Size, anisotropy and doping effects on the coercive field of ferromagnetic nanoparticles

The influence of size, anisotropy and doping effects on the hysteresis loop of ferromagnetic nanoparticles is studied, based on the modified Heisenberg model. A Green's function technique in real space allows the calculation of the dependence of the magnetization on the temperature, magnetic field, anisotropy, defects and particle size. It is demonstrated that the coercive field H(c) is very sensitive to the surface single-ion anisotropy, and to the exchange interaction constant on the surface J(s) and in the defect shells J(d). With respect to the strong surface single-site anisotropy D(s), we observe at small particle size, N = 4 shells, a maximum in the size dependence of the coercive field, whereas for the small surface anisotropy there is no maximum. Taking into account that J can be different in the defect shells compared to the case without defects, we have obtained for the first time that the coercive field H(c), the permanent magnetization M(r) and the Curie temperature T(C) can increase or decrease for different kinds of doping ions. The dependence on the particle size is discussed, too. The results are in accordance with the experimental data.