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.     

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.     

Domain walls in antiferromagnetically coupled multilayer films

We report experimentally observed magnetic domain-wall structures in antiferromagnetically coupled multilayer films with perpendicular anisotropy. Our studies reveal a first-order phase transition from domain walls with no net moment to domain walls with ferromagnetic cores. The transition originates from the competition between dipolar and exchange energies, which we tune by means of layer thickness. Although observed in a synthetic antiferromagnetic system, such domain-wall structures may be expected to occur in A-type antiferromagnets with anisotropic exchange coupling.     

Spin-wave theory for the dynamics induced by direct currents in magnetic multilayers

A spin-wave theory is presented for the magnetization dynamics in a ferromagnetic film that is traversed by spin-polarized carriers at high direct-current densities. It is shown that nonlinear effects due to four-magnon interactions arising from dipolar and surface anisotropy energies limit the growth of the driven spin wave and produce shifts in the microwave frequency oscillations. The theory explains quantitatively recent experimental results in nanometric point contacts onto magnetic multilayers showing downward frequency shifts (redshifts) with increasing current, if the external field is on the film plane, and upward shifts (blueshifts), if the field is perpendicular to the film.     

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.     

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)     

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.     

Structural anisotropy and internal magnetic fields in trabecular bone: coupling solution and solid dipolar interactions

We investigate the use of intermolecular multiple-quantum coherence to probe structural anisotropy in trabecular bone. Despite the low volume fraction of bone, the bone-water interface produces internal magnetic field gradients which modulate the dipolar field, depending on sample orientation, choice of dipolar correlation length, correlation gradient direction, and evolution time. For this system, the probing of internal magnetic field gradients in the liquid phase permits indirect measurements of the solid phase dipolar field. Our results suggest that measurements of volume-averaged signal intensity as a function of gradient strength and three orthogonal directions could be used to non-invasively measure the orientation of structures inside a sample or their degree of anisotropy. The system is modeled as having two phases, solid and liquid (bone and water), which differ in their magnetization density and magnetic susceptibility. A simple calculation using a priori knowledge of the material geometry and distribution of internal magnetic fields verifies the experimental measurements as a function of gradient strength, direction, and sample orientation.     

Tailoring interacting magnetic nanodots via dimensionality variation of mediating electrons

Nature produces ferromagnetic materials based on nearest neighbor exchange interaction between atomic spins. For artificially fabricated nanomagnets, it is those “small” magnetic energies, e.g. anisotropy, dipolar interaction and indirect exchange interaction that play crucial roles against the thermal fluctuation. We have developed strong capabilities to grow nanodot assemblies in ultrahigh vacuum with controllable size and density on/in both metallic and insulating templates. Based on our novel synthesis capability, we have studied artificial nanomagnets with tunable coupling strength via dimensionality control of the mediating electrons in one-dimensional (1-D), 2-D, and 3-D. We show that such kind of dimensional confinement provides a unique way to induce novel magnetic properties and to gain control of them. The research outlined in this work provides the science base to understand, modify, and manipulate the magnetic properties through dimensional confinement.     

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.     

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.     

Evaluation of the magnetic dipolar fields from layered systems on atomic scale

Exact analytical expressions for the magnetic dipolar fields produced by a plane square lattice with localized magnetic moments are derived. Basing on these expressions surface roughness of a magnetic thin film is considered. Influence of the bipolar fields on the surface anisotropy and hyperfine fields is discussed.     

Magnetostrictive and quadrupolar anisotropy in nuclear magnetic fcc systems

The spin hamiltonian for nuclear magnetic order in copper is investigated with respect to magnetoelastic couplings to the lattice. These arise due to the dipolar, Ruderman Kittel and the quadrupolar interaction. While the latter is quenched for the ideal fcc-lattice, it is found that for copper it will dominate the magnetoelastic terms of the nuclear spin hamiltonian. The absolute size of the quadrupole contribution is determined by the effective charge and (anti-) shielding effects. This interaction can give rise to an effective anisotropy in the fcc-system which can be quite large compared to the small stabilisation energies for nuclear order in copper. Consequences for the nuclear ordering in copper are briefly discussed and compared to the available experimental and theoretical data.     

Accurate CSA measurements from uniformly isotopically labeled biomolecules at high magnetic field

Obtaining chemical shift anisotropy (CSA) principal values from large biomolecular systems is often a laborious process of preparing many singly isotopically labeled samples and performing multiple independent CSA measurements. We present CSA tensor principal values measured in the biomolecular building blocks tyrosine.HCl, histidine.HCl, and all-E-retinal in both isotopically labeled and unlabeled forms at 17.6 T. The measured tensor values are identical for most carbon sites despite significant dipolar couplings between the spins. Quantum mechanical simulations of an arbitrary three spin system were used to evaluate the accuracy of direct CSA measurement as a function of applied magnetic field strength and molecular parameters. It was found that for a CSA asymmetry of 0.2 or more, an accurate measure of the CSA parameters is obtained when the CSA anisotropy is more than six times the largest dipolar coupling in frequency units. If the CSA asymmetry is more than 0.5, this requirement is relaxed, and accurate results are obtained if the anisotropy is more than three times the dipolar coupling. While these limits are insufficient for measurement of CSA's for alpha-carbons and aliphatic sidechain sites in proteins at current field strengths, they open the way for routine systematic CSA measurements of sites with relatively large CSA tensor values in extensively isotopically labeled biomolecules in widely available magnetic fields.     

