  The electromagnetic instabilities excited by the temperature anisotropy have
been always one of the interesting issues in real high-density physical
systems, where the relativistic and quantum effects due to spin can be
important. This paper discusses the case where plasma is not strongly coupled
but is still in regimes where a classic plasma description is not fully
adequate. The length scale of the plasma can be larger than the de-Broglie
length so that the quantum effects relevance to the spin can be significant. In
addition, the only relativistic effects are due to the electrons spin, for
example the spin-orbit coupling effect (the weak (semi) relativistic effects).
Obtained results imply that these effects can not be important in the ICF
subjects while these can lead to significant results in the astrophysical
subjects because of the strong magnetic fields. It is found that the weakly
relativistic effects can cover the magnetic dipole force and the spin
precession effects so that the growth rate of the instability can increase
compared to the non relativistic spin polarized cases. Indeed, it is expected
that the probability of electron capture in the background magnetic fields and
the particle energy dissipation will be reduced so that there will be a high
portion of free energy in the system.
