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.     

Comparison of reversible and irreversible dipolar assemblies in a ferrofluid

Zero-field aggregation of magnetic nanoparticles in a ferrofluid can either be irreversible or result from a dynamic equilibrium; the two cases can be distinguished by measurements of the complex magnetic susceptibility and by cryogenic transmission electron microscopy (cryo-TEM). We demonstrate this by comparing two colloidal systems that show dipolar structure formation in zero field. A dispersion of magnetic iron nanoparticles is gradually oxidized to decrease the magnetic moments, and despite the vanishing dipolar attractions, thermal motion does not break up the dipolar structures into single particles. Instead, the dipolar structures become chemically fixed during the oxidation process, an example of irreversible aggregation. In contrast, the zero-field dipolar structures in a chemically stable magnetite dispersion are found to disintegrate upon dilution, indicating that the structures are reversible and result from a dynamic equilibrium.     

Magnetic dipolar ordering on geometrically frustrated brick-shaped lattices

The magnetic ordering of frustrated arrays of nanoscale islands can be strongly influenced by the array patterns. We theoretically present three kinds of artificial geometrically frustrated systems with different brick-shaped geometries, defined as brick-shaped lattices, and investigate their magnetic dipolar ordering at the ground state using the Monte Carlo method. The simulated results show that the magnetic ordering of three brick-shaped frustrated lattices depends strongly on the strength of dipolar interactions, depending on the lattice spacing. It is found that the long-range dipolar interactions tend to suppress the long-range ordered state and induce the short-range quasi-ice state at each vertex of the lattices. In addition, the correlations for neighboring spin pairs are closely related to not only the dipolar coupling strength but also the geometry of the lattices.     

Magnetization in uniaxial spherical nanoparticles: Consequence on the interparticle interaction

We investigate the interaction between spherical magnetic nanoparticles which present either a single domain or a vortex structure. First the magnetic structure of a uniaxial soft sphere is revisited, and then the interaction energy is calculated from a micromagnetic simulation. In the vortex regime the orientation of the vortex relative to the easy axis depends on both the particle size and the anisotropy constant. We show that the leading term of the interaction is the dipolar interaction energy between the magnetic moments. For particles presenting a vortex structure, we show that the polarization due to the dipolar field must be included. The parameters entering in the dipolar interaction are deduced from the magnetic behavior of the isolated particle.     

Hysteresis in small arrays of interacting magnetic nanoparticles

The out-of-plane hysteresis loops of small arrays of magnetic nanoparticles, under the influence of an external field applied perpendicular to the array and the dipolar interaction are investigated. The particles are assumed to have a perpendicular anisotropy energy that tends to align the magnetic moments to be perpendicular to the array. The magnetization is found to exhibit a plateaux-and-jumps structure as the external field is swept up and down. These jumps are associated with jumps in the energy of the system, and correspond to transition from one configuration of the moment orientation to another. The energy of different configurations of the magnetic moments for a 3×3 array in the limit of weak dipolar interaction is analyzed, as a means to understand the hysteresis loop. These jumps are more pronounced in arrays of smaller sizes and when the dipolar interaction is weak. The configuration of magnetic moments at zero external field as the field is swept up and down is found to be highly sensitive to the dipolar interaction.     

Magnetic field dependence of residual dipolar couplings measured in dilute liquid crystalline media

The effect of the magnetic field strength on the magnitude of residual dipolar couplings introduced by dilute liquid crystal media was investigated. One-bond heteronuclear residual dipolar couplings and residual deuterium quadrupolar splitting of the water were monitored at various static magnetic fields. It is suggested that the value of residual anisotropic NMR parameters resulting from exchange between ordered and non-ordered molecules decreases with increasing magnetic fields.     

Coupling of ferromagnetic nanoparticles through dipolar interactions

We consider two ferromagnetic nanoparticles coupled via long-range dipolar interactions. We model each particle by a three-dimensional array of classical spin vectors, with a central spin surrounded by a variable number of shells. Within each particle only ferromagnetic coupling between nearest neighbor spins is considered. The interaction between particles is of the dipolar type and the magnetic properties of the system is studied as a function of temperature and distance between the centers of the particles. We perform Monte Carlo simulations for particles with different number of shells, and the magnetic properties are calculated via two routes concerning the dipolar contribution: one assuming a mean-field like coupling between effective magnetic moments at the center of the particles, and other one, where we take into account interactions among all the pairs of spins, one in each particle. We show that the dipolar coupling between the particles enhances the critical temperature of the system relative to the case in which the particles are very far apart. The dipolar energy between the particles is smaller when the assumption of effective magnetic moment of the particles is used in the calculations.     

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.     

Spontaneously modulated spin textures in a dipolar spinor bose-einstein condensate

Helical spin textures in a 87Rb F=1 spinor Bose-Einstein condensate are found to decay spontaneously toward a spatially modulated structure of spin domains. The formation of this modulated phase is ascribed to magnetic dipolar interactions that energetically favor the short-wavelength domains over the long-wavelength spin helix. The reduction of dipolar interactions by a sequence of rf pulses results in a suppression of the modulated phase, thereby confirming the role of dipolar interactions in this process. This study demonstrates the significance of magnetic dipole interactions in degenerate 87Rb F=1 spinor gases.     

