Spin paramagnetism in d-wave superconductors

TL;DR

This paper derives Ginzburg-Landau equations incorporating Pauli paramagnetism for d-wave superconductors, calculates the upper critical field, and compares results with experiments on YBCO, highlighting the significance of spin effects.

Contribution

It introduces a microscopic derivation of Ginzburg-Landau equations including spin paramagnetism for d-wave superconductors, and applies them to YBCO to explain experimental observations.

Findings

Pauli paramagnetism significantly affects the upper critical field in YBCO.

Strong temperature dependence of magnetization slope due to spin effects.

Derived high-temperature spin susceptibility matches Knight shift data.

Abstract

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 $H_{c2}$ parallel to the $c$ axis is calculated. A comparison with the experimental data for YBCO suggests that, relative to the orbital effect, the Pauli paramagnetism contribution to $H_{c2}$ 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 a good agreement with the Knight shift measurements on YBCO.