Sharp spectroscopic fingerprints of disorder in an incompressible magnetic state

Disorder significantly impacts the electronic properties of conducting quantum materials by inducing electron localization and thus altering the local density of states and electric transport. In insulating quantum magnetic materials, the effects of disorder are less understood and can drastically impact fluctuating spin states like quantum spin liquids. In the absence of transport tools, disorder is typically characterized using chemical methods or by semi-classical modeling of spin dynamics. This requires high magnetic fields that may not always be accessible. Here, we show that magnetization plateaus -- incompressible states found in many quantum magnets -- provide an exquisite platform to uncover small amounts of disorder, regardless of the origin of the plateau. Using optical magneto-spectroscopy on the Ising-Heisenberg triangular-lattice antiferromagnet K$_2$Co(SeO$_3$)$_2$ exhibiting a 1/3 magnetization plateau, we identify sharp spectroscopic lines, the fine structure of which serves as a hallmark signature of disorder. Through analytical and numerical modeling, we show that these fingerprints not only enable us to quantify minute amounts of disorder but also reveal its nature -- as dilute vacancies. Remarkably, this model explains all details of the thermomagnetic response of our system, including the existence of multiple plateaus. Our findings provide a new approach to identifying disorder in quantum magnets.