ferromagnetism in neutron matter jpw diener 1, fg scholtz 1,2, hb geyer 1, gc hillhouse 3 1...
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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.
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