Magnetostatic interactions in dense nanowire arrays

We demonstrate the importance of magnetostatic interactions in dense arrays of ferromagnetic nanowires. Beginning from a simple micromagnetic model, we have calculated the interaction field for saturated magnetization in the plane of the array (perpendicular to the axes of the wires) and normal to the plane, using a hybrid (numerical and analytical) strategy. The slope of interaction field versus wire length changes dramatically at the transition between a dipolar regime (at very small lengths) and a monopolar regime (for longer nanowires). We present the interaction fields and the applied fields at saturation for large nanowire arrays. These results are compared with experiment for electrodeposited arrays, and very good agreement is obtained. This shows that the high field behavior of such arrays is dominated by magnetostatic effects and that a nanowire array behaves like a double-sided distribution of magnetic monopoles.     

Magnetic dipolar coupling and collective effects for binary information codification in cost-effective logic devices

Physical limitations foreshadow the eventual end to traditional Complementary Metal Oxide Semiconductor (CMOS) scaling. Therefore, interest has turned to various materials and technologies aimed to succeed to traditional CMOS. Magnetic Quantum dot Cellular Automata (MQCA) are one of these technologies. Working MQCA arrays require very complex techniques and an excellent control on the geometry of the nanomagnets and on the quality of the magnetic thin film, thus limiting the possibility for MQCA of representing a definite solution to cost-effective, high density and low power consumption device demand. Counter-intuitively, moving towards bigger sizes and lighter technologies it is still possible to develop multi-state logic devices, as we demonstrated, whose main advantage is cost-effectiveness. Applications may be seen in low cost logic devices where integration and computational power are not the main issue, eventually using flexible substrates and taking advantage of the intrinsic mechanical toughness of systems where long range interactions do not need wirings. We realized cobalt micrometric MQCA arrays by means of Electron Beam Lithography, exploiting cost-effective processes such as lift-off and RF sputtering that usually are avoided due to their low control on array geometry and film roughness. Information relative to the magnetic configuration of MQCA elements including their eventual magnetic interactions was obtained from Magnetic Force Microscope (MFM) images, enhanced by means of a numerical procedure and presented in differential maps. We report the existence of bi-stable magnetic patterns, as detected by MFM while sampling the z-component of magnetic induction field, arising from dipolar inter-element magnetostatic coupling, able to store and propagate binary information. This is achieved despite the array quality and element magnetic state, which are low and multi-domain, respectively. We discuss in detail shape, inter-element spacing and dot profile effects on the magnetic coupling. Numerical Finite Element Method (FEM) simulations show a possible microspin arrangement producing such magnetostatic coupling.     

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.     

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.     

Analytical model for shape anisotropy in thin-film nanostructured arrays: Interaction effects

When reducing the size of array elements and interelement separations to the nanoscale, long-range magnetostatic interactions become important. A methodology that extends the study of conventional single-element magnetostatics is presented, adding the effect of stacking nanoelements into close proximity in arrays and the consequent interaction effects. This would be very time consuming to model by micromagnetic simulations that are also very vulnerable to artifacts due to cell or boundary condition selection. The proposed method considers an analytical expression valid for short interelement separations and not very costly to evaluate by computational means. This approach allows the quantitative study of shape anisotropy in non-square-shaped arrays. It is also shown how it can be used to find anisotropy compensation conditions, where an anisotropy due to a magnetic element shape can be compensated by the shape anisotropy due to the array. The obtained results can be used to establish a criterion for the minimum number of elements to be considered for a micromagnetic simulation of an array to be realistic depending on the element size and separation.     

Micromagnetic evaluation of statistical and mean-field interactions in particulate ferromagnetic media

Samples with Stoner–Wohlfarth ferromagnetic particles interacting only through dipolar magnetostatic fields were computer generated and the effects of the interactions on the magnetisation processes have been analysed. In some geometrical configurations of the particles, magnetostatic mean-field interaction field was also obtained, in agreement with the usual assumption in the moving Preisach model. A micromagnetic analysis of the magnetostatic mean interaction field is made. Classical ΔM and integral generalised ΔM curves have been calculated and the results have been analysed.     

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.     

