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.     

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     

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.     

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.     

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.     

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.     

Ground state of finite arrays of magnetic dots in the presence of an external magnetic field

The ground state of an array of magnetic particles (magnetic dots), which are ordered in a square 2D lattice and whose magnetic moment is perpendicular to the lattice plane, in the presence of an external magnetic field has been analyzed. Such a model is applicable for sufficiently small dots with perpendicular anisotropy that are in a single-domain state and for dots in a strongly inhomogeneous vortex state whose magnetic moment is determined by the vortex core. For the magnetic field perpendicular to the system plane, the entire set of the states has been analyzed from the chessboard antiferromagnetic order of magnetic moments in low fields to the saturated state of the system with the parallel orientations of the magnetic moments of all dots in strong fields. In the presence of the border, the destruction of the chessboard order first occurs at the edges of the system, then near the extended sections of the surface, and finally expands over the entire interior of the array. The critical field at which this simplest state is destroyed is much more weakly than the value characteristic of the ideal infinite system. In contrast to this scenario, the destruction of the saturated state with decreasing field always begins far from the borders. Despite such different behaviors, the magnetic structure in the intermediate range of fields that is obtained with both increasing and decreasing field for finite arrays strongly differs from that characteristic of the ideal infinite system. The role of simple stacking faults of the magnetic dot lattice (such as single vacancies or their clusters) in the remagnetization of the system has been analyzed. The presence of such faults is shown to give rise to the appearance of local destructions of the chessboard antiferromagnetic order at fields that are much weaker than those for an ideal lattice.     

Decagonal quasiferromagnetic microstructure on the penrose tiling

The stable magnetization configurations of a ferromagnet on a quasiperiodic tiling have been derived theoretically. The magnetization configuration is investigated as a function of the ratio of the exchange to the dipolar energy. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated that for a weak exchange interaction the new structure, the quasiferromagnetic decagonal configuration, corresponds to the minimum of the free energy. The decagonal state represents a new class of frustrated systems where the degenerated ground state is aperiodic and consists of two parts: ordered decagon rings and disordered spin-glass-like phase inside the decagons.     

Creation of helical vortices during magnetization of aligned carbon nanotubes filled with Fe: theory and experiment

We report a novel magnetic phenomenon consisting of the formation of helical spin configurations during the magnetization of densely packed ferromagnetic nanowires encapsulated inside carbon nanotubes. We studied the hysteresis loops when the magnetic fields are applied parallel and perpendicular to the nanotubes axes. We also performed theoretical calculations on aligned nanowire arrays that clearly indicate the creation of helical spin vortices in the hysteresis loops. The latter are caused by the presence of strong dipolar interactions among neighboring wires.     

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 a dipolar Ising model

Zero-temperature Monte Carlo simulations are performed to study the magnetic hysteresis in a three-dimensional model with only dipolar interactions among the Ising spins located inside a sphere on a cubic lattice. Relevant differences are found in the site energy distributions between the up and down spins during the magnetization process. Variations of the dipolar energy and the density of incomplete columns are also discussed.     

Arrays of interacting ferromagnetic nanofilaments: Small-angle neutron diffraction study

Magnetic properties of spatially ordered arrays of interacting nanofilaments have been studied by means of small-angle diffraction of polarized neutrons. Several diffraction maxima or rings that correspond to the scattering of the highly ordered structure of pores/filaments with hexagonal packing have been observed in neutron scattering intensity maps. The interference (nuclear-magnetic) and pure magnetic contributions to the scattering have been analyzed during the magnetic reversal of the nanofilament array in a field applied perpendicular to the nanofilament axis. The average magnetization and the interference contribution proportional to it increase with the field and are saturated at H = H _S . The magnetic reversal process occurs almost without hysteresis. The intensity of the magnetic contribution has hysteresis behavior in the magnetic reversal process for both the positive and negative fields that form the field dependence of the intensity in a butterfly shape. It has been shown that this dependence is due to the magnetostatic interaction between the filaments in the field range of H ≤ H _S . A theory for describing the magnetic properties of the arrays of interacting ferromagnetic nanofilaments in the magnetic field has been proposed.     

