Equilibrium magnetic properties of dipolar interacting ferromagnetic nanoparticles

We use Monte Carlo simulations to study the influence of dipolar interaction on the equilibrium magnetic properties of monodisperse single-domain ferromagnetic nanoparticles. Low field magnetizations simulated in zero field cooling (ZFC)/field cooling (FC) procedures and field-dependent magnetization curves above the blocking temperatures show strong dependence on the concentration and the spatial arrangement (cubic or random) of the magnetic particles. The field-dependent magnetizations can not be simply described by the T^* model at relative low temperatures due to the interplay between anisotropy and dipolar interactions, as well as the spatial arrangement effect.     

Simulating magnetic nanoparticle behavior in low-field MRI under transverse rotating fields and imposed fluid flow

In the presence of alternating-sinusoidal or rotating magnetic fields, magnetic nanoparticles will act to realign their magnetic moment with the applied magnetic field. The realignment is characterized by the nanoparticle's time constant, τ. As the magnetic field frequency is increased, the nanoparticle's magnetic moment lags the applied magnetic field at a constant angle for a given frequency, Ω, in rad s⁻¹. Associated with this misalignment is a power dissipation that increases the bulk magnetic fluid's temperature which has been utilized as a method of magnetic nanoparticle hyperthermia, particularly suited for cancer in low-perfusion tissue (e.g., breast) where temperature increases of between 4 and 7 °C above the ambient in vivo temperature cause tumor hyperthermia. This work examines the rise in the magnetic fluid's temperature in the MRI environment which is characterized by a large DC field, B₀. Theoretical analysis and simulation is used to predict the effect of both alternating-sinusoidal and rotating magnetic fields transverse to B₀. Results are presented for the expected temperature increase in small tumors ( radius) over an appropriate range of magnetic fluid concentrations (0.002-0.01 solid volume fraction) and nanoparticle radii (1-10 nm). The results indicate that significant heating can take place, even in low-field MRI systems where magnetic fluid saturation is not significant, with careful the goal of this work is to examine, by means of analysis and simulation, the concept of interactive fluid magnetization using the dynamic behavior of superparamagnetic iron oxide nanoparticle suspensions in the MRI environment. In addition to the usual magnetic fields associated with MRI, a rotating magnetic field is applied transverse to the main B₀ field of the MRI. Additional or modified magnetic fields have been previously proposed for hyperthermia and targeted drug delivery within MRI. Analytical predictions and numerical simulations of the transverse rotating magnetic field in the presence of B₀ are investigated to demonstrate the effect of Ω, the rotating field frequency, and the magnetic field amplitude on the fluid suspension magnetization. The transverse magnetization due to the rotating transverse field shows strong dependence on the characteristic time constant of the fluid suspension, τ. The analysis shows that as the rotating field frequency increases so that Ωτ approaches unity, the transverse fluid magnetization vector is significantly non-aligned with the applied rotating field and the magnetization's magnitude is a strong function of the field frequency. In this frequency range, the fluid's transverse magnetization is controlled by the applied field which is determined by the operator. The phenomenon, which is due to the physical rotation of the magnetic nanoparticles in the suspension, is demonstrated analytically when the nanoparticles are present in high concentrations (1-3% solid volume fractions) more typical of hyperthermia rather than in clinical imaging applications, and in low MRI field strengths (such as open MRI systems), where the magnetic nanoparticles are not magnetically saturated. The effect of imposed Poiseuille flow in a planar channel geometry and changing nanoparticle concentration is examined. The work represents the first known attempt to analyze the dynamic behavior of magnetic nanoparticles in the MRI environment including the effects of the magnetic nanoparticle spin-velocity. It is shown that the magnitude of the transverse magnetization is a strong function of the rotating transverse field frequency. Interactive fluid magnetization effects are predicted due to non-uniform fluid magnetization in planar Poiseuille flow with high nanoparticle concentrations.     

