Monodomain Particles Research Articles

Optimal Control of Magnetization Reversal in a Monodomain Particle by Means of Applied Magnetic Field.

A complete analytical solution to the optimal reversal of a macrospin with easy-axis anisotropy is presented. An optimal control path minimizing the energy cost of the reversal is identified and used to derive the time-dependent direction and amplitude of the optimal switching field. The minimum energy cost of the reversal scales inversely with the switching time for fast switching, follows exponential asymptotics for slow switching, and reaches the lower limit proportional to the energy barrier between the target states and to the damping parameter at infinitely long switching time. For a given switching time, the energy cost is never smaller than that for a free macrospin. This limitation can be bypassed by adding a hard anisotropy axis that activates the internal torque in the desired switching direction, thereby significantly reducing the energy cost. A comparison between the calculated optimal control path and minimum energy path reveals that optimal control does not translate to the minimization of the energy barrier but signifies effective use of the system's internal dynamics to aid the desired magnetic transition.

Stochastic Modelling of Thermal Effects on a Ferromagnetic Nano Particle

In this work, we are interested in the behaviour of a single ferromagnetic mono-domain particle submitted to an external field with a stochastic perturbation. This model is a step toward the mathematical understanding of thermal effects on ferromagnets. In a first part, we discuss modelling issues and propose several ways to integrate a random noise in the deterministic model. Then, among all these approaches, we focus on the more natural one and study its long time behaviour. We prove that the system converges to the unique stable equilibrium of the deterministic model and determine the $$L^p$$ rate of the convergence. Finally, we illustrate the theoretical results by numerical simulations.

Trajectory dependent particle response for anisotropic mono domain particles in magnetic particle imaging

In magnetic particle imaging, scanners use different spatial sampling techniques to cover the field of view (FOV). As spatial encoding is realized by a selective low field region (a field-free-point, or field-free-line), this region has to be moved through the FOV on specific sampling trajectories. To achieve these trajectories complex time dependent magnetic fields are necessary. Due to the superposition of the selection field and the homogeneous time dependent fields, particles at different spatial positions experience different field sequences. As a result, the dynamic behaviour of those particles can be strongly spatially dependent. So far, simulation studies that determined the trajectory quality have used the Langevin function to model the particle response. This however, neglects the dynamic relaxation of the particles, which is highly affected by magnetic anisotropy. More sophisticated models based on stochastic differential equations that include these effects were only used for one dimensional excitation. In this work, a model based on stochastic differential equations is applied to two-dimensional trajectory field sequences, and the effects of these field sequences on the particle response are investigated. The results show that the signal of anisotropic particles is not based on particle parameters such as size and shape alone, but is also determined by the field sequence that a particle ensemble experiences at its spatial position. It is concluded, that the particle parameters can be optimized in terms of the used trajectory.

Magnetic anisotropy and magnetization dynamics of Fe nanoparticles embedded in Cr and Ag matrices

Static and dynamical magnetic properties of Fe nanoparticles (NPs) embedded in non-magnetic (Ag) and antiferromagnetic (Cr) matrices with a volume filling fraction (VFF) of 10% have been investigated. In both Fe@Ag and Fe@Cr nanocomposites, the Fe NPs have a narrow size distribution, with a mean particle diameter around 2 nm. In both samples, the saturation magnetization reaches that of Fe bulk bcc, suggesting the absence of alloying with the matrices. The coercivity at 5 K is much larger in Fe@Cr than in Fe@Ag as a result of the strong interaction between the Fe NPs and the Cr matrix. Temperature-dependent magnetization and ac-susceptibility measurements point out further evidence of the enhanced interparticle interaction in the Fe@Cr system. While the behaviour of Fe@Ag indicates the presence of weakly interacting magnetic monodomain particles with a wide distribution of blocking temperatures, Fe@Cr behaves like a superspin glass produced by the magnetic interactions between NPs.

