AC multiple hopping conduction in Ni-Mn spinel magnetic ferrites

AC conductivity sigma(omega) on a series of Ni1+xMnxFe2-2xO4 spinel magneti c ferrites was measured as a function of: (a) Temperature (T) from room tem perature up to about 700 K and (b) frequency in the range from 200 Hz up to 100 kHz. The composition (x) was chosen to be x = 0.4, 0.6 and 0.8. AL the higher temperature range sigma(omega) is independent of frequency. However , at low T the frequency dependence is quite obvious and the conductivity i s of hopping nature following a relation of the form sigma(omega) similar t o omega T-s(d). The frequency exponent factor s depends on temperature; it decreases as T is increased. On the other hand, the temperature exponent d varies loth with the angular frequency omega and the composition x, it incr eases as omega or x are decreased. These features were discussed in terms o f a multiple hopping process.