Magnetic relaxation in a spin-1 Ising model near the second-order phase transition point

The magnetic relaxation of a spin-1 Ising model with bilinear and biquadratic interactions is formulated within the framework of statistical equilibrium theory and the thermodynamics of irreversible processes. Using a molecular-field expression for the magnetic Gibbs energy, the magnetic Gibbs energy produced in the irreversible process is calculated and time derivatives of the dipolar and quadrupolar order parameters are treated as fluxes conjugate to their appropriate generalized forces in the sense of Onsager theory. The kinetic equations are obtained by introducing kinetic coefficients that satisfy the Onsager relation. By solving these equations an expression is derived for the dynamic or complex magnetic susceptibility. From the real and imaginary parts of this expression, magnetic dispersion and absorption factor are calculated and analyzed near the second-order phase transition.     

Sedimentation equilibria of ferrofluids: I. Analytical centrifugation in ultrathin glass capillaries

Analytical centrifugation is used for the first time to measure sedimentation equilibrium concentration profiles of a ferrofluid, a concentrated colloidal dispersion of strongly absorbing magnetic nanoparticles. To keep the optical absorbance from becoming too strong, the optical path length is restricted to 50 μm by placing the dispersion in a flat glass capillary. The concentration profile is kept from becoming too steep, despite the relatively high buoyant mass of the nanoparticles, by making novel use of a low-velocity analytical centrifuge that was not designed to measure equilibrium profiles. The experimental approach is validated by comparison with profiles obtained using an analytical ultracentrifuge. At concentrations of a few hundred grams per liter, the osmotic pressures calculated from the equilibrium profiles are lower than expected for hard spheres or non-interacting particles, due to magnetic dipolar interactions. By following the presented experimental approach, it will now also be possible to characterize the interparticle interactions of other strongly absorbing colloidal particles not studied before by analytical centrifugation.     

A Diffusion Model of Field-Induced Aggregation in Ferrofluid Film

By introducing Arrhenius behaviour to the ferroparticles on the surface of the aggregated columnar structure in a diffusion model, equilibrium equations are set up. The solution of the equations shows that to keep the aggregated structures stable, a characteristic field is needed. The aggregation is enhanced by magnetic fields, yet suppressed as the temperature increases. Analysing the influence of the magnetic field on the interaction energy between the dipolar particles, we estimate the portion of the diffusing particles, and provide the agreeable ratio of the column radius over the centre-to-centre spacing between columns in a hexagonal columnar structure formed under a perpendicular magnetic field.     

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.     

One-dimensional assemblies of silica-coated cobalt nanoparticles: Magnetic pearl necklaces

Silica-coated cobalt nanoparticles were found to organize into chains when driven by a weak external magnetic field. Strong dipole–dipole magnetic interactions are believed to be the driving force of the self-organization once the cobalt nanoparticles undergo the superparamagnetic to ferromagnetic (SP–FM) transition, as increasing their size during the synthesis process. The method, although simple, produces structures resembling pearl necklace-like structures, comparable to one-dimensional species obtained in more laborious processes. Molecular dynamic simulations taking magnetic dipolar forces into account reproduce the observed self-assembled structures. The nanoscale engineering of this type of colloids is expected to extend the spectrum of magnetic effects and functionalities.     

Well-dispersed gold nanowire suspension for assembly application

A method for fabricating well-dispersed nanowire suspension has been demonstrated in the paper. Thin gold nanowires were prepared by template synthesis, and then functionalized with sulphonate group-terminated thiols before suspended in different solvents. The degree of aggregation of the obtained suspension was evaluated with transmission electron microscopy (TEM) and UV-vis spectroscopy. It was found that the degree of aggregation was predominated by the solvents, and the best degree of dispersion was obtained when isopropyl alcohol (IPA) was used as the solvent. The gold nanowires from the suspension can be selectively assembled onto chemically patterned substrates. This well-dispersed nanowire suspension is potentially useful for fabricating novel nanodevices.     

Monte Carlo simulation and optical transmission studies of lattice-tunable column arrays composed of ferrofluids

The aggregation and rearrangement of nanoparticles embedded in a thin cell of ferrofluid at various applied magnetic fields was studied by Monte Carlo simulation. Regular microcolumns with the axis parallel to the magnetic field were observed with column size and spacing depending on the ramp speed of the applied field. Our model successfully simulated the reported experimental results that the column size decreases as the ramp speed increases, which is attributed to the diminishing time to achieve the final assembled state at a given final magnetic field. Column arrays of tunable lattice constants characterizing various spectroscopic dispersions are elucidated. The hexagonal structure of the aggregation of magnetic nanoparticles and optical dispersion were observed through an optical microscope. The transmission diffraction spectra depending on column spacings and sizes of the column array are simulated to yield results comparable to the experiment.     

