Paramagnetic Effects in the Vortex Lattice Field Distribution of Strongly Type-II Superconductors

We present an analysis of the magnetic field distribution in the Abrikosov lattice of high-$\kappa$ superconductors with singlet pairing in the case where the critical field is mainly determined by the Pauli limit and the superfluid currents partly come from the paramagnetic interaction of electron spins with the local magnetic field. The derivation is performed in the frame of the generalized Clem variational method which is valid not too close to the critical field and furthermore with the Abrikosov type theory in the vicinity of it. The found vortex lattice form factor increases with increasing field and then falls down at approach of the upper critical field where the superconducting state is suppressed.