First-Order Vortex Lattice Melting and Magnetization ofYBa2Cu3O7−δ

We present the first non-mean-field calculation of the magnetization $M\left(T\right)$ of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ both above and below the flux-lattice melting temperature $T_m\left(H\right)$, in good agreement with experiment. Fluctuations in both order parameter $\psi \left(\mathbf{r}\right)$ and magnetic induction $B$ are included in the Ginzburg-Landau free energy. The second derivative $({\partial }^{2}M/\partial T^2{)}_H$ is predicted to be negative throughout the vortex liquid state and positive in the solid state. The discontinuity in entropy at melting is calculated to be $\sim {0.034k}_B$ per flux line per layer at 50 kOe.