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Order and disorder around Cr$^{3+}$ in chromium doped persistent luminescence AB$_2$O$_4$ spinels

X-ray absorption near edge structure (XANES) spectroscopy technique is used to better understand the charging and decharging processes of the persistent luminescence in the Cr$^{3+}$ doped AB$_2$O$_4$ spinels (A = Zn, Mg and B = Ga and Al) with low photon energy excitation by visible light. Cr K edge XANES spectra have been simulated for different near neighbour environments around the Cr$^{3+}$ recombination centres and compared with the experimental curve. In Cr$^{3+}$:ZnGa$_2$O$_4$ compound, the Cr$^{3+}$ local structure corresponds mostly to that of a normal spinel ($\sim$70\%), while the rest comprises of distorted octahedral environment arising from cationic site inversion and a contribution from chromium clustering. This local structure is strongly different in Cr$^{3+}$:MgGa$_2$O$_4$ and Cr$^{3+}$:ZnAl$_2$O$_4$ where, for both cases, chromium clustering represents the main contribution. The strong correlation between the intensity of persistent luminescence and \% of Cr in clusters leads us to infer that presence of Cr clusters is responsible for decrease of the intensity of the visible light induced persistent luminescence in the Cr$^{3+}$ doped AB$_2$O$_4$ spinels.