Micromagnetic simulation on the dynamic susceptibility spectra of cobalt nanowires arrays: the effect of magnetostatic interaction

<正>Micromagnetic simulations have been performed to obtain the dynamic susceptibility spectra of 4×4 cobalt nanowire arrays with different spatial configurations and geometries.The susceptibility spectra of isolated wires have also been simulated for comparison purposes.It is found that the susceptibility spectrum of nanowire array bears a lot of similarities to that of an isolated wire,such as the occurrences of the edge mode and the bulk resonance mode. The simulation results also reveal that the susceptibility spectrum of nanowire array behaves like that of single isolated wire as the interwire distance grows to an extent,which is believed due to the decrease of magnetostatic interaction among nanowires,and can be further confirmed by the static magnetic hysteresis simulations.In comparison with single nanowire,magnetostatic interaction may increase or decrease the resonance frequencies of nanowire arrays assuming a certain interwire distance when the length of array increases.Our simulation results are also analysed by employing the Kittel equation and recent theoretical studies.     

Multipolar ordering and magnetization reversal in two-dimensional nanomagnet arrays

The low-temperature stable states and the magnetization reversal of realistic two-dimensional nanoarrays with higher-order magnetostatic interactions are studied theoretically. For a general calculus of the multipole-multipole interaction energy we introduce a Hamiltonian in spherical coordinates into the Monte Carlo scheme. We demonstrate that higher-order interactions considerably change the dipolar ground states of in-plane magnetized arrays favoring collinear configurations. The multipolar interactions lead to enhancement or decrease of the coercivity in arrays with in-plane or out-of-plane magnetization.     

Magnetostatic interaction effects in an ordering hexagonal array of ferromagnetic nanoparticles

The results from investigating magnetostatic interaction effects in ordered hexagonal arrays of anisotropic single-domain ferromagnetic nanoparticles are presented. It is demonstrated theoretically and experimentally that two stable states (with quasi-uniform configurations of magnetic moments and with zero averaged magnetic moment configurations) can be easily attained in such arrays. It is shown that the structure of an ferromagnetic resonance spectrum depends strongly on the extent of magnetostatic interaction and the spatial configuration of the magnetic moments in the array.     

Ni纳米线阵列的铁磁共振研究

通过改变氧化电压和酸性溶液制备了孔径、孔隙率不同的阳极氧化铝模板，用电沉积方法在模板中制备了Ni有序纳米线阵列，并用铁磁共振技术和振动样品磁强计对其进行了研究.研究表明Ni纳米线阵列存在着较强的偶极相互作用，偶极相互作用与纳米线的形状各向异性之间的竞争决定了纳米线的易磁化方向.随着纳米线阵列密度的增加，线间的偶极相互作用增加，使得纳米线易磁化方向从平行于纳米线方向渐趋向于垂直于纳米线的平面内. 关键词： 纳米线 铁磁共振 偶极相互作用 氧化铝模板     

Magnetization of the ferromagnetic-superconductor structures

The magnetization of a structure consisting of a thin superconducting film lying on a thin ferromagnetic substrate with uniaxial anisotropy is considered. It is shown that if a ferromagnet is in a multidomain state, then due to the presence of a superconducting film, the period of its domain structures decreases, which is caused by the increase of the magnetostatic energy of the system owing to Meissner currents. In a certain range of the constant of uniaxial anisotropy, under the action of a superconducting film, a domain structure may transform from a strip structure to the structure with closure domains. It is found that due to the nonuniform magnetic field of a multidomain ferromagnet, Abrikosov vortices may exist in a thin film only at certain parameters of the magnetic field.     

基于单丝行为的平面型丝阵Z箍缩模拟

平面型丝阵负载是近年来Z箍缩实验中研究较多的一种非圆柱型丝阵负载.基于平面型丝阵中单丝的静磁场分析并结合单丝的径向运动方程,计算获得了聚爆过程中负载电流在每根丝上分配、每根丝所受磁场力、丝阵负载区磁场分布、负载总电感及聚爆过程中负载动能变化等规律.模拟计算了平面型丝阵负载Z箍缩聚爆轨迹及聚爆时间,并与"强光一号"加速器上进行的平面型丝阵实验结果进行了对比.结果表明,基于单丝行为的模拟误差约为10%,可较为准确地获得平面型丝阵负载聚爆时间.计算结果有助于深入理解平面型丝阵负载Z箍缩物理过程,同时该模型可用于平面型丝阵负载参数设计.     

Dipolar Bose–Einstein condensate soliton on a two-dimensional optical lattice

Using a three-dimensional mean-field model we study one-dimensional dipolar Bose–Einstein condensate (BEC) solitons on a weak two-dimensional (2D) square and triangular optical lattice (OL) potentials placed perpendicular to the polarization direction. The stabilization against collapse and expansion of these solitons for a fixed dipolar interaction and a fixed number of atoms is possible for short-range atomic interaction lying between two critical limits. The solitons collapse below the lower limit and escapes to infinity above the upper limit. One can also stabilize identical tiny BEC solitons arranged on the 2D square OL sites forming a stable 2D array of interacting droplets when the OL sites are filled with a filling factor of 1/2 or less. Such an array is unstable when the filling factor is made more than 1/2 by occupying two adjacent sites of OL. These stable 2D arrays of dipolar superfluid BEC solitons are quite similar to the recently studied dipolar Mott insulator states on 2D lattice in the Bose–Hubbard model by Capogrosso-Sansone et al. [B. Capogrosso-Sansone, C. Trefzger, M. Lewenstein, P. Zoller, G. Pupillo, Phys. Rev. Lett. 104 (2010) 125301].     

Plasmon enhanced light trapping in thin film GaAs solar cells by Al nanoparticle array

Light trapping is a crucial factor to enhance the performance of thin film solar cells. For effective light trapping, we introduced Al nanoparticle array on the top and rear surface of thin film GaAs solar cells. The effect of both array on the optical absorption and current density of solar cells is investigated by using finite difference time domain (FDTD) method. The optimization process of top and rear array in solar cells is done systematically. The results indicate that by plasmonic action of arrays, the optical absorption is significantly enhanced and optimized structure yields a current density of 25.77 mA/cm². These enhancements are mainly attributed to surface plasmon effects induced by Al nanoparticles and the light grating properties of the arrays.     

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.     

Motion-induced magnetic resonance of Rb atoms in a periodic magnetostatic field

We demonstrate that transitions between Zeeman-split sublevels of Rb atoms are resonantly induced by the motion of the atoms (velocity: approximately 100 m/s) in a periodic magnetostatic field (period: 1 mm) when the Zeeman splitting corresponds to the frequency of the magnetic field experienced by the moving atoms. A circularly polarized laser beam polarizes Rb atoms with a velocity selected using the Doppler effect and detects their magnetic resonance in a thin cell, to which the periodic field is applied with the arrays of parallel current-carrying wires.     

Magnetic characterization of FeCo nanowire arrays by first-order reversal curves

FeCo nanowire arrays have been obtained by current pulse electrodeposition into nanoporous alumina templates. First-order reversal curve (FORC) diagrams have been used to investigate magnetostatic interaction and average coercivity of individual FeCo nanowires embedded in porous alumina templates. The FeCo nanowires with a wires length up to 3 μm and wires diameter ranging from 25 to 50 nm showed interacting single-domain behavior. Using FORC diagrams, the spread of coercivity distribution was seen to be almost independent of the wires diameter, but with increase in diameter the inter-wire magnetostatic interaction was increased. It was found that for arrays with higher diameter, the coercivity of the arrays is lower than the average coercivity of the individual wires. It was detected that an increase in wire diameter results in a considerable increase in the spread of the distribution in the H_u direction of FORC distribution. Curve fitting on the experimental data proved a relatively linear relation between interaction field and square diameter of the nanowires.     

Plasma resonance guiding of surface magnetoplasmons by thin semiconductor films

Theoretical investigation on surface magnetoplasmons maintained by the plasma resonance in a thin (comparing to the wavelength) semiconducting film placed on a perfectly conducting substrate is presented. Dispersion characteristics and nonreciprocal behaviour of surface magnetoplasmons are studied for arbitrary orientation of externally applied magnetostatic field and for various profiles of film inhomogeneity.     

Experimental magnetic study and evidence of the exchange bias effect in unidimensional Co arrays produced by interference lithography

A simple process for fabricating submicrometric magnetic arrays employing interference lithography, sputtering deposition and lift-off processes is proposed and demonstrated. The magnetic properties of cobalt (Co) arrays were measured and compared with those of a continuous Co magnetic film. The results show a dependence of the hysteresis curve on the orientation of the field as regards the array, which is correlated with the anisotropy of the structures and a dependence of the coercive field on the periodicity of the arrays. Moreover, an exchange bias effect was observed, which is ascribed to a ferromagnetic/antiferromagnetic (FM/AFM) coupling between Co and a thin surface cobalt oxide (CoO) layer.