Magnetic excitations in the superconducting and pseudogap states of the slightly underdoped high-temperature superconductor HgBa$_{2}$CuO$_{4+\, \delta }$

We present an inelastic neutron scattering study of the dynamic magnetic susceptibility for slightly underdoped cuprate high-temperature superconductor HgBa$_{2}$CuO$_{4+\, \delta }$ (Hg1201, p$=$0.117, T$_{c}$ $=$ 88 K). Unlike more underdoped Hg1201, the magnetic spectrum exhibits an X - shaped hourglass dispersion with an incommensurate low energy response and a clear resonance mode in the superconducting state. At temperatures above T$_{c}$, the low energy incommensurate excitations disappear, replaced by a commensurate Y-shaped spectrum characteristic of the pseudogap state. The magnetic excitations become weaker with increasing temperature and are no longer discernable above the pseudogap temperature T*. The temperature evolution of the magnetic spectrum across T$_{c}$ is consistent with models based on excitations of itinerant spins with a d-wave superconducting order parameter. Our work suggests that itinerant carriers should play an integral part for the understanding of the pseudogap state as well.