Dynamic single-domain particle model for magnetite particles with combined crystalline and shape anisotropy

The dynamical behaviour of superparamagnetic iron oxide nanoparticles (SPIONs) is not yet fully understood. In magnetic particle imaging (MPI) SPIONs are used to determine quantitative real-time medical images of a tracer material distribution. For reaching spatial resolution in the sub-millimetre range, MPI requires a well engineered instrumentation providing a magnetic field gradient exceeding 2 T m. However, as the particle performance strongly affects the sensitivity of the imaging process, optimization of the particle parameters is a crucial factor, which is not easy to address. Today most simulations of MPI use the Langevin model to describe the particle behaviour. In equilibrium, the model matches the measured data. If alternating fields in the mid kHz frequency range are applied, the dynamic behaviour of the particles differs from the Langevin theory due to anisotropy effects, particle–particle-interactions and/or exchange interaction in case of multi-core particles. In this paper a model based on previous work is introduced, which was adopted to include crystal and shape anisotropy of immobilised mono-domain single-core particles. The model is applied to typical MPI frequencies and field strengths with different possible superposition of the anisotropy effects, leading to differences in the particle response. It is shown that, despite comparatively high anisotropy constants, the magnetocrystalline anisotropy energy does not quench the signal response for MPI. The constructive superposition of shape and crystal anisotropy leads to the best performance in terms of sensitivity and resolution of the associated imaging modality and slightly reduces the energy barriers compared to a sole-shape anisotropy.

Dense and half-dense NiZnCo ferrite ceramics: Their respective relevance for antenna downsizing, according to their dielectric and magnetic properties at microwave frequencies

Spinel ferrite Ni0.5Zn0.3Co0.2Fe1.98O4−x nanoparticles were synthesized by co-precipitation method, and samples were realized by moulding and annealing at key temperatures (TM = 800 °C, 900 °C, 1050 °C, determined beforehand through shrinkage measurements) going with calcining and sintering processes. Annealing at 800 °C and 900 °C led to half-dense ceramics (porosity ∼50 vol. %), whereas bulky ferrite was obtained after annealing at 1050 °C. Elemental analysis, X-ray diffraction and ion chromatography analysis were performed. Complex dielectric permittivity (ε*) and magnetic permeability (μ*) were investigated up to 6 GHz. With increasing TM, a decreasing amount of Fe2+ was observed, going with increasing sample density. Coupled effects of the Fe2+ concentration and of the porosity, both on dielectric and magnetic properties, were chiefly investigated and discussed. The materials show almost constant permittivities (ε′ = 5.0, 6.0, and 14.8 for TM = 800 °C, 900 °C and 1050 °C, respectively). The bulk value at f = 1 GHz (ε′ = 14.8) can be interpreted well according to Shannon's theory. The permittivities of the half-dense ceramics are discussed on the basis of Bruggeman's Effective Medium Theory. The materials annealed at 800 °C and 900 °C show almost constant magnetic permeabilities in the frequency range from 0.2 to 1 GHz (μ′ = 3.4 and 6.0 for TM = 800 °C and 900 °C). The observed permeability behavior is typical of monodomain particles, except for the sample annealed at 1050 °C, for which domain wall contribution to μ* is suspected because of non-negligible losses at low frequency (μ″ = 1.3–1.8 at f < 0.3 GHz). This finding is supported by estimations of the upper and lower values for the critical grain size, on the basis of Brown–Van der Zaag's theory. Facing bulk ceramics, and in view of using Ni0.5Zn0.3Co0.2Fe1.98O4−x ferrite as substrate for antenna miniaturization, the electromagnetic properties of half-dense ceramics materials seem to be very competitive at frequencies beyond 0.2 GHz, and up to 0.7–0.8 GHz.

Long time behaviour of a stochastic nanoparticle

In this article, we are interested in the behaviour of a single ferromagnetic mono-domain particle submitted to an external field with a stochastic perturbation. This model is the first step toward the mathematical understanding of thermal effects on a ferromagnet. In a first part, we present the stochastic model and prove that the associated stochastic differential equation is well defined. The second part is dedicated to the study of the long time behaviour of the magnetic moment and in the third part we prove that the stochastic perturbation induces a non-reversibility phenomenon. Last, we illustrate these results through numerical simulations of our stochastic model.The main results presented in this article are on the one hand the rate of convergence of the magnetization toward the unique stable equilibrium of the deterministic model and on the other hand a sharp estimate of the hysteresis phenomenon induced by the stochastic perturbation (remember that with no perturbation, the magnetic moment remains constant).

