Dynamic properties of nanoparticle magnetic systems (original) (raw)

This thesis is concerned with the study of the dynamic properties of ferrofluids, which are an important class of physical systems where microscopic magneto-mechanical effects can be manifested. There are two processes involved with the dynamic properties of a ferrofluid: (a) the magnetic relaxation effect that is due to the rotation of the magnetic moment, , of the ferroparticle, which can be due to Brownian or Néel relaxation or a combination of both, and (b) the resonance effect which is due to the precession of . The typical frequency range in which the magnetic relaxation appears is below 100 MHz, whilst resonance is detected in the microwave band. The parameter we can quantify is the complex magnetic susceptibility, , which is frequency, ω, and field, , dependent and can be estimated by impedance measurements. The complex susceptibility provides information on the microscopic parameters of a ferroparticle, namely the particle radius, , the magnetic radius, , the anisotropy constant, K, the internal anisotropy field, , and the gyromagnetic ratio, . Measurements of the complex susceptibility are made on a number of samples. Our study can be summarised in three separate themes, as follows: (a) To examine the field dependence of the static, , and the dynamic susceptibility, χ(ω), within the relaxation range by scanning between 10 Hz to 1 MHz and for various values of the static polarizing field, , up to 13 kA/m. (i) The study in the field dependence of was performed by constant frequency measurements at 10 kHz. At this frequency the value of can be approximated very well. The data shows that the dependence of on field is in accordance with theory, which predicts that and , where , are the susceptibilities parallel and perpendicular to , L is the Langevin function and . (ii) The study of the dynamic susceptibility, χ(ω), was carried out in the linear and nonlinear regions of the magnetization curve. From the polarised measurements we found that the dynamic susceptibility can be described by an equation which incorporates the frequency dependence (Debye equation), the field dependence of the static susceptibility as mentioned in (i) and also the field dependence of the relaxation time which is in accordance with theory is given by , being the relaxation time of the unpolarised susceptibility. In order to fit the data we modified the Cole-Cole equation in order to include the field dependence of and . This equation is global and can fit both linear and nonlinear susceptibility. In particular the nonlinear susceptibility data can be also fitted by the equations proposed by Coffey and Paranjape and further modified by Déjardin, who expanded the susceptibility to include higher order . The nonlinear portion of χ(ω) is given by the susceptibility increment, Δχ(ω), which can be detected in our experiments. (b) To examine the field dependence of the dynamic susceptibility, χ(ω), within the microwave frequency range between 1 MHz to 20 GHz, for values of the biasing field, , up to approximately 100 kA/m. In the microwave band, magnetic resonance appears. The study in this frequency range is concerned with analysing the field dependence of the Landau-Lifshitz equation and fitting this equation to the susceptibility data by means of Cole-Cole diagrams. It is shown that the Landau-Lifshitz equation can adequately describe the dependence of χ(ω) on the biasing field. (c) To present a theoretical analysis with equivalent electrical circuits which can be used to describe relaxation and resonance in ferrofluids.