Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet.

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.