Excitations in antiferromagnetic cores of superconducting vortices

We study excitations of the predicted antiferromagnetically ordered vortex cores in the superconducting phase of the newly proposed SO(5) model of strongly correlated electrons. Using experimental data from the literature we show that the susceptibilities in the spin sector and the charge sector are nearly equal, and likewise for the stiffnesses. In the case of strict equality SO(5) symmetry is possible, and we find that if present the vortices give rise to an enhanced neutron scattering cross section near the so called $\pi$ resonance at 41 meV. In the case of broken SO(5) symmetry two effects are predicted. Bound excitations can exist in the vortex cores with “high” excitation energies slightly below 41 meV, and the massless Goldstone modes corresponding to the antiferromagnetic ordering of the core can acquire a mass and show up as core excitation with “low” excitation energies around 2 meV.