Two-dimensional small particles coupled by dipolar interactions

We study the effect of the dipolar coupling on the magnetic properties of two small interacting ferromagnetic particles. Each particle is a two-dimensional array of Ising spins with a central spin surrounded by a variable number of shells. The coupling between spins inside each particle is ferromagnetic and the dipolar interaction between the particles is determined as a function of the number of shells, temperature, and distance between their centers. We investigate the system by mean-field approximation and Monte Carlo simulations. The dipolar interaction is calculated in two ways, one assuming effective spins in the centers of the particles, and the other directly computing the interactions among all the pairs of spins, one in each particle. We show that the difference in the corresponding dipolar energies is a power law on the distance with exponent 5. We calculate the magnetization and susceptibility as a function of temperature, number of shells and distance between the particles’ centers. We show that the critical temperature increases with the number of spins in each particle, and it is more noticeable in the mean-field calculations than in the Monte Carlo simulations.     

The role of dipolar interactions for the magnetic properties of ferromagnetic nanoring

We investigate numerically the effects of the dipolar interactions on magnetic properties in small ferromagnetic nanorings using a Monte Carlo technique. Our simulated results show that the strength of dipolar interaction in the magnetic nanoring has an important influence on the magnetization reversal processes and further the coercivity and the remanence. As the dipolar interaction increases, the transition of magnetization reversal processes from the onion-rotation state to the vortex state can occur, which results in an increase in coercivity and a decrease in remanence. On the other hand, it is found that the coercivity and the remanence depend more strongly on the strength of dipolar coupling for the relatively small size nanoring than for the large size nanoring in width. This can be attributed to the stable vortex state without core in smaller width nanoring in contrast to the metastable vortex state with core in larger width nanoring, induced by strong dipolar interactions. Additionally, the temperature dependence of coercivity and remanence in magnetic nanoring is also studied at a fixed dipolar interaction.     

From dipolar interactions of a random distribution of ferromagnetic particles to magnetostriction

The magnetostriction of a soft matrix, nonmagnetic, randomly filled by ferromagnetic particles is measured and calculated. Dipolar forces between particles have been calculated using a simple model of particles with the same permanent magnetic moment. Forces are injected in an FEM software to evaluate the strain of the composite. The longitudinal strain calculated for a cylinder-shape distribution is positive. A sample with the same shape has been prepared and shows the same strain.     

Effect of dipolar and exchange interactions on magnetic blocking of maghemite nanoparticles

Magnetic interparticle interactions compete with the magnetic blocking of ultrafine magnetic nanoparticles. We have prepared maghemite (γ-Fe₂O₃) nanoparticles by microwave plasma synthesis as a loose powder and in compacted form. In ZFC/FC measurements, blocking temperature of the compacted sample C is larger than that of the powder sample P. The frequency dependence of AC susceptibility of the sample C shows a large shift of blocking temperature with increasing frequency. Vogel-Fulcher law gives a large value of T₀ for the sample C. To get evidence of a possible spin-glass freezing in both samples, scaling law fitting is applied to the AC susceptibility data. The value of the exponent (zv) of the critical slowing down dynamics fits to the spin-glass regime for both samples. For the sample P, spin-glass freezing occurs on the surface of individual nanoparticles, while in the sample C surface spin-glass freezing is concomitant with a superspin-glass formation as a consequence of coupling between particles. The sample C also shows an enhancement of coercivity due to dipolar interactions among the nanoparticles. Exchange interactions are attributed only to touching nanoparticles across their interfaces. All these measurements indicate the presence of strong interparticle dipolar interactions in the compacted sample C.     

Magnetization curves of randomly oriented ferromagnetic single-domain nanoparticles with combined symmetry of magnetic anisotropy

The magnetization curves of randomly oriented nanoparticles with combined symmetry of magnetic anisotropy were studied. The composite mode of the Stoner–Wolfarth model has been used. In terms of this model each nanoparticle is characterized by random cubic crystalline magnetic anisotropy and by random uniaxial magnetic anisotropy. The series of simulated magnetization curves have been obtained. Each curve corresponds to different contributions of cubic and uniaxial magnetic anisotropy energy to the full energy of an individual nanoparticle k_u. Within this series we discuss the values of remnant magnetization, coercive force, both initial and maximal susceptibilities as the function of k_u. It is found that the magnetic properties are not monotonous functions of k_u. We discuss the possibility of comparing the calculated magnetization curves with the experimental curves in order to obtain new information on the magnetic constant.     

