Color-flavor locked superconductor in a magnetic field

We study the effects of moderately strong magnetic fields on the properties of color-flavor locked color superconducting quark matter in the framework of the Nambu-Jona-Lasinio model. We find that the energy gaps, which describe the color superconducting pairing as well as the magnetization, are oscillating functions of the magnetic field. Also, we observe that the oscillations of the magnetization can be so strong that homogeneous quark matter becomes metastable for a range of parameters. We suggest that this points to the possibility of magnetic domains or other types of magnetic inhomogeneities in the quark cores of magnetars.