Phase structure of neutron ${}^3{P}_2$ superfluids in strong magnetic fields in neutron stars

Abstract

We discuss the effect of a strong magnetic field on neutron ${}^3{P}_2$ superfluidity. Based on the attraction in the ${}^3{P}_2$ 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 $B=0$, D${}_2$-biaxial nematic (BN) and D${}_4$-BN phases in finite $B$ and strong $B$ such as magnetars, respectively, where D${}_2$ and D${}_4$ are dihedral groups. We find that, compared with the leading order in the magnetic field known before, the region of the D${}_2$-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, D${}_2$-BN, and D${}_4$-BN phases. This information will be useful to understand the internal structures of magnetars.

Comments: 11 pages, 3 figures