If cosmic background neutrinos interact very weakly with each other, through spin-spin interactions, then they may have experienced a phase transition, leading to a ferromagnetic ordering. The small magnetic field resulting from ferromagnetic ordering - if present before galaxy formation - could act as a primordial seed of the magnetic fields observed in several galaxies. Our findings suggest that the magnetization could occur in the right epoch, if the exchange boson of neutrino-neutrino interaction is a massless boson beyond the Standard Model, with a coupling constant of 2.2 x 10(-13)(m(v)/10(-4) eV)(2) < g < 2.3 x 10(-7). The estimation of the magnetic seed is 2.3 x 10(-27) G less than or similar to B-CNB less than or similar to 6.8 x 10(-10) G. (C) 2014 The Authors. Published by Elsevier B.V.