Reported here are the results and their analysis from our detailed investigations of the effects of Cu doping ([Formula: see text]) on the electronic structure and magnetic properties of the spinel [Formula: see text]O. A detailed comparison is given for the [Formula: see text] and [Formula: see text] cases for both the bulk-like samples and nanoparticles. The electronic structure determined from x-ray photoelectron spectroscopy and Rietveld analysis of x-ray diffraction patterns shows the structure to be: ([Formula: see text]) [Formula: see text] [Formula: see text] [Formula: see text]] [Formula: see text] i.e. [Formula: see text] substitutes for [Formula: see text] on the octahedral B-sites. For the bulk samples, the ferrimagnetic [Formula: see text] K for [Formula: see text] is lowered to [Formula: see text] K for the [Formula: see text] sample, this decrease being due to the effect of Cu doping. For the nanosize [Formula: see text] ([Formula: see text]) sample, the lower [Formula: see text] K ([Formula: see text] K) is observed using [Formula: see text] analysis, this lowering being due to finite size effects. For [Formula: see text], fits of dc paramagnetic susceptibility data of [Formula: see text] versus T in nanosize samples to the Néel expression are used to determine the exchange interactions between the A and B sites with exchange constants: [Formula: see text] K (4.1 K), [Formula: see text] K (16.3 K) and [Formula: see text] K (13.8 K) for [Formula: see text]. The temperature dependence of ac susceptibilities [Formula: see text] and [Formula: see text] at different frequencies shows that in bulk samples of [Formula: see text] and [Formula: see text], the transition at T is the normal second order transition. But for the nanosize [Formula: see text] and 0.2 samples, analysis of the ac susceptibilities shows that the ferrimagnetic transition at T is followed by a re-entrant spin-glass transition at lower temperatures [Formula: see text] K (138 K) for [Formula: see text] ([Formula: see text]). Analysis of the ac susceptibilities, [Formula: see text] and [Formula: see text], versus T data is done in terms of two scaling laws: (i) Vogel-Fulcher law [Formula: see text] [Formula: see text]; and (ii) power law of critical slowing-down [Formula: see text]. These fits confirm the existence of glassy behavior below T with the parameters [Formula: see text] (8.91), [Formula: see text] (9.6 × 10[Formula: see text]) and [Formula: see text] K (∼138 K) for the samples [Formula: see text] (0.2), with similar results obtained for other samples. The linear behavior of the peak maximum in [Formula: see text] versus [Formula: see text] (AT-line) further supports the existence of glassy states in nanosize samples. For [Formula: see text], the temperature and composition dependence of the hysteresis loop parameters are investigated; all the samples with x ⩾ 0.1 have the coercivity H and remanence [Formula: see text]. Since the results reported here in these nanostructures are significantly different from those in bulk [...