Effects of strong magnetic fields on neutron ³P₂superfluidity with spin-orbit interactions

We discuss neutron ³P₂phases in the core of neutron stars in strong magnetic field (magnetars). The neutron ³P₂pairing provides a wide variety of condensates, such as the uniaxial nematic and (D2 and D4) biaxial nematic, with different symmetries stemming from the combinations of spin and momentum. Based on the spin-orbital angular momentum coupling and the spin-magnetic field coupling of the neutrons, we derive the Ginzburg-Landau equation containing higher order terms of the magnetic field. We investigate the phase diagram of the neutron ³P₂superfluidity, and find that the D2 biaxial nematic phase is extended by the higher order terms of the magnetic field. We also discuss the thermodynamic properties, the heat capacity and the spin susceptibility.