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.     

Thermal diffusivity of rhodamine 6G incorporated in silver nanofluid measured using mode-matched thermal lens technique

Dual beam mode-matched thermal lens method has been employed to measure the heat diffusion in nanofluid of silver with various volumes of rhodamine 6G, both dispersed in water. The important observation is an indication of temperature dependent diffusivity and that the overall heat diffusion is slower in the chemically prepared Ag sol compared to that of water. The experimental results can be explained assuming that Brownian motion is the main mechanism of heat transfer under the present experimental conditions. Light induced aggregation of the nanoparticles can also result in an anomalous diffusion behavior.     

The crossover from atomistic to continuous dynamic symmetry at the magnetic phase transition

It is suggested that the change from Curie-Weiss susceptibility to critical susceptibility has to be identified as crossover from atomistic to continuous dynamic symmetry. At this crossover the correlation length becomes of the order of the near neighbour distance. This enables dynamic percolation for lower temperatures and crossover to continuous symmetry. Continuous dynamic symmetry implies universality, i.e. a temperature dependence that is independent of the atomistic structures. This is in disagreement with the material specific magnon dispersion relations evaluated by inelastic neutron scattering. On the basis of these magnon dispersions the observed universality at the stable fixed point T=0 cannot be explained. Instead a linear dispersion has to be postulated for all magnets. According to Goldstone, Salam and Weinberg (GSW) the quasi particles of this linear dispersion are non-interacting and massless. No interaction between the quasi particles requests that they have no magnetic moment and, as a consequence, must be spin compensated, in a similar way as is known from the Cooper pairs of superconductivity. Observation by neutron scattering therefore is impossible. The magnetic specific heat provides, so far, the only indirect access to the hypothesized spin-less magnetic quasi particles. We investigate experimental data of the ferromagnet EuS as a simple model material.     

Tailoring optical properties of TiO2 nanowires coated with Ag nanoparticles by plasmon coupling of Ag nanoparticles

TiO₂ nanowires were grown on titanium foil by an alkali hydrothermal growth method. The as-synthesized nanowires are structurally uniform with diameters of 50-100 nm and lengths of up to a few micrometers. The as-prepared TiO₂ nanowires were coated with Ag nanoparticles by reducing AgNO₃ in solution. The experimental results indicate that the Ag nanoparticles can aggregate together on the surfaces of TiO₂ nanowires by interconnection between nanoparticles. The degree of aggregation of Ag nanostructures can be controlled by changing the concentrations of Ag nanoparticles. The as-prepared nanostructures exhibit a wide optical absorption from 387 to 580 nm that can be easily tuned by controlling the degree of aggregation of Ag nanostructures. The results reveal that optical properties of the Ag-coated TiO₂ nanowires can be enhanced by plasmon coupling of Ag nanoparticles. The as-prepared nanostructures may find potential applications in the field of solar cells.     

Tunable dipolar magnetism in high-spin molecular clusters

We report on the Fe17 high-spin molecular cluster and show that this system is an exemplification of nanostructured dipolar magnetism. Each Fe17 molecule, with spin S=35/2 and axial anisotropy as small as D approximately -0.02 K, is the magnetic unit that can be chemically arranged in different packing crystals while preserving both the spin ground state and anisotropy. For every configuration, molecular spins are correlated only by dipolar interactions. The ensuing interplay between dipolar energy and anisotropy gives rise to macroscopic behaviors ranging from superparamagnetism to long-range magnetic order at temperatures below 1 K.     

Theoretical simulations of magnetic nanotubes using Monte Carlo method

We present the results of the Monte Carlo simulations of magnetic nanotubes, which are based on the plane structures with the square unit cell at low temperatures. The spin configurations, thermal equilibrium magnetization, magnetic susceptibility and the specific heat are investigated for the nanotubes of different diameters, using armchair or zigzag edges. The dipolar interaction, Heisenberg model interaction and also their combination are considered for both ferromagnetic and anti-ferromagnetic cases. It turns out that the magnetic properties of the nanotubes strongly depend on the form of the rolling up (armchair or zigzag). The effect of dipolar interaction component strongly manifests itself for the small radius nanotubes, while for the larger radius nanotubes the Heisenberg interaction is always dominating. In the thermodynamic part, we have found that the specific heat is always smaller for the nanotubes with smaller radii.     

