Polarization-dependent heating of the cosmic microwave background   radiation by a magnetic field
  The changes in the cosmic microwave background (CMB) spectrum seen as an increase of temperature due to a strong magnetic field are determined and their influence on the polarization of the radiation is exhibited. The effect is due to the coupling of the CMB photons to the magnetic field in the QED vacuum via the interaction with virtual pairs. In spite of the fact that the distortion of the CMB spectrum for magnetic fields that exist in the vicinity of magnetars is quite large, this effect is very difficult to detect at present because the required angular resolutions is not yet available. 
Zofia Bialynicka-Birula and Iwo Bialynicki-Birula
astro-ph.CO