Configurational spin reorientation phase transition in magnetic nanowire arrays

Classical microscopic spin reorientation phase transitions (RPT) are the result of competing magnetocrystalline anisotropies. RPTs can also be observed in discrete macroscopic systems induced by competing shape anisotropies and magnetostatic coupling. Such a configurational RPT was recently observed in series of self-organized hexagonal arrays of 2.5 μm long, 25-60 nm diameter circular permalloy nanowires grown in anodic alumina matrix. This RPT is a crossover transition from a one-dimensional easy axis “wire” behavior of weakly interacting uniaxial nanowires to a two-dimensional behavior of strongly coupled “wire film” having an easy plane anisotropy. It is shown that RPT takes place due to the competition between the intrinsic dipolar forces in individual wires and the external dipolar field of interacting nanowires in the array. The crossover occurs at a volume ratio of 0.38 for 65 nm periodicity. The experimental results are in agreement with the semi-analytical calculations of the dipolar interaction fields for these arrays of circular ferromagnetic nanowires, and are interpreted in terms of the Landau phase transition theory. The conditions for the crossover and the order of the phase transition are established. Based on the contribution to the magnetic energy from the flower state at the ends of the wires, it is concluded that the observed transition is of the first order.     

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.     

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.     

Magnetic properties of ferrocholesterics with soft particle anchoring

The influence of the external magnetic field on the orientational structure and magnetic properties of the ferrocholesteric is analyzed. A soft homeotropic coupling between the magnetic particles and the cholesteric molecules is assumed. The diamagnetic anisotropy of the matrix is chosen to be positive. In this case, the dipolar and quadrupolar mechanisms of orientational interaction with the external field compete with each other. The field being applied normal to the helix. Using the continuum theory, the occurrence of magnetic-field-induced ferrocholesteric–ferronematic transition is studied. The transition field as a function of the material parameters of a ferrocholesteric is found. It is shown that rising the field strength in the ferronematic phase leads to a change in the coupling between the particles and the director from homeotropic to planar one. A study on the structure of the domain walls in ferronematic phase is undertaken.     

Colloidal assembly on magnetically vibrated stripes

We investigate the collective organization of paramagnetic colloidal particles externally driven above the periodic stripes of a uniaxial ferrimagnetic garnet film. An external field modulation induces vibration of the stripe walls and produces random motion of the particles. Defects in the stripe pattern break the symmetry of the potential and favor particle nucleation into large clusters above a critical density. Mismatch between particle size and pattern wavelength generates assemblies with different morphological order. At even higher field strengths, repulsive dipolar interactions between the particles induce cluster melting. We propose a novel approach to generate and externally control a variety of colloidal assemblies.     

强磁场作用下Cu熔体中富Fe颗粒的迁移与排列

凝固界面前沿颗粒间的相互作用决定了颗粒的运动轨迹、分布和材料的性能,控制熔体中颗粒的迁移可用于材料的净化和提纯.在Cu-30%Fe合金液固两相区施加不同的强磁场条件,富Fe颗粒的分布和排列不尽相同.当无强磁场作用时,富Fe颗粒较均匀地分布在Cu熔体中;随着施加稳恒强磁场磁感应强度的增加,富Fe颗粒向远离重力方向的试样上端迁移,样品底部几乎无富Fe颗粒;而施加向下的梯度磁场作用后,富Fe颗粒沿重力方向向下迁移.结合强磁场作用下颗粒的受力情况,分析了Fe颗粒的迁移行为.不同磁场条件和不同区域的颗粒直径统计分析表明,随磁感应强度增加,Fe颗粒聚合增加,但施加梯度强磁场后颗粒的团聚又逐渐减弱,对此从影响颗粒运动的Stokes和Marangoni凝并速度进行了讨论.从能量最低的角度解释了富Fe相沿平行磁场方向的取向排列.     

