  There exists increasing evidence that the phase diagram of the
high-transition temperature (Tc) cuprate superconductors is controlled by a
quantum critical point. One distinct theoretical proposal is that, with
decreasing hole-carrier concentration, a transition occurs to an ordered state
with two circulating orbital currents per CuO2 square. Below the 'pseudogap'
temperature T* (T* > Tc), the theory predicts a discrete order parameter and
two weakly-dispersive magnetic excitations in structurally simple compounds
that should be measurable by neutron scattering. Indeed, novel magnetic order
and one such excitation were recently observed. Here, we demonstrate for
tetragonal HgBa2CuO4+d the existence of a second excitation with local
character, consistent with the theory. The excitations mix with conventional
antiferromagnetic fluctuations, which points toward a unifying picture of
magnetism in the cuprates that will likely require a multi-band description.
