# Effects of strong magnetic fields on neutron $^{3}P_{2}$ superfluidity with spin-orbit interactions

## TL;DR

This paper explores how strong magnetic fields influence neutron $^{3}P_{2}$ superfluid phases in neutron star cores, revealing phase diagram modifications and thermodynamic property changes due to magnetic interactions.

## Contribution

It derives a Ginzburg-Landau equation with higher order magnetic field terms and analyzes the resulting phase diagram of neutron $^{3}P_{2}$ superfluidity.

## Key findings

- The D$_{2}$ biaxial nematic phase is extended by magnetic field effects.
- Higher order magnetic field terms significantly alter the phase diagram.
- Thermodynamic properties like heat capacity and spin susceptibility are affected.

## Abstract

We discuss neutron $^{3}P_{2}$ phases in the core of neutron stars in strong magnetic field (magnetars). The neutron $^{3}P_{2}$ pairing provides a wide variety of condensates, such as the uniaxial nematic and (D$_{2}$ and D$_{4}$) 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 $^{3}P_{2}$ superfluidity, and find that the D$_{2}$ 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.