We discuss the effect of a strong magnetic field on neutron P23 superfluidity. Based on the attraction in the P23 pair of two neutrons, we derive the Ginzburg-Landau equation in the path-integral formalism by adopting the bosonization technique and leave the next-to-leading order in the expansion of the magnetic field B. We determine the (T,B) phase diagram with temperature T, comprising three phases: the uniaxial nematic (UN) phase for B=0, D2-biaxial nematic (BN) and D4-BN phases in finite B and strong B such as magnetars, respectively, where D2 and D4 are dihedral groups. We find that, compared with the leading order in the magnetic field known before, the region of the D2-BN phase in the (T,B) plane is extended by the effect of the next-to-leading-order terms of the magnetic field. We also present the thermodynamic properties, such as heat capacities and spin susceptibility, and find that the spin susceptibility exhibits anisotropies in the UN, D2-BN, and D4-BN phases. This information will be useful to understand the internal structure of magnetars.
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