Magnetism of powder samples and of single crystals

The temperature dependence of the magnetic order parameter of NiF2, MnCO3 and K2NiF4 measured on powder samples is compared with data obtained on single crystals. It is found that the dynamic dimensionality of the NiF2 and MnCO3 powder samples is one-dimensional (1D) for all temperatures T<TN. This shows that the powder grains are mono-domain particles. In the multi-domain single crystals isotropic 3D dynamic symmetry is observed. In order to explain isotropy in the bulk single crystals a dynamic averaging process over all domain orientations has to be postulated. For single crystal material of K2NiF4 a critical exponent of β=0.14±0.01 has been reported. Our neutron diffraction measurements on powder material yield to a very good approximation mean field critical behaviour indicating isotropic dynamics in the critical range. This unexpected result points to a dynamic averaging process over all differently oriented powder grains. As we have argued earlier, the observed universality in the dynamics of ordered magnets is due to a boson guiding field. Averaging over all powder grains, requests that the mean free path of the field bosons is larger than the size of the grains. Additionally, it must be assumed that the field quanta are able to tunnel across the interface between adjacent grains. In polycrystalline bulk samples of the 2D ferromagnet Rb2CrCl4 and of the 1D antiferromagnet KCuF3 also mean field critical behaviour is identified. As a consequence, a similar averaging process as in the K2NiF4 powder sample can be assumed to average over the mosaic structure of polycrystalline bulk material of Rb2CrCl4 and KCuF3. High quality single crystals of Rb2CrCl4 and of KCuF3 exhibit critical exponent of β~0.3. Dependence of the critical exponents on the mesoscopic morphology of the sample is considered as a typical indication of a boson controlled dynamics, and may partly explain the surprisingly broad distribution of critical exponent values reported in literature.

Folic acid conjugated magnetic drug delivery system for controlled release of doxorubicin

Targeting tumors by means of their vascular endothelium is a promising strategy, which utilizes targets that are easily accessible, stable, and do not develop resistance against therapeutic agents. Folate receptor is a highly specific tumor marker, frequently over expressed in cancer tumors. In the present study, an active drug delivery system, which can effectively target cancer cells by means of folate receptor-mediated endocytosis, have ability to escape from opsonization and capability of magnetic targeting to withstand the drag force of the body fluid have been designed and synthesized. The core of the drug delivery system is of mono-domain magnetic particles of magnetite. Magnetite nanoparticles are shielded with PEG, which prevents their phagocytosis by reticuloendothelial system. These PEG shielded magnetite nanoparticles are further decorated with an antitumor receptor—folic acid and loaded with an antineoplastic agent doxorubicin. An in vitro drug loading and release kinetics study reveals that the drug delivery system can take 52 % of drug load and can release doxorubicin over a sustained period of 7 days. The control and sustained release over a period of several days may find its practical utilities in chemotherapy where frequent dosing is not possible.

Study of Heating Efficiency as a Function of Concentration, Size, and Applied Field in γ-Fe2O3 Nanoparticles

The specific absorption rate (SAR) of γ-Fe2O3 nanoparticles (NPs) under an alternating magnetic field has been investigated as a function of size, concentration, coating, liquid carrier, and frequency and amplitude of the applied magnetic field. The NPs have been synthesized by coprecipitation method with sizes ranging from 6 to 14 nm with low polydispersity (0.2) and high crystallinity degrees. The small NPs size (6–14 nm) and the value of the maximum applied field (<7.5 kA/m) allow the use of the linear response theory for the analysis of the experimental SARs values. Under this condition, Neel–Brown relaxation times of about 10–7 s are obtained from SAR field frequency dependence. The NPs have been immobilized in agar to investigate the heating mechanisms, i.e., inversion of the magnetic moments inside the monodomain volume or particle rotation. The results suggest that there is a critical size of around 12 nm for obtaining the most effective heating in viscous media. Furthermore, the surface modification by aminopropylsilane coating does not affect the heating efficiency, making these NPs good candidates for hyperthermia treatment as well as model samples for standardization of hyperthermia apparatus.

A method for determining a uniaxial magnetic anisotropy constant of monodomain particles of powdered permanent magnets

A method for determining the uniaxial magnetic anisotropy constant of monodomain particles of powdered permanent magnets is based on the Mossbauer spectroscopy. The method is experimentally verified on a powdered permanent magnet made of barium ferrite BaFe12O19.

