1. Ferromagnetism in neutron matter
...and how it could apply to neutron stars
JPW Diener1 , FG Scholtz1,2, HB Geyer1, GC Hillhouse3
1 Institute of Theoretical Physics, Stellenbosch University
2 National Institute for Theoretical Physics, Stellenbosch
3 New York Institute of Technology, Nanjing, China

2. Introduction We are investigating pulsar/neutron star matter.
One of the densest states of matter.
Aiming to better understand the magnetic field of these stars.
Pulsars are made up (in part at least) of nuclear matter.
We are investigating the spontaneous magnetisation of neutron matter.

3. Ferromagnetism
Ferromagnetism is a property of any system that can undergo a phase transition from an unmagnetised to a magnetised state.
(Ferro)magnetised matter
Unmagnetised matter

4. Neutrons Neutrons are neutral particles, with spin ±½.
Dipole moment reacts to a external magnetic field.
Aligned dipole moments induce a magnetic field.
Spontaneous magnetisation will occur if a stable, lower energy (magnetic) configuration is available.
Neutron with the magnetic dipole moment

5. Relativity Relativistic description of ferromagnetism.
Relativity: Albert Einstein’s most famous equation:
More general form:
Considering plane waves solution and natural units (ћ = c = 1)
Non-relativistic energy-momentum relationship:

6. Neutron matter dispersion relationship

7. Magnetic neutron matter
Including the magnetic field in a relativistic fashion, the energy-momentum relationship is modified:
For zero momentum:
(External) magnetic field introduces a specific direction, breaking spherical symmetry.

8. Neutron matter dispersion relationship (2)

9. Magnetised vs unmagnetised system

10. Ferromagnetic state
External magnetic field makes a lower energy state available.
If lower energy state is favoured, a magnetic field is induced.
Ferromagnetic state would be stable if the induced magnetic field is equal to the external field.

11. Conclusions and way forward
Have shown that lower energy state exists.
Strength of induced magnetic field as function of density still unknown.
To be calculated.
Compare to experimental known properties of the neutron to determine accuracy.
If there is agreement, then we would be able to predict at what densities a ferromagnetic phase would present itself.

12. Acknowledgements This research is support by the SA SKA project, and,
Stellenbosch University.