I recently prepared cobalt ferrite by a mixed solution of cobalt chloride and iron chloride precipitation in a sodium hydroxide solution. When I measured the obtained powder by XRD, I found very broad peaks that did not match cobalt ferrite (although after annealing I found the peaks expected). The same sample (not annealed) was measured in Mossbauer spectroscopy and found no ferromagnetism.
Well, the stuff is probably superparamagnetic (i.e. each particle a single magnetic domain). If you have very broad lines in XRD be aware that 3 nm is rather small crystallites leading to broadening of the lines in their own. Is the particle size after annealing still 3 nm?
In the ferrite particles the spin-glass shell with the thickness of about 1 nm is often formed. Thus the particle with diameter of 3 nm can be fully in spin-glass state.
The annealed sample shows the higher grain size as expected and the diffraction peaks of the cubic crystal structure of cobalt ferrite; also the annealed sample shows ferromagnetism (sextets) in Mossbauer spectroscopy as expected. What was a little odd to me was the results in the "as made" (not annealed) sample principally in Mossbauer spectroscopy.
Superparamagnetism seems the most likely cause as mentioned by Nikolaus. Annealing for longer times and at higher temperatures can result in increase in the size of the particles.
I also believe it is superparamagnetism. It could show an EPR spectrum but also some ferromagnetic-like properties, that could decrease the Q factor of the EPR spectrometer at B = 0, revealed by an unusually large detector current, and reveling a high dynamic magnetic susceptibility. So try an EPR spectrum. Then as you know the size of the nanoparticles you can compare it with estimations from the linwidths.
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