Control of magnetic anisotropy of Co nanowires

Cobalt nanowires were fabricated by DC electrodeposition onto anodic aluminium oxide (AAO) templates. The effects of AAO pore diameter, current density, pH, annealing and deposition under external magnetic fields on the structure and magnetic properties of the nanowire arrays were studied. It is found that the smaller pore size produces high crystallinity, resulting in improved magnetic performance at low current density. The pH can transform fcc-Co phase to hcp-Co phase, with the easy axis along the nanowire axis switched over to the perpendicular direction. Annealing demonstrates excellent thermal stability of the magnetic nanowire arrays at high temperature. The application of external magnetic field during deposition influences the growth habit of the nanowires, leading to the change in the magnetic properties.     

Observation of condensed phases of quasiplanar core-softened colloids

We experimentally study the condensed phases of repelling core-softened spheres in two dimensions. The dipolar pair repulsion between superparamagnetic spheres trapped in a thin cell is induced by a transverse magnetic field and softened by suitably adjusting the cell thickness. We scan a broad density range and we materialize a large part of the theoretically predicted phases in systems of core-softened particles, including expanded and close-packed hexagonal, square, chainlike, stripe or labyrinthine, and honeycomb phase. Further insight into their structure is provided by Monte Carlo simulations.     

Formation of phase domain structures in thin films under conditions of a first-order magnetic phase transition

This paper reports on the results of a theoretical investigation into the magnetic and resonance properties of thin films in the range of the transition from a paramagnetic state to a ferromagnetic state in the case where the magnetic transition is a first-order phase transformation. It is demonstrated that, in an external magnetic field directed perpendicular to the film plane, the formation of a specific domain structure consisting of domains of the coexisting paramagnetic and ferromagnetic phases can appear to be energetically favorable. The parameters of the equilibrium system of stripe phase domains and their dependences on the temperature, the magnetic field, and the characteristics of the material are calculated. The specific features of the magnetic resonance spectra under the conditions of formed stripe phase domains are considered. A relationship is derived for the dependence of the resonance field of the system of ferromagnetic domains on the magnetization and temperature. It is shown that the alternating external field can fulfill an orientation function in the formation of stripe phase domains.     

Magnetic dimer motion effects in a rotating magnetic field (A qualitative model of magnetoviscosity and permittivity in magnetorheological suspensions)

The motion of a pair of uniform interacting spherical mesoscopic particles situated in a viscous fluid under the influence of a rotating magnetic field was studied. The coupling interactions between the particles were chosen as a superposition of steric and dipolar pair potentials (for the dipoles parallel to the external field). The model dynamics consisting of particular rotation and vibration modes is the result of the interplay of viscous and interaction forces. The transition from the synchronous to the asynchronous regime of dimer rotation has been found. The results were discussed from a synergetic point of view. A qualitative picture of behaviour of the effective magnetoviscosity and permittivity for dimerized magnetorheological suspension has been given.     

Angular dependence of the coercivity and remanence of ordered arrays of Co nanowires

The angular dependence of the coercivity and remanence of ordered hexagonal arrays of Co nanowires prepared using anodic aluminum oxide templates was investigated. The experimental evolution of coercivity as a function of the angle, in which the external field is applied, is interpreted considering micromagnetic simulations. Depending on the angle between the axis of the wire and the applied magnetic field direction our results show that the magnetization reversal mode changes from vortex to a transverse domain wall. Besides, we observed that the dipolar interactions cause a reduction in coercive fields, mainly in the direction of easy magnetization of the nanowires. Good agreement between numerical and experimental data is obtained.     

Array anisotropy in structured thin film arrays: Influence on the magnetodynamics

The dynamic magnetic properties of soft-ferromagnetic thin film element arrays are strongly influenced by long range interelement magnetostatic interaction. In order to estimate the effective array dipolar field a quantitative model is presented, which is based on the superposition of stray fields that arise from the neighborhood of a reference element. Kittel's equation, that describes the magnetodynamics, is generalized for magnetically saturated arrays by additional array dipolar field terms. Measurements of the magnetodynamic response of quasi-saturated arrays with a rectangular base agree with theoretical predictions. Thus, our model allows the estimation of the frequency of the uniform precessional mode in mesoscopic thin film arrays with non-negligible magnetostatic interaction.     

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.     

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.     

