System Of Single-domain Particles Research Articles

Magnetic properties of barium ferrite nanoparticles: Quantitative test of the Stoner–Wohlfarth theory for uniaxial single-domain magnetic particles

Abstract We have successfully synthesized single-domain barium ferrite particles with uniaxial anisotropy. We have coated them with amorphous silica to reduce interparticle interactions so that the assembly of these particles behaves like a noninteracting randomly oriented uniaxial single-domain particle system, a prototype for the Stoner–Wohlfarth model. From the magnetic hysteresis loops of the particle system in a wide temperature range ( 10 – 700 K ), we simultaneously determine the magnetic anisotropic field H K , the reduced remanence M r / M s , and the coercive field H C in the whole temperature range below the Curie temperature. These complete sets of data allow us to quantitatively test the Stoner–Wohlfarth theory and the agreement between experiment and theory is good.

Temperature dependence of magnetic anisotropy constant in iron chalcogenide Fe3Se4: Excellent agreement with theories

Magnetic hysteresis loops were measured for ferrimagnetic iron chalcogenide [Formula: see text] nanoparticles in the whole temperature range below the Curie temperature [Formula: see text] (315 K). The coercivity of the material is huge, reaching about 40 kOe at 10 K. The magnetic anisotropy constant K was determined from the magnetic hysteresis loop using the law of approach to saturation. The deduced anisotropy constant at 10 K is [Formula: see text], which is over one order of magnitude larger than that of [Formula: see text]. We also demonstrated that the experimental magnetic hysteresis loop is in good agreement with the theoretical curve calculated by Stoner and Wohlfarth for a noninteracting randomly oriented uniaxial single-domain particle system. Moreover, we show that K is proportional to the cube of the saturation magnetization [Formula: see text], which confirms earlier theoretical models for uniaxial magnets.

Extracting anisotropy energy barrier distributions of nanomagnetic systems from magnetization/susceptibility measurements

Anisotropy barrier distributions of single domain particle systems are an important issue in the nanomagnetism and its applications. Different methods to extract the distribution from temperature, field, or time-dependent magnetization/susceptibility are reviewed and compared. A single domain particle system is measured to test the methods.

Characteristic times of relaxation peaks of magnetic fluids

The use of the Fokker–Planck equation in theoretical studies of relaxation processes in single-domain particle systems is a well-established technique. However this method has a particular disadvantage in that it can give analytical results solely in some limiting cases. An alternative method, which avoids this difficulty, is that of the use of the integral relaxation time, τ int, which is presented in this work. Complex magnetic susceptibility measurements, χ( ω)= χ′( ω)−i χ″( ω), over the frequency range 10–100 MHz, were performed on a commercial kerosene-based magnetic fluid with magnetite particles stabilized with oleic acid. Based on these measurements, the integral relaxation time, τ int, the effective relaxation time, τ eff and the maximum absorption time, τ max =(2 πf max) −1, where f max is the frequency at which χ″( ω) exhibits a maximum, were determined. These characteristic times of a relaxation peak are always different, except for the idealized case of a homogeneous system with a single relaxation time. Due to the fact that τ int can be found analytically in a wide range of parameters, without solving the Fokker–Planck equation of the stochastic process, the presented experimental method can be successfully involved in the investigation of relaxation processes in single-domain magnetic particle systems, enabling a comparison to be made between experimental and theoretical results.

Nanomagnetism: extension of the Stoner–Wohlfarth model within Néel’s ideas and usefulplots

This paper deals with the extension of the well known Stoner–Wohlfarth (SW) modelwidely used to compare magnetic properties of real single-domain particle systems with itsideal predictions. The model is often discussed in connection with nanomagnetism. Theextension of this successful SW model is gained by combining it with Néel’s ideas concerningthe dynamical behavior and relaxation of the magnetization in such systems. We presentthe derivation of a universal relaxation equation which holds for the populations of theSW energy levels defined by the SW model. By solving this differential equationwith properly chosen initial conditions, a number of magnetization phenomenaobserved experimentally versus temperature, time, and external magnetic fieldscan be understood and described quantitatively. So, hysteresis loops, includingthose in high-frequency external magnetic fields, can be calculated within thismodel as a function of temperature, and demagnetization curves for arbitraryheating rates in different external magnetic fields can be simulated. In contrast tothe difficulties encountered when treating the experimental data within moregeneral stochastic models based on the Landau–Lifshitz–Gilbert equation, one caneasily fit to a first approximation a wide set of data taken from the same samplewithin the extended SW model. The well known Henkel and Thamm–Hesse plotsare reviewed and it is shown that by using these for plotting experimental datadeviations from the ideal SW behavior and influences caused by relaxation can bedetected. The plot recently proposed by Michele–Hesse–Bremers is shown not to besensitive to relaxation influences and therefore reveals only the particle–particleinteraction.

