$20~$km). The internal composition of neutron stars (still poorly understood) is described by all sorts of exotic dense matter in form of hyperons, a Bose Einstein Condensate (BEC) of mesons or deconfined quark matter in presence of strong magnetic fields [@Lattimer:2004pg]. Size and shape of a compact object depends on its composition but also on the magnetic field [@0954-3899-36-7-075202]. There are also some phenomena at astrophysical scale without explanation, as jets of pulsars, where magnetic fields might be relevant [@MNL2:MNL2848; @Charbonneau:2009ax].

Even though some theories have been proposed to explain the origin of such magnetic fields, this issue is far from being exhausted and it is still under great debate. In this regard, spin one bosons seems to be good candidates as magnetic field sources since, at low temperature, they are known to show an spontaneous magnetization. As a consequence, under certain conditions, a gas of bosons can generate and sustain its own magnetic field [@Yamada; @Elizabeth].

The study of BEC and magnetization for a charged scalar or vector boson gas in presence of a constant magnetic field was tackled in [@ROJAS1996148; @PEREZROJAS2000; @Khalilov:1999xd; @Khalilov1997; @Bargueno; @Jian]. For low temperatures, the charged vector boson gas is paramagnetic, can be self 