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 Hc2 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.

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We theoretically study the magnetic field orientation dependence of longitudinal and transverse flux line lattice form factors in uniaxial superconductors with anisotropy ratio corresponding to YBa 2 Cu 3 O 7−δ . We discuss influences of the anisotropy ratio of coherence length and differences between the s-wave and the d x 2 −y 2 -wave pairings. The calculations are performed by two methods, the Eilenberger theory and the London theory comparatively, and we study the cutoff function of the extended London theory, which will be helpful in the analysis of the small angle neutron scattering in the vortex states.

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We study vortex states when a magnetic field is applied nearly parallel to the ab-plane in a chiral p-wave superconductor with large anisotropy ratio of ab and c as in Sr 2 RuO 4 . After calculating the spatial structure of the pair potentials and the internal magnetic field in the vortex lattice state on the basis of Eilenberger theory, we estimate the field dependence of the pair potentials and the flux line lattice form factors. We discuss how the chiral-nonchiral transition vanishes and how the transverse field components of internal fields change, when a magnetic field is slightly tilted from the ab plane. In the chiral state, the transverse components do not vanish even for exactlly parallel fields to the ab plane due to the internal angular momentum of chiral p-wave pairing.