Magnetic microstructure of the spin reorientation transition: a computer experiment

The scenario of the spin reorientation in two-dimensional films within first-order anisotropy approximation is theoretically studied by means of Monte Carlo simulations. The magnetic microstructure is investigated as a function of the ratio of the perpendicular anisotropy energy to the dipolar one. If the anisotropy dominates, out-of-plane domains will be found while in-plane vortices appear for a vanishing anisotropy. In the range of comparable anisotropy and dipolar energies a complex domain pattern evolves yielding a continuous transition between the two structures. The structure with equally distributed magnetic moment orientations is stable at the point where anisotropy and dipolar energies cancel each other.     

Proton NMR signals of intra- and interpair dipolar order in liquid crystals

We demonstrate the existence of magnetic intrapair and interpair dipolar order in aligned liquid crystalline samples. The relaxation times of the corresponding dipolar signals are different and depend strongly on the system.     

Effects of magnetic structure distortion near a μ + meson in μSR spectroscopy

Possible effects of strong local anisotropy in the vicinity of a μ meson occupying a rare-earth metal interstitial site are considered. The distortion of the magnetic structure and the corresponding contribution to the dipolar field at the muon are calculated. A threshold-type change of the dipolar field depending on the local anisotropy or external magnetic field is predicted for the case where the direction toward the muon is perpendicular to the magnetic moment of one in the ions. The possibility of existence of two strengths of the dipolar field for the ferromagnetic phases of Dy and Tb, and of its abrupt change depending on the direction of the magnetic moment of the plane is predicted for helical antiferromagnetic structures. Fiz. Tverd. Tela (St. Petersburg) 40, 1298–1304 (July 1998)     

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.     

Observation of dipole-dipole interaction in a degenerate quantum gas

We have investigated the expansion of a Bose-Einstein condensate of strongly magnetic chromium atoms. The long-range and anisotropic magnetic dipole-dipole interaction leads to an anisotropic deformation of the expanding chromium condensate which depends on the orientation of the atomic dipole moments. Our measurements are consistent with the theory of dipolar quantum gases and show that a chromium condensate is an excellent model system to study dipolar interactions in such gases.     

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.     

Sedimentation equilibria of ferrofluids: II. Experimental osmotic equations of state of magnetite colloids

The first experimental osmotic equation of state is reported for well-defined magnetic colloids that interact via a dipolar hard-sphere potential. The osmotic pressures are determined from the sedimentation equilibrium concentration profiles in ultrathin capillaries using a low-velocity analytical centrifuge, which is the subject of the accompanying paper I. The pressures of the magnetic colloids, measured accurately to values as low as a few pascals, obey Van 't Hoff's law at low concentrations, whereas at increasing colloid densities non-ideality appears in the form of a negative second virial coefficient. This virial coefficient corresponds to a dipolar coupling constant that agrees with the coupling constant obtained via independent magnetization measurements. The coupling constant manifests an attractive potential of mean force that is significant but yet not quite strong enough to induce dipolar chain formation. Our results disprove van der Waals-like phase behavior of dipolar particles for reasons that are explained.     

Simultaneous measurement of D and T2 using the distant dipolar field

The presence of long-range dipolar fields in liquids is known to introduce a non-linear term in the Bloch-Torrey equations which is responsible for many interesting effects in nuclear magnetic resonance as well as in magnetic resonance imaging. We show here, for the first time, that the diffusion coefficient D and the spin-spin relaxation time T2 can be obtained simultaneously from the time evolution profile of the long-range dipolar field refocused signal. In a COSY Revamped by Z-asymmetric Echo Detection sequence, the analytical first-order approximation solution of the Bloch-Torrey equations modified to include the effect of the distant dipolar field is used to demonstrate the technique in an experiment using doped water.     

Magnetization of nanomagnet assemblies: Effects of anisotropy and dipolar interactions

We investigate the effect of anisotropy and weak dipolar interactions on the magnetization of an assembly of nanoparticles with distributed magnetic moments, i.e., assembly of magnetic nanoparticles in the one-spin approximation, with textured or random anisotropy. The magnetization of a free particle is obtained either by a numerical calculation of the partition function or analytically in the low and high field regimes, using perturbation theory and the steepest-descent approximation, respectively. The magnetization of an interacting assembly is computed analytically in the range of low and high field, and numerically using the Monte Carlo technique. Approximate analytical expressions for the assembly magnetization are provided which take account of the dipolar interactions, temperature, magnetic field, and anisotropy. The effect of anisotropy and dipolar interactions are discussed and the deviations from the Langevin law they entail are investigated, and illustrated for realistic assemblies with the lognormal moment distribution.     

Low temperature linear dynamical susceptibility of dipolar spin glasses

The dissipative part of the linear magnetic dynamic susceptibility of dipolar spin glasses is considered. Due to the transition of the system (at enough high concentration of the magnetic dipoles) from a paramagnetic phase to a magnetic dipolar one, an anomalous temperature dependence of the dissipative part of the magnetic susceptibility is found. Some considerations related to the experimental results for LiHo_xY _1?xF₄ are made.