Non-equilibrium effects in the magnetic behavior of Co3O4 nanoparticles

We report detailed studies of the non-equilibrium magnetic behavior of antiferromagnetic Co₃O₄ nanoparticles. The temperature and field dependence of magnetization, wait time dependence of magnetic relaxation (aging), memory effects, and temperature dependence of specific heat have been investigated to understand the magnetic behavior of these particles. We find that the system shows some features that are characteristic of nanoparticle magnetism such as bifurcation of field-cooled (FC) and zero-field-cooled (ZFC) susceptibilities and a slow relaxation of magnetization. However, strangely, the temperature at which the ZFC magnetization peaks coincides with the bifurcation temperature and does not shift on application of magnetic fields up to 1 kOe, unlike most other nanoparticle systems. Aging effects in these particles are negligible in both FC and ZFC protocols, and memory effects are present only in the FC protocol. We show that Co₃O₄ nanoparticles constitute a unique antiferromagnetic system which enters into a blocked state above the average Néel temperature.     

Particle size effect on phase and magnetic properties of polymer-coated magnetic nanoparticles

Polymer-coated magnetic nanoparticles are hi-tech materials with ample applications in the field of biomedicine for the treatment of cancer and targeted drug delivery. In this study, magnetic nanoparticles were synthesized by chemical reduction of FeCl₂ solution with sodium borohydride and coated with amine-terminated polyethylene glycol (aPEG). By varying the concentration of the reactants, the particle size and the crystallinity of the particles were varied. The particle size was found to increase from 6 to 20 nm and the structure becomes amorphous-like with increase in the molar concentration of the reactant. The magnetization at 1 T field (M_1T) for all samples is > 45 emu/g while the coercivity is in the range of 100-350 Oe. When the ethanol-suspended particles are subjected to an alternating magnetic field of 4 Oe at 500 kHz, the temperature is increased to a maximum normalized temperature (3.8 °C/mg) with decreasing particle size.     

Investigations of magnetic and dielectric properties of cupric oxide nanoparticles

Cupric oxide nanoparticles of ∼8-10 nm width and 40-45 nm length self assembled as large particles ∼1-1.5 μm have been investigated, in the 10-325 K temperature range, using magnetic and dielectric measurements. In magnetic measurements a single broad peak at ∼230 K in a zero field cooled sample has been observed. Coercivity, in magnetization measurements at 10 K, suggests that the nanoparticles are core-shell type particles with an antiferromagnetic core and a ferromagnetic shell. Dielectric measurements, at various frequencies from 3.7 Hz to 949 kHz, exhibit a sharp peak at 284 K followed by weak anomalies around 213 and 230 K.     

Magnetization reversal of ferromagnetic nanoparticles under inhomogeneous magnetic field

We investigated remagnetization processes in ferromagnetic nanoparticles under inhomogeneous magnetic field induced by the tip of magnetic force microscope (MFM) in both theoretical and empirical ways. Systematic MFM observations were carried out on arrays of submicron-sized elliptical ferromagnetic particles of Co and FeCr with different sizes and periods. It clearly reveals the distribution of remanent magnetization and processes of local remagnetization of individual ferromagnetic particles. Modeling of remagnetization processes in ferromagnetic nanoparticles under magnetic field induced by MFM probe was performed on the base of Landau–Lifshitz–Gilbert equation for magnetization. MFM-induced inhomogeneous magnetic field is very effective to control the magnetic state of individual ferromagnetic nanoparticles as well as to create different distribution of magnetic field in array of ferromagnetic nanoparticles.     