Time-quantifiable Monte Carlo method for simulating a magnetization-reversal process

We propose a time-quantifiable Monte Carlo (MC) method to simulate the thermally induced magnetization reversal for an isolated single domain particle system. The MC method involves the determination of density of states and the use of Master equation for time evolution. We derive an analytical factor to convert MC steps into real time intervals. Unlike a previous time-quantified MC method, our method is readily scalable to arbitrarily long time scales, and can be repeated for different temperatures with minimal computational effort. Based on the conversion factor, we are able to make a direct comparison between the results obtained from MC and Langevin dynamics methods and find excellent agreement between them. An analytical formula for the magnetization reversal time is also derived, which agrees very well with both numerical Langevin and time-quantified MC results, over a large temperature range and for parallel and oblique easy axis orientations.

Magnetic relaxation in a model of interacting nanoparticles in terms of microscopic energy barriers

Monte Carlo simulations are used to study the magnetic relaxation of a system of single domain particles with dipolar interactions modeled by a chain of Heisenberg classical spins. We show that the so-called T ln (t/τ0) method can be extended to interacting systems and how, from the computed master relaxation curves, the effective energy barrier distributions responsible for the relaxation can be obtained. A transition from a quasi-logarithmic to power-law behavior of the relaxation as the interaction strength is increased is found. By direct computation of the effective energy barriers of the system, we show that this is due to the appearance of an increasing number of small energy barriers caused by the reduction of the anisotropy energy barriers as the local dipolar fields increase. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetic relaxation in terms of microscopic energy barriers in a model of dipolar interacting nanoparticles

The magnetic relaxation and hysteresis of a system of single domain particles with dipolar interactions are studied by Monte Carlo simulations. We model the system by a chain of Heisenberg classical spins with randomly oriented easy-axis and log-normal distribution of anisotropy constants interacting through dipole-dipole interactions. Extending the so-called $T\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(t∕{\ensuremath{\tau}}_{0})$ method to interacting systems, we show how to relate the simulated relaxation curves to the effective energy barrier distributions responsible for the long-time relaxation. We find that the relaxation law changes from quasilogarithmic to power-law when increasing the interaction strength. This fact is shown to be due to the appearance of an increasing number of small energy barriers caused by the reduction of the anisotropy energy barriers as the local dipolar fields increase.

Temperature dependence of the coercive field in single-domain particle systems

The magnetic properties of ${\mathrm{Cu}}_{97}{\mathrm{Co}}_{3}$ and ${\mathrm{Cu}}_{90}{\mathrm{Co}}_{10}$ granular alloys were measured over a wide temperature range $(2--300\phantom{\rule{0.3em}{0ex}}\mathrm{K})$. The measurements show an unusual temperature dependence of the coercive field. A generalized model is proposed and explains well the experimental behavior over a wide temperature range. The coexistence of blocked and unblocked particles for a given temperature raises difficulties that are solved here by introducing a temperature dependent blocking temperature. An empirical factor gamma $(\ensuremath{\gamma})$ arises from the model and is directly related to the particle interactions. The proposed generalized model describes well the experimental results and can be applied to other single-domain particle system.

First order approximation for interactions in particulate single-domain particle systems

In most cases the interparticle interactions are essential in the evaluation of the magnetic properties of the ferromagnetic particulate systems. Usually, in first approximation, a mean interaction field linearly dependent on the magnetic moment of the sample is considered and other interactions are neglected. Using micromagnetic simulations on a system of interacting uniaxial single-domain particles we have shown that both the mean interaction field and interaction fields distribution dispersion depend on the magnetic moment of the sample. When the magnetic moment of the sample is small the statistical interactions are more important than the mean field ones and cannot be neglected.

Stochastic Resonance in Finely Dispersed Magnetics: a Comparison of Discrete and Continuous Models

The phenomenon of a stochastic resonance in a system of single-domain particles with easy-axis magnetic anisotropy is treated theoretically for the thermally activated system. The results of calculations for the discrete model based on the control equation for the Kramers transition rates of the magnetic moment vector and for the continuous model based on numerical solution of the Fokker–Planck equation with a periodic drift term are analyzed. The phase shifts between input and output signals and the values of the signal-to-noise ratio calculated for iron superparamagnetic particles in the context of these two models are compared.

Stochastic resonance in low-disperse magnets: Mechanism of subbarrier magnetization reversal

The phenomenon of stochastic resonance is studied theoretically in a system of single-domain particles with an “easy-axis”-type magnetic anisotropy at temperatures close to absolute zero, for which the tunneling of the magnetic moment vector between stable states dominates. Calculations are made on the basis of the master equation in the model of discrete orientations in the quasi-adiabatic approximation. The dynamic magnetic susceptibility components of the system under the action of a weak rf field are calculated. The critical temperature at which a transition from the above-the-barrier mechanism of magnetization reversal to the subbarrier mechanism occurs is estimated.