Micro-magnetic simulation study on the magnetic particle imaging performance of anisotropic mono-domain particles

The performance of magnetic mono-domain particles is of crucial importance in magnetic particle imaging (MPI). So far, the behavior of mono-domain particles has been modeled within the framework of Langevin theory. This theory predicts the dependence of the MPI signal on the particle core size, but cannot account for the influence of the shape, i.e. the anisotropy of the particle core. In this study we present the first micro-magnetic ab initio simulation of spectra of anisotropic particles with different core diameters in an oscillating magnetic field at 25 and 100 kHz. We find that the MPI signal strongly depends on the anisotropy of the magnetic core. Thus, a difference of 3 nm between the principal axes of a prolate ellipsoid with the volume of a 30 nm sphere can result in a complete loss of the MPI signal. Smaller anisotropies, however, can increase the MPI performance of the particle. The simulations show that the effect of the anisotropy on the MPI signal depends on the frequency of the oscillating magnetic field. At 100 kHz, the optimal signal is found at smaller anisotropies than at 25 kHz. Furthermore, the simulations show that experimental spectroscopic results for Resovist® can only be explained quantitatively by particles with a magnetic core size of at least 25 nm.

Magnetic Properties of TbAl2 Nanometric Alloys

The magnetic properties of nanometric TbAI2 alloys have been investigated. The Curie temperature (T(c)) of these nanometric alloys is strongly size dependent and decreases from 103 K for the bulk alloy down to 98 K for the 14 nm alloy, as the particle volume is reduced. This reduction of T(c) has been explained by a finite-size scaling law of type [T(c)(D) -T(c)(infinity)]/T(c)(infinity) = -(D/D0)-(1/vp), with v = 0.7 and D0 = 2.2a (a, the lattice parameter), in agreement with the three-dimensional Heisenberg model. The size dependence of the coercivity has also been established. An increase of the coercivity from 0.08 kOe (bulk) to 1 kOe for 10 h milled alloy, indicates the crossover from multidomain to single domain behavior around 85 nm, as expected from the estimate of the critical size of monodomain particles. The field dependence of the magnetization indicates a faster thermal reduction of the magnetization of the nanosized alloys (17% in 300 h milled alloy with mean particle size of 14 nm) related to the bulk (3%), in the temperature range between 5 K and 30 K. The results can be explained as a direct consequence of the competing effects of the surface and the purely finite-size effects, in an ensemble of nanometric particles suffering interactions.

Preparation and characterisation of magnetically ordered columnar structures of barium ferrite particles

In this study, we report on the columnar structures of barium ferrite particles that were prepared from water suspensions by applying a magnetic field during drying. Commercial barium ferrite (BaFe12O19) monodomain particles were used, and the surfaces of the particles were treated with an organic surfactant to reduce their agglomeration. The columnar structures were obtained by drying the water suspensions of BaFe12O19 particles on Al2O3 substrates under an applied magnetic field of 1 T. After the degradation of the organic components, the samples were sintered at 1350°C. X-ray powder diffraction, scanning electron microscopy and magnetic measurements were used to characterise the samples. When the magnetic field was applied perpendicularly to the sample plane, the as-deposited sample exhibited a higher coercivity (H c = 5434 Oe) and a higher squareness ratio (SQR = 0.76) than the sintered sample (H c = 625 Oe, SQR = 0.58). However, the sintered sample showed a higher anisotropy of the magnetic behaviour than the as-deposited sample.

The influence of long range interparticle correlations on the magnetically induced optical anisotropy in magnetic colloids

In this paper we develop a theoretical model for the magnetically induced optical anisotropy in dense magnetic colloids made of spherical and un-aggregated magnetic monodomain nanoparticles. Both dipole–field and dipole–dipole magnetic and electric interactions between the magnetic monodomain particles are taken into account in the Hamiltonian of the system. Using the pair correlation function in a colloidal suspension of magnetic nanoparticles developed by Ivanov and Kuznetsova (2001) [11], the complex dielectric constant of a magnetic colloid is modeled as a function of the light polarization direction, the magnetic field intensity and magnetic particle concentration and diameter. The two main features of the model are that, on the one hand, it predicts the possibility of magnetically induced optical anisotropy in dense magnetic colloids made of spherical and un-aggregated monodomain nanoparticles, and on the other hand, unlike the existing models for diluted samples, it predicts a non-linear dependence of dichroism and birefringence on magnetic particle concentration.

