  The microscopic origins of emergent behaviours in condensed matter systems
are encoded in their excitations. In ordinary magnetic materials, single
spin-flips give rise to collective dipolar magnetic excitations called magnons.
Likewise, multiple spin-flips can give rise to multipolar magnetic excitations
in magnetic materials with spin $\mathbf{S} \boldsymbol{\ge} \mathbf{1}$.
Unfortunately, since most experimental probes are governed by dipolar selection
rules, collective multipolar excitations have generally remained elusive. For
instance, only dipolar magnetic excitations have been observed in isotropic
$\mathbf{S}\boldsymbol{=}\mathbf{1}$ Haldane spin systems. Here, we unveil a
hidden quadrupolar constituent of the spin dynamics in antiferromagnetic
$\mathbf{S}\boldsymbol{=}\mathbf{1}$ Haldane chain material
Y$_\mathbf{2}$BaNiO$_\mathbf{5}$ using Ni $\mathbf{L_3}$-edge resonant
inelastic x-ray scattering. Our results demonstrate that pure quadrupolar
magnetic excitations can be probed without direct interactions with dipolar
excitations or anisotropic perturbations. Originating from on-site double
spin-flip processes, the quadrupolar magnetic excitations in
Y$_\mathbf{2}$BaNiO$_\mathbf{5}$ show a remarkable dual nature of collective
dispersion. While one component propagates as non-interacting entities, the
other behaves as a bound quadrupolar magnetic wave. This result highlights the
rich and largely unexplored physics of higher-order magnetic excitations.
