Effect of Copper Substitution on Magnetic Properties of NiFe2O4 Ferrite

The many-body Green’s function theory has been used to study the magnetic properties of Cu x Ni 1−x Fe 2 O 4 spinels. We present a new method to calculate the expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green’s functions. Magnetization and magnetic susceptibility are given when external magnetic field is applied in ( x – z ) plane. The mean field theory has been used to calculate nearest-neighbor exchange and next-nearest-neighbor superexchange interactions. The intraplanar and the interplanar interactions are deduced. The magnetic phase diagram is deduced using high-temperature series expansions. The ferrimagnetic and paramagnetic phases are determined. The critical exponents associated with the magnetic susceptibility γ and the correlation lengths ν have been deduced. These results are comparable with those obtained by magnetic measurements and are comparable with those of 3D Heisenberg model.