Magnetic properties of extremely bimodal magnetite suspensions

In this paper, we investigate the magnetic properties of aqueous suspensions of extremely bimodal magnetite particles, including micro- (size ∼1450 nm) and nano-(size ∼9 nm) units. It is found that the addition of increasing concentrations of small particles increases the saturation magnetization, the coercive field, and the low-field susceptibility. The results are explained considering that the nano-magnetite used has a moderately wide size distribution, that embraces both the range of superparamagnetism (the lowest size interval) and of finite coercivity, all being single domain. In addition, the formation of a cloud of small particles surrounding the larger ones favors the chain formation by dipolar magnetic aggregation. It is concluded that the admixture of even small amounts of nanoparticles offers an excellent tool for the control of the magnetic properties of magnetite suspensions.     

Mechanism of chain formation in nanofluid based MR fluids

Mechanism of structure formation in bidispersed colloids is important for its physical and optical properties. It is microscopically observed that the mechanism of chain formation in magnetic nanofluid based magnetorheological (MR) fluid is quite different from that in the conventional MR fluid. Under the application of magnetic field the magnetic nanoparticles are filled inside the structural microcavities formed due to the association of large magnetic particles, and some of the magnetic nanoparticles are attached at the end of the chains formed by the large particles. The dipolar energy of the large particles in a magnetic nanofluid matrix becomes effective magnetic permeability (μ_eff) times smaller than that of the neutral medium. Inclusion of magnetic nanoparticles (∼10 nm) with large magnetic particles (∼3-5 μm) restricts the aggregation of large particles, which causes the field induced phase separation in MR fluids. Hence, nanofluid based MR fluids are more stable than conventional MR fluids, which subsequently increase their application potentiality.     

A remark on an anomaly of the spin-wave spectrum in spiral spin structures

It is shown that magnetic dipolar interaction gives rise to a discontinuity in the magnon dispersion relation for antiferromagnetic spiral spin structures. Some numerical results for the magnon energy in dysprosium are presented.     

Quantitative real-space analysis of self-assembled structures of magnetic dipolar colloids

We present the first real-space analysis on a single-particle level of the dipolar chains and branched clusters self-assembling in magnetic fluids in zero field. Spatial correlations and chain-length distributions directly obtained from tracked particle positions in vitrified films of synthetic magnetic (Fe3O4) dispersions provide a quantitative test for simulations and theory of dipolar fluids. A pertinent example is the cluster-size distribution that can be analyzed with a one-dimensional aggregation model to yield a dipolar attraction energy that agrees well with the dipole moment found from independent magnetization measurements.     

Tunneling magnetoresistance in small dot arrays with perpendicular anisotropy

The tunneling magnetoresistance (TMR) of a small magnetic dot array with perpendicular anisotropy, is studied by using a resistor network model. Because of the competition between dipolar interaction and perpendicular anisotropy, the TMR ratio can be up to a maximum value (~26%) as predicted by a theoretical model. At moderate dipolar interaction strength, the perpendicular TMR ratio exhibits abrupt jumps due to the switching of magnetic moments in the array when the applied field (normal to the array plane) decreases from a saturation field. This novel character does not occur if the dipolar interaction between particles is quite strong. Furthermore, the effect of the array size N on TMR is also studied and the result shows that TMR ratio fluctuates when N increases for a moderate dipolar interaction strength. When the applied field h_e is parallel to the array plane, the in-plane TMR curve seems insensitive to the dipolar interaction strength, but the maximum TMR ratio (~26%) can also be obtained at h_e=0.     

In situ imaging of field-induced hexagonal columns in magnetite ferrofluids

Field-induced structures in a ferrofluid with well-defined magnetite nanoparticles with a permanent magnetic dipole moment are analyzed on a single-particle level by in situ cryogenic transmission electron microscopy (2D). The field-induced columnar phase locally exhibits hexagonal symmetry and confirms the structures observed in simulations for ferromagnetic dipolar fluids in 2D. The columns are distorted by lens-shaped voids, due to the weak interchain attraction relative to field-directed dipole-dipole attraction. Both dipolar coupling and the dipole concentration determine the dimensions and the spatial arrangement of the columns. Their regular spacing manifests long-range end-pole repulsions that eventually dominate the fluctuation-induced attractions between dipole chains that initiate the columnar transition.     

Microwave Magnetic Permeability of Fe3O4 Nanoparticles

Well-dispersed Fe3O4 nanoparticles are synthesized via an oxidization method with NANO2 as oxidant. The microwave magnetic properties of the composites are studied with different volume fractions of fe3O4 nanoparticles. It is found that a lower volume fraction corresponds to a higher magnetic resonance frequency. This could be ascribed to the enhancement of exchange interaction with a weakened dipolar interaction when the volume fraction decreases.