  The effect of symmetry on the resonance spectra of antiferromagnetically
coupled oscillators has attracted new interest with the discovery of
symmetry-breaking induced anti-crossings. Here, we experimentally characterise
the resonance spectrum of a synthetic antiferromagnet Pt/CoFeB/Ru/CoFeB/Pt,
where we are able to independently tune the effective magnetisation of the two
coupled magnets. To model our results we apply the mathematical methods of
group theory to the solutions of the Landau Lifshitz Gilbert equation. This
general approach, usually applied to quantum mechanical systems, allows us to
identify the main features of the resonance spectrum in terms of symmetry
breaking and to make a direct comparison with crystal antiferromagnets.