Analogue of a spin flop phase transition for an array of magnetic moments with dipole interaction

In a two-dimensional array of magnetic moments with planar magnetization and relatively weak anisotropy in the basal plane, a stepwise phase transition is induced by an external magnetic field parallel to the easy axis of the system. This transition is similar to the spin flop phase transition in weakly anisotropic Heisenberg antiferromagnets with the significant difference that it is accompanied by the rearrangement of the sublattice structure of the magnet; i.e., it can be interpreted as a topological transition. The transition should manifest itself for arrays of submicron magnetic particles (magnetic dots) on nonmagnetic substrates, which have recently become the object of intensive research.     

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.     

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.     

外场作用下铁电/铁磁双层膜的极化磁化性质

建立了铁电/铁磁双层膜模型,铁电层的电矩用连续标量描述,而铁磁层的自旋应用经典矢量描述.利用蒙特卡罗方法模拟了体系的热力学性质和极化、磁化行为.给出了零场下体系的内能、比热、极化和磁化随温度变化的关系,并分别研究了体系在外磁场和外电场下的极化和磁化行为.模拟结果表明,双层膜体系的内能、比热、极化和磁化性质因层间耦合系数的不同而明显不同,当界面耦合较弱时,双层膜表现出各自的热力学性质,当层间耦合增强到一定程度时,双层膜耦合为一个整体,表现出统一的热力学性质.该双层膜在外场中形成电滞回线和磁滞回线,并表现出偏置特性,界面耦合强度和温度影响滞后回线和偏置现象.     

Structural and magnetic properties of electrodeposited Cobalt nanowire arrays

Ordered magnetic nanowires have tremendous potential in future magnetic storage and high frequency magnetic logic devices. Here, we present the fabrication of ordered arrays of Cobalt nanowires by electrodeposition through porous polycarbonate membranes. Vertically and horizontally aligned nanowires were produced in presence of an external bias field during post deposition etching of the polycarbonate membrane. Structural and compositional analyses have been carried out to establish the material and structural purity. The magneto-optical Kerr effect was employed to measure the magnetic hysteresis loops for the nanowires assembled in the substrate plane. A good magneto-optical signal to noise ratio is observed with clean ferromagnetic hysteresis loops. The loops measured with external magnetic field applied parallel and perpendicular to the axis of the nanowires show a clear difference in the shape and the coercive field, indicating the effect of shape anisotropy in these samples. Micromagnetic simulations were performed to understand the experimental results and to obtain insight to the magnetization reversal mechanism in magnetic nanowires.     

Magnetization reversal process at atomic scale in systems with itinerant electrons

The magnetic response of itinerant electrons systems to an external magnetic field is investigated on the basis of a microscopic Hamiltonian from which the spin-polarized electronic structure is determined. The magnetic moment and grand thermodynamic potential of the d-electronic subsystem on a particular atomic site in the presence of the external field are calculated as a function of the moment's orientation for fixed electron configuration of its local environment. Self-consistent magnetic solutions strongly depend on the d-electron number, determined by the position of the d level relative to the Fermi energy. For parameters corresponding to α-Fe, two branches of self-consistent solutions with high and low magnetic moments are found. For parameters corresponding to bulk Cr, a Fe impurity in the Cr matrix and a Cr impurity in the Fe matrix, there are only low-spin solutions. The theory is also applied for describing magnetization reversal processes in exchange spring magnets. A slab of Fe was considered as a soft magnetic layer. The influence of the hard magnet is modeled by the inclusion of an external magnetic field applied to the interface Fe layers. The dependence of the hysteresis loop on the thickness of the Fe slab and on the value of the interface field is investigated.     

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].     

Generation of subharmonic shapiro steps in ladder arrays of overdamped superconducting junctions

Summary Subharmonic Shapiro Steps (SSS) are usually observed in 2D arrays of superconducting junctions when their dynamical states are perturbed by factors like disorder, frustration, current inhomogeneities and so on. In order to clarify the conditions under which SSS can be generated we decided to investigate arrays of very simple shape like the ladder ones. In particular we have studied the influence of the frustration (i.e. of an external magnetic field) on the time evolution of the vortex configuration and the commensurability of the latter with the geometry and the dimension of the array. Ladders, parallel or perpendicular to the bias current, turn out to be systems where the properties of the square arrays can be suitably tested. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.