Experimental investigation of dipolar interaction in suspensions of magnetic nanoparticles

The structure and the magnetisation behaviour of two different systems of magnetic nanoparticles (MNP), namely Resovist^® with a wide core size distribution (diameter, σ=0.3) and SHP-20 with a rather narrow distribution (σ=0.1), were investigated by magnetorelaxometry (MRX) and magnetisation measurements in a wide concentration range. MRX on fluid and solid suspensions yielded the distribution of hydrodynamic diameters and effective magnetic anisotropy energies (E_A), where towards higher iron concentrations the spatial particle correlation, i.e. aggregation, and also the width of the E_A distribution were increased significantly. It was further found that these effects quantitatively depend on the suspension medium, where an increased salt concentration enhanced the aggregate size distribution and E_A dispersion. At mentioned higher MNP concentrations, the quasistatic magnetisation, normalised with respect to the iron content, decreased by up to 40%. In the case of SHP-20, where single core MNPs dominate, the maximum of this drop down of the magnetisation occurred at a field strength that corresponds to the strength of mean squared dipolar interaction.     

Dynamic simulations of the dipolar driven demagnetization process of magnetic multi-core nanoparticles

In this work, we investigate dynamically the dipolar driven demagnetization process of magnetic multi-core particles by solving the Landau-Lifshitz equation for single-domain particles distributed on a three-dimensional sphere. We analyze the relaxation time in respect to different geometry and material parameters. Further we show that the demagnetization times differ from the behaviour of a single magnetic sphere in the case of low damping. To explain these dynamics nanoparticular systems of different dimensions are investigated. We show that deviations can be attributed to a confinement of the relaxation dynamics to a lower dimensional submanifold of the k-space.     

Theoretical investigations of magnetic properties of ferromagnetic single-walled nanotubes

The magnetic behaviors of ferromagnetic single-walled nanotubes are systematically investigated by use of the many-body Green's function method of quantum statistical theory. The spontaneous magnetization, absolute value of ferromagnetic energy, area of hysteresis loop and coercivity increase with diameter of the tubes and spin quantum number, and decrease with temperature. Curie temperature increases with diameter and spin quantum number. As the diameter of the tube tends to infinity, all the numerical results approach to those of a two-dimensional monolayer. The dependences of initial susceptibility on temperature and diameter below and above Curie point are contrary. The calculated results are compared with experimental results where possible, and are qualitatively in agreement with the latter. The Curie temperature is determined by the tube diameter and independent of rolling helicities.     

Cluster analysis of an Ising-Preisach interacting particle system

The paper deals with the analysis of clusters' size in diverse magnetization states of a system of ferromagnetic particles organized in a perfect 2D array with all the anisotropy axes perpendicular to the plane (perpendicular medium) following the evolution of the clusters in correlation with various parameters like applied field or interaction strength. We present numerical simulations for a two-level Ising-type model each magnetic entity being characterized by a Stoner-Wohlfarth nonlinear energy barrier and a rectangular hysteresis loop (Ising-Preisach hysteron). In the simulations we took into account, the long-range inter-particle magnetostatic interactions in an attempt to mimic as accurately as possible with a still simple model, materials like Bit-Patterned media that are now considered as good candidates for the magnetic memories of the future.     

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.     

Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions

The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system apart from the typical Arrhenius relaxation to a Vogel-Fulcher-Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel-Fulcher-Tamann dynamical slowing down and the freezing mechanism.     

Reorientation phase transitions in planar arrays of dipolarly interacting ferromagnetic particles

Reorientation phase transitions (RPT) taking place in regular arrays of rectangular submicron-size ferromagnetic particles due to the competition between the external magnetic field of arbitrary direction and internal dipolar fields are analysed in this article. Dipolar interaction between particles is taken into account via real-space calculations of magnetometric demagnetizing factors. Long stripe arrays are also under consideration. I find that the direction of the external magnetic field determines the kind of the phase transition, while the dipolar interaction between particles can significantly change the values of RPT critical field. Calculations were presented for a set of submicron particles/stripe arrays, which were under experimental investigations recently.     

Interfacial roughness and temperature effects on exchange bias properties in coupled ferromagnetic/antiferromagnetic bilayers

Monte Carlo simulations have been used to study the relationship between the exchange bias properties and the interface roughness in coupled ferromagnetic/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. It is shown that the variation of the exchange bias field versus the AFM anisotropy strongly depends on the FM/AFM interface. Unlike the flat interface, a non-monotonic dependence is observed for the roughest FM/AFM interface. This is explained by canted magnetic configurations at the FM/AFM interface, which appear after the first reversal due to the magnetic frustration. The temperature dependence of the exchange field is also dependent on the roughness. While the exchange field is roughly constant for the flat interface, a decrease is observed for the roughest interface as the temperature increases. This has been interpreted as a significant decrease of the effective coupling between the FM and the AFM due to the disordering of the moments at the FM/AFM interface because of the combination of magnetic frustration and temperature activation.     

