Ferromagnetism in neutron matter

JPW Diener1 , FG Scholtz1,2, HB Geyer1, GC Hillhouse3

1 Institute of Theoretical Physics, Stellenbosch University2 National Institute for Theoretical Physics, Stellenbosch

3 New York Institute of Technology, Nanjing, China

...and how it could apply to neutron stars

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.

Ferromagnetism

Unmagnetised matter (Ferro)magnetised matter

Ferromagnetism is a property of any system that can undergo a phase transition from an unmagnetised to a magnetised state.

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.

Neutrons

Neutron with the magnetic dipole moment

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:

2E = mc2 2 2 2 4E = p c +m c

2 2 2E = k +m

2kE = 2m

Neutron matter dispersion relationship

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.

22 2 2 2

z zE = k + k +m ± b

zE = m ± b

Neutron matter dispersion relationship (2)

Magnetised vs unmagnetised system

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.

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.

Acknowledgements

This research is support by the SA SKA project,

and, Stellenbosch University.