Backbone-only restraints for fast determination of the protein fold: the role of paramagnetism-based restraints. Cytochrome b562 as an example

CH(alpha) residual dipolar couplings (Deltardc's) were measured for the oxidized cytochrome b562 from Escherichia coli as a result of its partial self-orientation in high magnetic fields due to the anisotropy of the overall magnetic susceptibility tensor. Both the low spin iron (III) heme and the four-helix bundle fold contribute to the magnetic anisotropy tensor. CH(alpha) Deltardc's, which span a larger range than the analogous NH values (already available in the literature) sample large space variations at variance with NH Deltardc's, which are largely isooriented within alpha helices. The whole structure is now significantly refined with the chemical shift index and CH(alpha) Deltardc's. The latter are particularly useful also in defining the molecular magnetic anisotropy parameters. It is shown here that the backbone folding can be conveniently and accurately determined using backbone restraints only, which include NOEs, hydrogen bonds, residual dipolar couplings, pseudocontact shifts, and chemical shift index. All these restraints are easily and quickly determined from the backbone assignment. The calculated backbone structure is comparable to that obtained by using also side chain restraint. Furthermore, the structure obtained with backbone only restraints is, in its whole, very similar to that obtained with the complete set of restraints. The paramagnetism based restraints are shown to be absolutely relevant, especially for Deltardc's.     

The roles of the exchange and dipole couplings on the magnetoresistance for the nanoparticle arrays

Based on Monte Carlo simulations and resistor network model, the tunneling magnetoresistance (TMR) for the square anisotropic magnetic nanoparticle arrays with the exchange coupling J and dipolar coupling D has been studied. The simulated results reveal that, the coercivity H_c increases with decreasing value of D and increasing magnitude of J; the value of TMR_max decreases with enhancing value of J; for D<0.1, the value of TMR_max decreases with increasing value of D, while in contrast for D>0.1, it increases with increasing value of D. Those behaviours have been interpreted with the competition of the different energies, including the random anisotropy, exchange and dipolar energies.     

Dynamics of two interacting dipoles

We study the deterministic spin dynamic of two interacting magnetic moments with anisotropy and dipolar interaction under the presence of an applied magnetic field, by using the Landau–Lifshitz equation with and without a damping term. Due to different kinds of interactions, different time scales appear: a long time scale associated with the dipolar interaction and a short time scale associated with the Zeeman interaction. We found that the total magnetization is not conserved; furthermore, for the non-dissipative case it is a fluctuating function of time, with a strong dependence on the strength of the dipolar term. In the dissipative case there is a transient time before the total magnetization reaches its constant value. We examine this critical time as a function of the distance between the magnetic moments and the phenomenological damping coefficient, and found that it strongly depends on these control parameters.     

Critical temperature of weakly interacting dipolar condensates

We calculate perturbatively the effect of a dipolar interaction upon the Bose-Einstein condensation temperature. This dipolar shift depends on the angle between the symmetry axes of the trap and the aligned atomic dipole moments, and is extremal for parallel or orthogonal orientations, respectively. The difference of both critical temperatures exhibits most clearly the dipole-dipole interaction and can be enhanced by increasing both the number of atoms and the anisotropy of the trap. Applying our results to chromium atoms, which have a large magnetic dipole moment, shows that this dipolar shift of the critical temperature could be measured in the ongoing Stuttgart experiment.     

Magnetization reversal in weakly coupled magnetic patterns

Ion irradiation is an original process to pattern the structural and as a consequence the magnetic properties of ultra-thin films, down to the nanometer scale. Patterns of dots and tracks have been fabricated by focused Ga⁺ ion beam scanned onto a Co layer with perpendicular magnetic anisotropy. Depending on the dose, the magnetic behaviour of the nanometric irradiated lines can be tuned from the ferromagnetic with reduced coercivity to paramagnetic. The larger the fluence, the smaller is the exchange between dots or tracks. These systems enabled investigations of the competition between exchange and dipolar interactions. For arrays designed with high irradiation doses and only coupled by dipolar interactions, the magnetic relaxation proceeds by the magnetization reversal of individual dots and follows a power-law time decay. Monte Carlo simulations reproduce this time dependence.     

High Magnetic Field Consequences on the NMR Hyperfine Shifts in Solution

Pseudocontact shifts arise from the isotropic reorientational average of the dipolar coupling between unpaired electron and nuclei, in the presence of magnetic susceptibility anisotropy. The effect of residual orientation due to high magnetic fields on pseudocontact shifts is evaluated here. The effect is found to be smaller and of opposite sign with respect to another novel effect of high magnetic fields on hyperfine shifts due to saturation of the electron spin magnetic moment as described by the Brillouin equation.