Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: We consider the ferromagnetic phase in pure neutron matter as well as charge neutral, betaequilibrated nuclear matter. We employ Quantum Hadrodynamics, a relativistic field theory description of nuclear matter with meson degrees of freedom, and include couplings between the baryon (proton and neutron) magnetic dipole moment as well as between their charge and the magnetic field in the Lagrangian density describing such a system. We vary the strength of the baryon magnetic dipole moment till a non-zero value of the magnetic field, for which the total energy density of the magnetised system is at a minimum, is found. The system is then assumed to be in the ferromagnetic state. The ferromagnetic equation of state is employed to study matter in the neutron star interior. We find that as the density increases the ferromagnetic field does not increase continuously, but exhibit sudden rapid increases. These sudden increases in the magnetic field correspond to shifts between different configurations of the charged particle’s Landau levels and can have significant observational consequences for neutron stars. We also found that although the ferromagnetic phase softens the neutron star equation of state it does not significantly alter the star’s massradius relationship. The properties of magnetised symmetric nuclear matter were also studied. We confirm that magnetised matter tends to be more proton-rich but become more weakly bound for stronger magnetic fields. We show that the behaviour of the compressibility of nuclear matter is influenced by the Landau quantisation and tends to have an oscillatory character as it increases with the magnetic field. The symmetry energy also exhibits similar behaviour. / AFRIKAANSE OPSOMMING: In hierdie studie het ons die ferromagnetiese fase in suiwer neutronmaterie, sowel as in ladingsneutrale, beta-ge¨ekwilibreerde neutronstermaterie, ondersoek. Vir die doeleindes het ons die Kwantum Hadrodinamika-model van kernmaterie gebruik. Dit is ’n relatiwistiese, veldteoretiese model wat mesone inspan om die interaksies tussen die protone en neutrone te bemiddel. Om die impak van die magneetveld te bestudeer, sluit ons ’n koppeling tussen die barioonlading en die magneetveld, asook barioondipoolmoment en die magneetveld, in by die Lagrange digtheid wat ons sisteem beskryf. Om die ferromagnetiese fase te ondersoek, varieer ons die sterkte van die barioondipoolmoment om ’n nie-nul waarde van die magneetveld wat energie digtheid sal minimeer te vind. Die ferromagnetiese toestandsvergelyking word toegepas op materie aan die binnekant van die neutronster en die impak hiervan op die waarneembare eienskappe van die ster word ondersoek. Ons vind dat die ferromagnetiese magneetveld nie kontinu toeneem soos die digtheid verhoog nie. Die skielike toenames in die magneetveld is die gevolg van die sisteem wat die konfigurasie van die gelaaide deeltjies se Landau-vlakke skielik verander en dit kan beduidende waarneembare gevolge vir die ster inhou. Ons vind ook dat die ferromagnetiese fase die toestandsvergelyking versag, maar dat die versagting die massa-radius verhouding van die ster nie grootliks beïnvloed nie. Die eienskappe van gemagnetiseerde kernmaterie word ook ondersoek. Ons bevestig dat gemagnetiseerde materie meer proton-ryk, maar minder sterk gebind word. Ons wys dat die saampersbaarheid van kernmaterie deur die teenwoordigheid van Landau-vlakke beïnvloed word en ossilerend saam met die magneetveld toeneem. Die simmetrie-energie manifesteer ook soortgelyke gedrag.