Investigation of micromagnetism and magnetic reversal of Ni nanoparticles using a magnetic force microscope

Isolated Ni nanoparticles were studied in situ by atomic and magnetic force microscopy in the presence of an additional external field up to 300 Oe. By comparing topographic and magnetic images, and also by computer modeling of magnetic images, it was established that particles smaller than 100 nm are single-domain and easily undergo magnetic reversal in the direction of the applied external magnetic field. For large magnetic particles, the external magnetic field enhances the magnetization uniformity and the direction of total magnetization of these particles is determined by their shape anisotropy. Characteristics of the magnetic images and magnetic reversal of particles larger than 150 nm are attributed to the formation of a vortex magnetization structure in these particles. Fiz. Tverd. Tela (St. Petersburg) 40, 1277–1283 (July 1998)     

Numerical micromagnetics of interacting superparamagnetic nanoparticles assembled in clusters with different dimensionalities

We analyze here the equilibrium magnetization state of densely packed interacting superparamagnetic nanoparticles assembled in clusters of various sizes and dimensionalities by comparison with the non-interacting case. We demonstrate that the average magnetization of individual particles is strongly increased in linear chains aligned parallel with the external magnetic field. Two-dimensional (2D) distributions of superparamagnetic nanoparticles present weaker increases of their average magnetization with respect to the non-interacting approximation whereas volume distributions (3D) are almost equivalent with the non-interacting case. A large number of nanoparticles densely packed in 2D superparamagnetic clusters present almost the same magnetic moment as infinite superparamagnetic chains. The effect of mutual interactions on the total magnetic moment of 3D surfaces (spheroids with various aspect ratios) uniformly covered with densely packed monolayers of superparamagnetic nanoparticles is also investigated.     

Monte Carlo calculation of the magnetization behavior and the magnetocaloric effect of interacting particles

The magnetization behavior and the magnetic entropy change of a system made up of ferromagnetically interacting particles are calculated by using Monte Carlo simulation. The effect of the magnetic anisotropy of particles and the dipolar–dipolar interaction between particles on the magnetization and the magnetic entropy change of the system are discussed. It is found that there is no spontaneous magnetization, both the magnetic anisotropy of particles and the dipolar–dipolar interaction between particles restrains the system's magnetizing in the external magnetic field. The magnetic entropy change decreases with the increase in temperature in the system without the dipolar–dipolar interaction; however, the dipolar–dipolar interaction between particles makes the magnetic entropy change of the system have maximum value at low temperatures.     

Viscous effects on nanoparticle magnetization harmonics

Dynamic magnetization of nanoparticles is a promising means of functional biosensing. We demonstrate a method for rapid monitoring of relative changes in the viscous environment of superparamagnetic nanoparticles using a ratio of magnetization harmonics. Initial results are capable of detecting changes in viscosity on the order of 0.05 cP. This technique should allow for real-time monitoring of many of the dynamic magnetization applications which have been proposed using AC susceptibility. Further, incorporation of this technique into a harmonic-based imaging system like magnetic particle imaging would allow for in vivo functional imaging capabilities.     

Magnetic properties of the bond and crystal field dilution Blume-Emery-Griffiths model in the presence of magnetic field

The magnetic properties of the spin-1 bond and crystal field dilution Blume-Emery-Griffiths (BEG) model in the presence of magnetic field are investigated on a simple cubic lattice by using effective field theory (EFT). In the M-H plane, the common action of bond and crystal field dilution leads to the exhibition of an irregular initial magnetization curve and slows down the magnetization process. The peak of the susceptibility curve has an explicit decline and shows a distinct shift toward the direction of increase of magnetic field. On the other hand, in the M-T plane, the magnetization curves show a discontinuity and a vertical leap in the small range of magnetic field when the negative crystal field is larger and the ratio of biquadratic and exchange interaction is positive (α>0). These results have not been revealed in previous works.     

Low-temperature first-order reversal curves and interaction effects on assemblies of iron oxide nanoparticles

We present the synthesis and magnetic properties of high quality uncoated and gold-coated iron oxide magnetic nanoparticles. The structural properties of these nanoparticles are investigated by transmission electron microscopy, UV-visible spectroscopy and X-ray diffraction. Experimental results and theoretical simulations indicate that the synthesized nanoparticles present a very good monodispersity, and well defined size and shape. The coercive field of these particles is identified by low-temperature first-order reversal curves and the results used in order to fit zero-field-cooled magnetization processes with theoretical models. The identification of the parameters in this analysis suggests that the coating process hardly affects the morphology and the overall magnetic properties of the cores inside coated particles.     

