The Study Of The Magnetic Properties Of Magnetic Nanoparticle And The Magnetic Nanoparticle Assembly

This dissertation is subject to the nanomagnetism which as a new discipline deals with the magnetic properties of the structures in size of submicrometer or below submicrometer. Here it focuses on magnetic nanoparticles and the magnetic nanoparticle assembly. The research aims at a better understanding of the physics in a multi-body dipolar system, and a promotion of the applications such as magnetic recording materials, and magnetic fluids.The relaxation phenomena play an important and basic role on the magnetic properties of the magnetic nanoparticle assembly, because it is related to how the multi-body dipolar system responses to the external detect, and the time stability of magnetic recording. It is interesting but yet unclear about the effects of randomly distributed anisotropy and the dipolar interactions between particles on the relaxation in magnetic nanoparticle assembly. This dissertation was trying to explore the two effects, i.e. dipolar interaction effect and randomly distributed anisotropy effect. Emphases were put on the relaxation and the energy barrier distribution.Being different from the commonly used Monte Carlo simulation, a local partition function and a master equation were employed to study the relaxation properties of the assembly. Two methods were used for the investigation of the dipolar interaction: one is the mean field approximation to calculate the magnetization; the other is the simulation of the magnetic moment on the basis of the Landau-Lifshitz-Gilbert (LLG) equation, which covers the precession of the moment in comparison to the method of Monte Carlo. To verify the simulation techniques used in the dissertation, we calculate the equilibrium magnetic properties of a single magnetic particle, and apply the LLG simulation to the study of the magnetic hysteresis loop of the magnetic particle assembly. The obtained results were in agreement with the published experiments and theories.To analyze the stable state of the magnetic-field-induced aggregated structures in a ferrofluid, a particle diffusion model was set up to describe the aggregated phase and dispersed phase of the particles, and applied to the case of the hexagonal columnar structure formed in a magnetic field perpendicular to the ferrofluid film. By introducing a mean field method, we calculated the interaction field between the particles in the column, and ultimately obtained the agreeable ratio of the radius to the spacing between the columns. It was concluded that there would be considerable particles dispersed in the ferrofluid film under a perpendicular field, especially when the particles are small. This meant that at least the assumption of total aggregation of the particles should be modified in the minimization analysis of the system's free energy. The interaction between the columns was also discussed. (see Chapter 2)Based on the partition function, we calculated the magnetic properties of a single magnetic particle, the average anisotropy energy, the average Zeeman energy, and the specific heat of the particle. It was found that, in the case of the easy axis parallel to the magnetic field, the peak on the specific heat (vs temperature) shifted to higher temperature with the magnetic field; but to lower in that perpendicular to the field. This was explained by the character of the magnetic energy map of the particle. (see Chapter 3)In regard to the relaxation, we took into account the effects of the randomly distributed anisotropy and the heating rate, and successfully reproduced the relaxation properties of the magnetic particle assembly, such as the magnetization curves (vs temperature) after zero-field-cooling (ZFC) and field-cooling (FC) processes, the relaxation and the memory effect. The followings are concluded.â‘ In the studied system, the temperature (Tp) at the peak of the magnetization curve after a ZFC process could be fitted to Eq. (4-14), which predicts the H2/3 dependence commonly observed by experiments and simulations. Since the good agreement in quantification on H2/3 dependence, we believed Eq. (4-14) would reflect the nature of Tp, rather than the simple H2/3 dependence, and give more physics.â‘¡The model supported the Tln(t/Ï„0) scaling and the investigation on the active barrier distribution from the curve of S(t) vs Tln(t/Ï„0). Meanwhile, for a strong applied magnetic field, the Tln(t/Ï„0) scaling is improved, and the peak of the S(t) corresponds well to the active barrier in the studied system. The barrier distribution derived from S(t) was not necessarily the real distribution in the system.â‘¢The model reproduced the memory effect after temporary cooling, indicating that without a volume distribution and particle interaction, the particle assembly still possesses the memory effect if a randomly distributed anisotropy is set. (see Chapter 4)Regarding the dipolar interaction, it was shown that in the studied system (2D hexagonal lattices and multilayer structures) the particle moments favor two kinds of alignment, ferromagnetic alignment and anti-ferromagnetic alignment, depending on the direction of the applied magnetic field. The ferromagnetic alignment acts on the magnetization, while the anti-ferromagnetic against the magnetization. As the layer number of the system increased, the system's favorite alignment could be changed. Then we go further to the barrier distribution during the magnetization. In the case of the non-interacting assembly, we reproduced the reported phenomena, behind which, the applied magnetic field broadens the barrier distribution and causes the peak position of the distribution to shift to lower barrier area. It was also concluded that, under the magnetic field with the same magnitude, the barrier distribution was wide when the system was initially magnetized from a zero field value; and uniform in the process of reducing field down to zero; while narrow in that of reversing field. It means that the barrier distribution can be controlled by the magnetization. In the case of the interacting assembly, the effects of the dipolar interactions on the peak and the width of the barrier distribution are also related to the magnetization process. During the initial magnetization, there was a threshold field below which the effects were negligible. Particularly, for the studied 2-dimensional particle system with hexagonal configuration, as the field was dropped to zero and then became inversed, the behaviors of the peak and the width of the barrier distribution were related to a field offset. The peak may shift to lower energy and be broadened as the magnitude of the magnetic field increases. (see Chapter 5)Finally, we stressed the following two points of view.â‘ In spite of the uniform size of the particle in the assembly, the randomly distributed anisotropy could be, at least one of the, the origins of several kinds of observed relaxation phenomena.â‘¡The energy barrier distribution could be controlled by the external magnetic field together with the dipolar interaction between the particles. In addition, the relaxation model and the diffusion model could be applied to the study of the static magnetic properties, and to the aggregation in electrofluids.