Theory of magnetic excitons in the heavy-fermion superconductor $UP{d}_{2}A{l}_3$

We analyze the influence of unconventional superconductivity on the magnetic excitations in the heavy fermion compound UPd${}_2$Al${}_3$. We show that it leads to the formation of a bound state at energies well below 2${\mathrm{\Delta }}_0$ at the antiferromagnetic wave vector {\textbf Q}=$(0,0,\pi \mathrm{/}c)$. Its signature is a resonance peak in the spectrum of magnetic excitations in good agreement with results from inelastic neutron scattering. Furthermore we investigate the influence of antiferromagnetic order on the formation of the resonance peak. We find that its intensity is enhanced due to intraband transitions induced by the reconstruction of Fermi surface sheets. We determine the dispersion of the resonance peak near {\textbf Q} and show that it is dominated by the magnetic exciton dispersion associated with local moments. We demonstrate by a microscopic calculation that UPd${}_2$Al${}_3$ is another example in which the unconventional nature of the superconducting order parameter can be probed by means of inelastic neutron scattering and determined unambiguously.