Pauli Paramagnetism of Neutron Star Matter and the Upper Limit for Neutron Star Magnetic Fields

A relativistic version of Pauli paramagnetism for $n-p-e$ system inside a strongly magnetized neutron star has been developed. An analytical expressions for the saturation value of magnetic field strength for each of these constituents at which they are completely polarized have been obtained. From the fully polarized configuration of electronic component, an upper limit for neutron star magnetic field is predicted. It has been concluded that indeed, magnetars, as stronly magnetized young neutron stars can not exist if the constituents are electron, proton and neutron in $\beta$-equilibrium. An alternative model has been proposed.