Short Note on Spin Magnetization in QGP

Abstract: We outline the theory of spin magnetization applicable to the QGP (quark-gluon plasma) epoch of the Universe. We show that a fully spin-polarized single flavor up-quark gas could generate a cosmic magnetic fields in excess of $10^{15}$ Tesla, far in excess of a possible upper limit to the primordial field. The complete multi component ferro-magnetized primordial fermion gas we consider consists of (five) nearly free electrically charged quarks, and leptons (electrons, muons, tau). We present details of how the magnetization is obtained using a grand partition function approach and point to the role of the nonrelativistic particle component. In the range of temperature 150 MeV to 500 MeV our results are also of interest to laboratory QGP experiments. We show that the required polarization capable to explain large scale structure magnetic fields observed has $1/T$ scaling in the limit of high $T$, and could be very small, at pico-scale. In the other limit, as temperature decreases in the expanding Universe, we show that any magnetic fields present before hadronization can be carried forward to below quark confinement condition temperature by polarization of electrons and muons.