The Ginzburg-Landau equations are derived from the microscopic theory for clean layered superconductors with $d_{x^2-y^2}$ pairing symmetry, including the Pauli paramagnetism effect. The upper critical field $H_{c2\mathrm{}}$ parallel to the c axis is calculated. A comparison with the experimental data for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ suggests that, relative to the orbital effect, the Pauli paramagnetism contribution to $H_{c2\mathrm{}}$ is significant. The reversible magnetization M in high magnetic fields is also calculated, showing strong temperature dependence of the slope $dM/dH,$ as a consequence of the spin paramagnetism. A simple expression for the high-temperature spin susceptibility is derived, in good agreement with the Knight-shift measurements on ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8.$

• Received 19 October 1999

DOI:https://doi.org/10.1103/PhysRevB.62.138