I'm researching organic solar cells and usually use UV-Vis to study the materials' optical properties. Generally, we calculate the bandgap by the formula 1240/(λonset, nm) (unit is eV), which originates from the formula Eg=hc/λ. Although ferrites are not solvable in water, you can also characterize them in solid-state, such as films or even powders (?). Then the calculation method will be the same.
Please see the link below. Mainly you can use diluted acids to dissolve ferrites. Some organic solvents are also recommended, but mainly dispersed into it by ultrosonic bath.
Bandgap can estimate by the onset. In order to determine the band gap from UV-VIS data it is necessary to measure both transmittance and reflectance. Then, calculate the absorption coefficient and analyze its spectrum.
You can find additional information in the discussion bellow: