Novel magnetic excitations in the high-temperature superconductor HgBa$_{2}$CuO$_{4+ \delta }$

We report on the observation of novel magnetic excitations in the pseudogap phase of the cuprate superconductor HgBa$_{2}$CuO$_{4+\delta }$ (Hg1201) using neutron scattering, and on their relationship with antiferromagnetic (AF) fluctuations. Following polarized neutron diffraction experiments that demonstrated a novel (q=0) magnetic order in the pseudogap phase [B. Fauqu\'{e} \textit{et al.} PRL 96, 197001 (2006); Y. Li \textit{et al.}, Nature 455, 372 (2008)], our inelastic measurements revealed two weakly-dispersive magnetic excitation branches in Hg1201 [Y. Li \textit{et al.}, Nature 468, 283 (2010), and preprint]. These excitations are observed in the pseudogap phase and appear to be associated with the q=0 magnetic order. In our optimally-doped sample, the magnetic resonance occurs at the dispersion maximum of the higher-energy branch. In under-doped Hg1201, the two excitation branches exhibit local intensity maxima at q$_{AF}$, and we find evidence for an hourglass dispersion associated with the lower branch. These results reveal a profound connection between the novel excitations and the conventional AF fluctuations.