We have carried out a detailed study of the morphological, structural, optical and magnetic properties of Cr doped TiO₂ nanocrystals with doping concentrations varying from 3 to 12 atomic weight%. The results obtained from transmission electron microscopy analysis, size-strain plots of all the Cr-doped samples and crystallite size estimation reveal the particle size of the prepared nanocrystals to be well below 10 nm, which is observed to exhibit a decreasing trend with an increase in the Cr dopant concentration. All the samples crystallize in the anatase tetragonal phase of TiO₂, which is confirmed from the Rietveld refinement of the X-ray diffraction patterns and the different modes present in the Raman spectra. The E_g(1) mode shows a clear red shift and broadening with increase in the Cr concentration, which indicates the replacement of Ti ions with Cr ions in the TiO₂ lattice. The possibility of the presence of different functional groups present is verified by Fourier transform infra-red spectroscopy. The presence of Cr³⁺ and Ti⁴⁺ is confirmed from the X-ray photoelectron spectroscopy (XPS) results suggesting the formation of oxygen vacancies to compensate for the charge neutrality. The XPS results validate the Cr³⁺ existence in the Cr:TiO₂ system and corroborate with a slight peak shift towards lower diffraction angle and further confirm the substitutional doping in the present case. Enhanced visible range optical absorption and a clear red shift associated with the absorption edge also suggest the incorporation of Cr³⁺ ions into the host system. The estimated band-gap of Cr-doped TiO₂ nanocrystals reveals a decreasing trend with increasing Cr concentration. The Urbach energy associated with all the Cr-doped samples signifies the presence of oxygen vacancy related defects in the present system, which is further verified using photoluminescence (PL) spectra, and the deconvolution of the PL spectra provides an insight into the oxygen vacancy defects associated with the system. Paramagnetic (PM) behaviour is observed with an increase in the PM moment, suggesting the increase in isolated Cr ions with increase in the Cr concentration, which is further explained using a bound magnetic polaron (BMP) model. Isolated BMP formation could be the reason for the observed PM behavior of the present system, where the trapping of 3d electrons associated with Cr³⁺ in the vacancy sites could ultimately lead to fewer overlapped BMPs, yielding a net PM moment. The present Cr:TiO₂ system could be modified with tailored optical and magnetic properties for functional applications such as magneto-optics and optoelectronic devices.

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