superconducting layers, and the critical temperature. This is reflected in the observation of systematic changes, similar trends, and universal behaviors in the signatures of the FOT when the particular normalization is applied to the scales. Based on the results, the mechanism of the FOT in high-temperature superconductors is discussed.