Monte Carlo simulation of magnetic multi-core nanoparticles

In this paper, a Monte Carlo simulation is carried out to evaluate the equilibrium magnetization of magnetic multi-core nanoparticles in a liquid and subjected to a static magnetic field. The particles contain a magnetic multi-core consisting of a cluster of magnetic single-domains of magnetite. We show that the magnetization of multi-core nanoparticles cannot be fully described by a Langevin model. Inter-domain dipolar interactions and domain magnetic anisotropy contribute to decrease the magnetization of the particles, whereas the single-domain size distribution yields an increase in magnetization. Also, we show that the interactions affect the effective magnetic moment of the multi-core nanoparticles.     

Size distribution effect on the magnetization and magneto-resistance in ferromagnetic nanostructured manganites

We present experimental data of magnetization and magneto-resistance of nanostructured La_2/3B_1/3MnO₃ with B=Ca, Sr, which present difference between the coercive field in the magnetization loop with their corresponding maximum value in the magneto-resistance. This difference is described by a model that include, size distribution of magnetic particles, randomly oriented anisotropy axis and electronic transfer between the particles, which is mediated by spin-polarized tunneling process. Also, the model predicts that the maximum magneto-resistance can be, in the magnetic disorder state, two times larger than the experimental value. The model results can be used to estimate the size dispersion of nanoparticles in similar systems.     

Temperature-dependent magnetic anomalies of CuO nanoparticles

Copper oxide (CuO) nanoparticles with an average size of 25 nm were prepared by a sol-gel method. A detailed study was made of the magnetization of CuO nanoparticles using a maximum field of 60 kOe for temperatures between 8 and 300 K. Antiferromagnetic CuO nanoparticles exhibit anomalous magnetic properties, such as enhanced coercivity and magnetic moments. Significantly, the magnitude of the hysteresis component tends to weaken upon increase in temperature (>8 K). In addition, a hysteresis loop shift and coercivity enhancement are observed at 8 K in the field-cooled (FC, at 50 kOe) case. It is thought that the change in hysteresis behavior is due to the uncompensated surface spins of the CuO nanoparticles. The susceptibility (χ) plot showed that χ varied substantially at temperatures below 12 K, and this transition is due to the exchange interactions between the neighboring atoms at the nanoscale.     

Experimental determination of ultra-sharp stray field distribution from a magnetic vortex core structure

The fine magnetic stray field from a vortex structure of micron-sized permalloy (Ni₈₀Fe₂₀) elements has been studied by high-resolution magnetic force microscopy. By systematically studying the width of the stray field gradient distribution at different tip-to-sample distances, we show that the half-width at half-maximum (HWHM) of the signal from vortex core can be as narrow as ∼21 nm at a closest tip-to-sample distance of 23 nm, even including the convolution effect of the finite size of the magnetic tip. a weak circular reverse component is found around the center of the magnetic vortex in the measured magnetic force microscope (MFM) signals, which can be attributed to the reverse magnetization around the vortex core. Successive micromagnetic and MFM imaging simulations show good agreements with our experimental results on the width of the stray field distribution.     

In situ hybridization to chitosan/magnetite nanocomposite induced by the magnetic field

Chitosan/magnetite nanocomposite was synthesized induced by magnetic field via in situ hybridization in ambient condition. Results of XRD patterns and TEM micrographs indicated that magnetite particles with 10–20 nm were dispersed in chitosan homogeneously. An interesting result is that magnetite nanoparticles were assembled to form chain-like structures under the influence of the external magnetic field, which mimics the magnetite chains inside of magnetotatic bacteria. The saturated magnetization (Ms) of nano-magnetite in chitosan was 50.54 emu/g, which is as high as 54% of bulk magnetite. The remanence (Mr) and coercivity (Hc) were 4 emu/g and14.8 Oe, respectively, which indicated that magnetite nanoparticles were superparamagnetic. The key of route is that a pre-precipitated chitosan hydrogel membrane, used as chemical reactor, which controlled the precipitation of chitosan precipitation and in situ transformation of magnetite from the precursor simultaneously in the magnetic field environment.     

