Unusual form factor of the novel pseudogap excitations in HgBa$_{2}$CuO$_{4+\delta}$

Following the discovery of a universal novel magnetic order in the pseudogap phase of the cuprates [B. Fauqu\'{e} et al. PRL 96, 197001 (2006); Y. Li et al., Nature 455, 372 (2008)], our inelastic neutron scattering measurements of HgBa2CuO4$+\delta $ (Hg1201) revealed two weakly-dispersive excitation branches associated with this ordered state [Y. Li et al., Nature 468, 283 (2010); Y. Li et al., Nature Phys. 8, 404 (2012).]. The dependences of the mode intensities on the momentum transfer Q $=$ (HKL) (r.l.u.) are inconsistent with traditional magnetic or structural form factors. The intensity of the high-energy mode is zero when Q is parallel to the copper-oxygen planes (i.e., for L$=$0), peaks at L $=$ 8 (r.l.u.), and decreases again at large L. We observe the opposite behaviour for the low- energy mode, which is strongest when L$=$0. In combination with polarized inelastic neutron scattering results, this indicates possible dual magnetic and structural characteristics of the novel excitations. Work supported by DOE-BES.