Visualization of residual anisotropic interactions in crosslinked natural rubbers by dipolar local field measurements and H natural abundance NMR spectroscopy

An extension of the exploitation of indirect observation of ¹H nuclei through ¹³C resonances is presented in the case of crosslinked elastomers. It is demonstrated that, by using this method in vulcanized elastomers above T_g a direct visualization of residual dipolar interactions on different functional groups as well as their dependence on motional constraints is available. It is also shown that ²H natural abundance NMR spectra of elastomers provide similar information on motional constraints by way of residual quadrupolar interactions.     

Surface modification of magnetic metal nanoparticles through irradiation graft polymerization

To tailor the interfacial interaction in magnetic metal nanoparticles filled polymer composites, the surfaces of iron, cobalt and nickel nanoparticles were grafted by irradiation polymerization. In the current report, effects of grafting conditions, including irradiation atmosphere, irradiation dose and monomer concentration, on the grafting reaction are presented. The interaction between the nanoparticles and the grafted polymer was studied by thermal analysis and X-ray photoelectron spectrometry. It was found that there is a strong interfacial interaction in the form of electrostatic bonding in the polymer-grafted nanoparticles. The dispersibility of the modified nanoparticles in chloroform was significantly improved due to the increased hydrophobicity.     

Clean TOCSY transfer through residual dipolar couplings

The transfer efficiency of cross-relaxation compensated (Clean) TOCSY sequences is analyzed for applications to residual dipolar couplings. Surprisingly most conventional Clean TOCSY sequences are very inefficient for dipolar transfer. It is shown theoretically, that this is a general property of all phase-alternating mixing sequences, i.e., for such sequences the suppression of cross-relaxation excludes dipolar transfer in the spin-diffusion limit. A new family of clean dipolar TOCSY sequences is derived which provides excellent transfer efficiencies for a broad range of offset frequencies.     

The influence of magnetic impurities in the vortex core dynamics in magnetic nano-disks

In this work we have used spin dynamics simulations to study the gyrotropic frequency behavior in nano-disks of Permalloy with magnetic impurities. We consider the effect of attractive impurity and repulsive impurity placed near the vortex core gyrotropic trajectory. We observed that the gyrotropic frequency is affected by the presence of impurity. The gyrotropic frequency shift depends on the relative position between the impurity and the vortex core gyrotropic trajectory and if impurity is attractive or repulsive. Our results agree with the analytical model and with experimental behavior for the gyrotropic frequency shown in the literature.     

Magnetic behavior of a nano-disk constrained in an antiferromagnetic substrate

In this work we report a numerical Monte Carlo study of the behavior of a magnetic nano-disk put over an antiferromagnetic substrate. Three approaches were considered for describe the substrate: (1) A stacked antiferromagnetic configuration, (2) an Ising like arrangement and (3) Heisenberg like spins. For the Heisenberg case we still have considered an easy-plane and an easy-axis symmetry of the substrate. The hysteresis loop for the nano-disk is obtained by considering the three cases. The signature of the vortex in the nano-disk appears as small jumps in the hysteresis curve. Exchange bias effects are observed since the substrate has an easy axis symmetry.     

Evolution of solid state systems containing mutually coupled dipolar and quadrupole spins: perturbation treatment

Perturbation approach to time evolution of multi-spin systems containing quadrupole and dipolar spins has been presented and discussed. The treatment comprises polarization transfer effects, field-dependent relaxation processes of dipolar as well as quadrupole spins and combined results of both of them. Complete theories dealing with various aspects of the spin dynamic processes have been proposed. Because of an educational character of this paper, relevant assumptions, limitations and even particular steps of the proposed treatments have been discussed in detail. Special emphasis is put on understanding of validity regimes of the perturbation treatment, depending on relative strengths of spin interactions and timescales of relevant motional processes affecting them. Motional regimes required for spins to be involved in essentially different evolution pathways like polarization transfers or relaxation have been illustrated by experimental examples.     

In vivo interactions of magnetic nanoparticles with the blood-brain barrier

Targeted drug delivery to the brain parenchyma, i.e., in brain tumor patients, by means of magnetically supported carrier delivery through the tight vascular endothelium of the blood-brain barrier is of critical biomedical importance. We were interested in delineating the first steps in successful brain drug delivery, which focuses on the interactions between magnetically guided yet freely blood circulating nanoparticles and the blood-brain barrier. We employed an in vivo model to quantitatively determine changes in cerebrovascular flow rate and volume during magnetically guided exposure of circulating nanoparticles.