Magnetic properties in BaFe12O19 nanoparticles prepared under a magnetic field

It was observed that the nanocrystallites of BaFe₁₂O₁₉ formed at 140°C under a 0.25 T magnetic field exhibited a higher saturation magnetization (6.1 emu/g at room temperature) than that of the sample (1.1 emu/g) obtained under zero magnetic field. Both of the two approaches yielded plain-like particles with an average particle size of 12 nm. However, the Curie temperature (T_c), a direct measuring of the strength of superexchange interaction of Fe³⁺–O²⁻–Fe³⁺, increased from 410°C for the nanoparticles prepared without an external field applied to 452°C for the particles formed under a 0.25 T magnetic field, which indicates that external magnetic fields can improve the occupancy of magnetic ions and then increase the superexchange interaction. This was confirmed by electron paramagnetic resonance and Mössbauer spectrum analysis. The results present in this paper suggest that in addition to oxygen defects, surface non-magnetic layer and a fraction of finer particles in the superparamagnetic range, cation vacancies should be responsible for the decreasing of saturation magnetization in magnetic nanoparticles.     

Study on magnetization reversal of cobalt nanowire arrays by magnetic force microscopy

The magnetic properties of self-assembly cobalt nanowire arrays formed in anodic porous alumina template were investigated by nanosize imaging method and macroscopic magnetic measurement. We have successfully made a wire-by-wire observation of magnetization reversal of a cobalt nanowire array using magnetic force microscopy with a home-made FePt tip. The nanowires in this medium have uniaxial anisotropy with easy axis along the wire due to the large aspect ratio of the wires (30 nm in diameter and 300 nm in length). Considering the nanowires as single-domain structures, we can obtain the average DC demagnetization curve from nanosize images by calculating the number of wires in each magnetized direction, and the results agreed well with the DC demagnetization curve measured by macroscopic measurement. The magnetostatic field between wires was evaluated by a new nanosize imaging method. Macroscopic measurement shows that reversible magnetization occurs in this medium. Nanosize images of the remanent and saturated states prove that the reversible magnetization processes mainly take place inside individual wires and reversed wires induced by magnetostatic field just give a little contribution to the reversible magnetization.     

Temperature behavior of the antiferromagnetic susceptibility of nanoferrihydrite from the measurements of the magnetization curves in fields of up to 250 kOe

The cross-breeding problem of the temperature dependence of the antiferromagnetic susceptibility of ferrihydrite nanoparticles is considered. Iron ions Fe3+ in ferrihydrite are ordered antiferromagnetically; however, the existence of defects on the surface and in the bulk of nanoparticles induces a noncompensated magnetic moment that leads to a typical superparamagnetic behavior of ensemble of the nanoparticles with a characteristic blocking temperature. In an unblocked state, magnetization curves of such objects are described as a superposition of the Langevin function and the linear-in-field contribution of the antiferromagnetic “core” of the nanoparticles. According to many studies of the magnetization curves performed on ferrihydrite (and related ferritin) nanoparticles in fields to 60 kOe, dependence χ_AF(T) decreases as temperature increases, which was related before to the superantiferromagnetism effect. As the magnetic field range increases to 250 kOe, the values of χ_AF obtained from an analysis of the magnetization curves become lower in magnitude; however, the character of the temperature evolution of χ_AF is changed: now, dependence χ_AF(T) is an increasing function. The latter is typical for a system of AF particles with random orientation of the crystallographic axes. To correctly determine the antiferromagnetic susceptibility of AF nanoparticles (at least, ferrihydrite) and to search for effects related to the superantiferromagnetism effect, it is necessary to use in experiments the range of magnetic field significantly higher than that the standard value 60 kOe used in most experiments. The study of the temperature evolution of the magnetization curves shows that the observed crossover is due to the existence of small magnetic moments in the samples.