Phase field simulation of spinodal decomposition under external magnetic field

A computational model was developed to simulate the spinodal decomposition process of ferromagnetic alloys under an external magnetic field. In this model, the temporal evolution of the modulated structure was described by a phase field method, and the magnetic configuration was solved by using a micromagnetic method. The spinodal decomposition and coarsening processes of a single magnetic particle and an A-B hypothetical system under an external magnetic field were simulated using the proposed model. The simulation results show that the precipitated particles were elongated along the direction of the external magnetic field. The dependence of the modulated structure of an A-B hypothetic system on external magnetic field is much more sensitive than that of the single particle structure. The simulation results also demonstrate that the modulation of the external magnetic field is effective even if the spinodal decomposition has been completed and a stable modulated structure was formed.     

Pair correlations in magnetic nanodispersed fluids

The pair distribution function of a monodisperse magnetic fluid simulated by a liquid made of dipolar hard spheres with constant magnetic moments is calculated. The anisotropy of the pair distribution function and the related structure factor of scattering in a dc uniform magnetic field are studied. The calculation is performed by diagrammatic expansion in the volume concentration of particles and the interparticle magnetic-dipole interaction intensity using a thermodynamic perturbation theory. Limitation by three-particle diagrams makes it possible to apply the results obtained to magnetic fluids with a moderate concentration. Even for low-concentration and weakly nonideal magnetic fluids, the anisotropic interparticle magnetic-dipole correlations in a magnetic field lead to the repulsion of particles in the direction normal to the field and to the formation of particle dimers along the field.     

Correlated magnetic vortex chains in mesoscopic cobalt dot arrays

Nucleation and annihilation of vortex states have been studied in two-dimensional arrays of densely packed cobalt dots. A clear signature of dipolar interactions both between single-domain state dots and vortex state dots has been observed from the dependence of vortex nucleation and annihilation fields on interdot separation. A direct consequence of these interactions is the formation of vortex chains as well as dipole chains aligned along the direction of the external field. In addition, short range correlation of chiralities within vortex chains has been observed using magnetic force microscopy imaging and has been attributed to cross-talking between adjacent elements.     

Quantum spin glass and the dipolar interaction

Anisotropic dipolar systems are considered. Such systems in an external magnetic field are expected to be a good experimental realization of the transverse field Ising model. With random interactions, this model yields a spin glass to paramagnet phase transition as a function of the transverse field. We show that the off-diagonal dipolar interaction, although effectively reduced, induces a finite correlation length and thus destroys the spin-glass order at any finite transverse field. We thus explain the behavior of the nonlinear susceptibility in the experiments on LiHo(x)Y(1-x)F(4), and argue that a crossover to the paramagnetic phase, and not quantum criticality, is observed.     

Geometric Phase for Two Entangled Spin-1/2 Particles in a Magnetic Field

In this paper the geometric phases of two entangled spin-1/2 particles in the presence and absence of spin-spin interaction are calculated. We also discuss the geometric phases when only one of the two particles is affected by the external magnetic field. Our results show that the geometric phase in this case is not equal to that of a single particle under the same evolution condition because of the effect of entanglement. We further study the entanglement dependence of the noncyclic geometric phases in the interacting and noninteracting spins under a time-independent uniform magnetic field. A general entanglement-dependence geometric phase is formulated.     

Two-dimensional Monte Carlo simulations of a suspension comprised of magnetic and nonmagnetic particles in gradient magnetic fields

Distributions of particles in a suspension comprised of magnetic particles (MPs) and nonmagnetic particles (NPs) under gradient magnetic fields are vitally important for the preparation of magnetic-nonmagnetic functionally graded materials (FGMs). In the present study, the effects of magnetic field gradient, magnetic interaction between MPs and concentration of NPs on the distributions of particles in the suspension are investigated using a two-dimensional Monte Carlo simulation. The results show that a gradient distribution of MPs is formed under gradient magnetic fields and increases with increasing the field gradient. However, as the interaction between MPs increases, the distribution gradient decreases, accompanied by the formation of chain-like MP clusters. Moreover, NPs are found to hinder the translation of MPs along the field direction. As the NP concentration increases, the translation of MPs becomes difficult.