10.1007/s11455-008-3021-3

A numerical model is proposed for simulating the magnetic properties of a system (N-cluster) comprising a finite number N of monodomain particles uniformly distributed over a spherical surface. The calculation algorithm is based on the Monte Carlo method. In the absence of an external magnetic field, the magnetic moment of any spherical N-cluster vanishes due to the formation of vortex structures, with a measure of vorticity offered by the toroid moment Q. The results of model calculations show that the value of Q in N-clusters with 4 < N < 20 amounts to about 80% of the maximum and is virtually independent of N, while exhibiting weak even-odd oscillations.

Magnetization reversal by a single pulse of magnetic field or spin-polarized current

One of the important requirements for spintronic devices concerns an efficient magnetization reversal, which may eventually lead to ultra-fast non-volatile magnetic memory applications. In particular, it is necessary to achieve stable sub-nanosecond switching times and to reduce magnetization “ringing”, so that the reversal will proceed along the shortest ballistic path connecting the initial and the target magnetization states. This paper is dedicated to the numerical simulations of a mono-domain ferromagnetic particle, described by the Landau–Lifshitz–Gilbert equation. We study the general case of arbitrary orientation of the applied field/current pulses, constructing dynamic diagrams for the reversal time. We have found that even short 50 ps pulses, applied at a proper angle, will induce magnetization reversal with minimal ringing effects.

Thermodynamic properties of magneto-anisotropic nanoparticles

The purpose of this paper is to study the thermodynamic equilibrium properties of acollection of non-interacting three-dimensional (3D) magnetically anisotropic nanoparticlesin the light of classical statistical physics. Pertaining to the angular dependence (α) of the magnetic field with the anisotropy axis, energy landscape plots are obtained whichreveal a continuous transition from a double well to a single well for and show an asymmetric bistable shape for other values ofα. The present analysis is related to the interpretation of equilibrium magnetization andstatic susceptibility of a nanomagnetic system as a function of external magnetic field,B, andtemperature, T. The magnetization and susceptibility confirm the non-Langevin behaviour ofmagneto-anisotropic monodomain particles. The susceptibility analysis establishesthe ferromagnetic-, antiferromagnetic- and paramagnetic-like coupling for variousα. This study reveals the essential role of magneto-anisotropic energy in the interpretation ofthe magnetic behaviour of a collection of non-interacting single-domain nanoparticles.

Dipolar interactions and thermal stability of two-dimensional nanoparticle arrays

We show results of Monte Carlo simulations of an array of monodispersed magnetic monodomain particles, in a square lattice with dipolar interactions and perpendicular uniaxial anisotropy. We first show the equilibrium phase diagram of the system, which shows three phases, superparamagnetic (SP), out-of-plane antiferromagnetic and in-plane antiferromagnetic with a reorientation transition between the last two. We then employ a recently introduced time quantified Monte Carlo method to study the relaxation of autocorrelations of the particle array for different ratios of dipolar to anisotropy energies. In the non-interacting case we show that relaxation is exponential in time with characteristic times obeying a classic result by Brown. When dipolar interactions are switched on, the relaxation is very well described by stretched exponential forms in the whole time window and in both the SP and ordered phases. Relaxation times still obey a nearly Arrhenius behaviour, with a single effective energy barrier that decreases as the dipolar interaction increases, a result that must be interpreted within the dynamics protocol. No signs of glassy behaviour were found, in agreement with the absence of disorder in the model system.

Magnetic structure of a spherical cluster of monodomain particles

A numerical model is proposed for simulating the magnetic properties of a system (N-cluster) comprising a finite number N of monodomain particles uniformly distributed over a spherical surface. The calculation algorithm is based on the Monte Carlo method. In the absence of an external magnetic field, the magnetic moment of any spherical N-cluster vanishes due to the formation of vortex structures, with a measure of vorticity offered by the toroid moment Q. The results of model calculations show that the value of Q in N-clusters with 4 < N < 20 amounts to about 80% of the maximum and is virtually independent of N, while exhibiting weak even-odd oscillations.