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

Abstract

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.

Composition dependence of the coercivity in magnetic nanoparticles suitable for magnetic hyperthermia

“…So we must look for ways to reduce this coercive field. It is well established that the magnetic properties of surfaces and nanostructures may differ drastically from those of the bulk [7]. Due to breaking of the symmetry at the surface, to the changed number of next neighbors on the surface or due to defects on the surface the exchange interaction constant J can take different values on the surface s J or in the defect shell d J compared to the value in the particle b .…”

“…The time-dependent term in Eq. (4) includes damping effects which are studied in our previous papers [7]. The spin excitation energy is calculated from Eq.…”

“…Further the magnetic nanoparticles must have high saturation magnetization and low coercive field. In our previous papers we have studied theoretically the size, anisotropy and doping effects on the magnetization, hysteresis loop and Curie temperature of ferromagnetic nanoparticles [7]. We have obtained that the coercive field c H in most ferromagnetic nanoparticles is enhanced in comparison to the bulk value.…”

“…The aim of the present paper is to apply and extend our theory [7] in order to find the size, shape and composition dependence of the coercive field, saturation magnetization and Curie temperature of magnetic nanoparticles which could be suitable for application in magnetic hyperthermia.…”

Size and anisotropy effects on magnetic properties of antiferromagnetic nanoparticles

“…In our previous papers we have studied theoretically the size, anisotropy and doping effects on the magnetization, hysteresis loop, Curie temperature and spin excitations of FM nanoparticles [27][28][29][30]. The aim of the present paper is to apply and extend our theory in order to find the size and anisotropy dependence of the magnetic properties of AFM nanoparticles and to compare them with those of magnetic nanoparticles.…”