Distribution function for random interaction fields in disordered magnets: Spin and macrospin glass

Systems with an arbitrary dependence of exchange integral on the distance between atoms which are randomly scattered in an amorphous substance are investigated by averaging over random fields of interaction in the framework of the Ising model. This method is also used for describing long-term magnetization relaxation in a system of single-domain particles scattered in a nonmagnetic matrix. Random field distribution functions are obtained for the dipole-dipole and the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions. Long-term relaxation in macrospin glasses is investigated.

Hard magnetic properties of melt-spun R(Fe,M)12 nitrides (R=Nd or Pr; M=Mo or V)

The hard magnetic properties of nitrided melt-spun R(Fe,M)12 (R=Pr and Nd, M=V and Mo) ribbons have been investigated. Hard magnetic powders were prepared by vacuum annealing of ground ribbons in the temperature range from 700 to 950 °C and subsequent nitrogenation. For NdFe10.5Mo1.5Nx and PrFe10.5Mo1.5Nx powders, coercivities as high as 10.4 and 4.5 kOe at room temperature, respectively, were achieved by carefully controlling the nitrogenation process. The coercivity strongly depends on the preparation route, i.e., annealing temperature as well as nitrogenation temperature and time. By the detailed investigation of the influence of these conditions, the optimum process parameters were determined. The coercivity mechanism of melt-spun NdFe10.5Mo1.5Nx powders shows characteristics of a randomly oriented single domain particle system. Poor coercivities have been obtained for Nd(Fe,V)12 and Pr(Fe,V)12. In these cases as well as for not optimally nitrogenated Nd(Fe,Mo)12, the low coercivity of the nitrided powders is related to (i) too large grain sizes, (ii) the presence of α-Fe additional to the ThMn12-type phase, or (iii) a nonhomogeneous nitrogenation of the powder.

Long-range order and magnetic relaxation in a system of single-domain particles

The paramagnetic-ferromagnetic phase transition and distinctive characteristics of relaxation of the magnetization in a system of interacting single-domain ferromagnetic particles distributed randomly in a nonmagnetic matrix are investigated in the mean-field approximation.

Computer simulation of slow magnetic relaxation

Abstract We present a computer simulation study of magnetic relaxation for a system of single-domain particles. We focus on the dependence of the magnetic viscosity coefficient with the shape of the distribution function of activation energies, and compare our computational results with known experimental results for a ferrofluid system.

Theory of R. F. Mössbauer Spectra of the Magnetics with Magnetic Anisotropy

AbstractThe theory of the r. f. collapse phenomenon in nuclear γ resonance (NGR) for magnetics is proposed. In contrast to the existing rotating‐field and stepwise‐field models this approach takes into consideration the detailed behaviour of the magnetization (consequently of hyperfine field (HF) under external r. f. field and magnetic anisotropy field. Using the Liouville superopetor technique the expression for NGR absorption cross‐section (57Fe) is obtained on the basis of time periodicity of the HF alone. The possibility of the chaotic evolution of the magnetization in some cases and the corresponding changes in the NGR spectra are shown. Numerical model calculations for a system of single domain particles with uniaxial anisotropy using the chain fraction method are carried out. So the matter under discussion is a quantitative to the r. f. collapse regime valid for an arbitrary time dependence of the HF.

Texture and angular dependence of magnetic viscosity in digital recording media

The effect of texture and angular variation on the time dependence coefficient S is studied. Magnetic measurements were made using a vibrating sample magnetometer with a resolution of 10/sup -5/ emu. Two types of sample were examined: for the angular dependence measurements a XIDEX UK IBM 3480 data tape was used, and for the texturing study special samples of XIDEX UK TK52 tape were prepared. Increasing the degree of texture results in the variation of S with H becoming more strongly peaked around the coercive force. An increase in texture, desirable for better recording performance, is compromised by an increase in the maximum value of magnetic viscosity by a factor of two, for an increase in squareness from 0.6 to 0.8. The angular variation of the coercivities illustrated the different switching behaviors of reversible and irreversible changes of a system of single domain particles. The switching field for irreversible changes increases monotonically with angle, while the intrinsic coercivity (reversible and irreversible changes) goes through a well-defined maximum with angle.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The coercivity of a system of single domain particles with randomly oriented easy axes and a distribution of particle size

The magnetization curve at 77 K for uniaxial cobalt particles with easy axes randomly oriented is shown to be in agreement with a theoretical curve calculated for a particle size distribution with a median diameter Dv= 63 Å, σ = 0.3 and anisotropy constant K = 2.8 × 106 erg cm-3. The values are consistent with magnetic measurements at 300 K and microscopy data.

A method for calculating hysteresis loops of interacting single-domain particle systems in a nonmagnetic binder

A method is given for calculating the minor and full hysteresis loops of a system of uniaxial single-domain particles with a common direction of easiest magnetization. A probabilistic approach is used in formulating the problem by means of two differential equations which are solved for the simple case of an infinite particle chain. The method is based on a model in which each particle is characterized by a rectangular hysteresis loop with a specific saturation field H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</inf> , and the loops are influenced by the (homogeneous) external magnetic field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> as well by the magnetization-dependent interaction of the particles among themselves.