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Inelastic neutron scattering is used to investigate the temperaturedependence of spin correlations in the 3-dimensional XY antiferromagnetNi(Cl$_{1-x}$Br$_x$)$_2$$\cdot$4SC(NH$_2$)$_2$, $ x = 0.14(1)$, tuned close tothe chemical-composition-induced soft-mode transition. The local dynamicstructure factor shows $\hbar\omega/T$ scaling behavior characteristic of aquantum critical point. The deviation of the measured critical exponent fromspin wave theoretical expectations are attributed to disorder. Another effectof disorder is local excitations above the magnon band. Their energy, structurefactor and temperature dependence are well explained by simple strong-bonddimers associated with Br-impurity sites.

Finite-temperature dynamics and the role of disorder in nearly critical Ni(Cl$_{1-x}$Br$_x$)$_2$$\cdot$4SC(NH$_2$)$_2$