Pauli paramagnetic effects on mixed-state properties in a strongly anisotropic superconductor: Application to Sr₂RuO₄

We study theoretically the mixed-state properties of a strong uniaxially anisotropic type-II superconductor with the Pauli paramagnetic effect, focusing on their behaviors when the magnetic field orientation is tilted from the conduction layer ab plane. On the basis of Eilenberger theory, we quantitatively estimate significant contributions of the Pauli paramagnetic effects on a variety of physical observables, including transverse and longitudinal components of the flux-line lattice form factors, magnetization curves, Sommerfeld coefficient, field distributions, and magnetic torques. We apply these studies to Sr₂RuO₄ and quantitatively explain several seemingly curious behaviors, including the H_c2 suppression for the ab-plane direction, the larger anisotropy ratio and intensity found by the spin-flip small-angle neutron scattering, and the first-order transition observed recently in magnetocaloric, specific-heat, and magnetization measurements in a coherent and consistent manner. Those lead us to conclude that Sr₂RuO₄ is either a spin-singlet or a spin-triplet pairing with the d-vector components in the ab plane.