Inhomogeneous configurations of magnetization of ferromagnetic films with biaxial anisotropy

The system of the Landau-Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out.     

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.     

Energy minimization and ac demagnetization in a nanomagnet array

We study ac demagnetization in frustrated arrays of single-domain ferromagnetic islands, exhaustively resolving every (Ising-like) magnetic degree of freedom in the systems. Although the net moment of the arrays is brought near zero by a protocol with sufficiently small step size, the final magnetostatic energy of the demagnetized array continues to decrease for finer-stepped protocols and does not extrapolate to the ground-state energy. The resulting complex disordered magnetic state can be described by a maximum-entropy ensemble constrained to satisfy just nearest-neighbor correlations.     

Radiophysics

The propagation of magnetostatic waves in a ferromagnetic waveguide created by a step bias field is studied by numerical methods. Bias field configurations and frequencies are taken such that the width of the magnetic waveguide accommodates either only bulk waves or surface and bulk waves in combination. This work is an extension of earlier works, in which the propagation of surface waveguide modes was considered.     

Ferromagnetic resonance in interacting magnetic microstrips

The results of the micromagnetic simulation of forced oscillations of the magnetization in a system of two interacting microstrips located at an angle to each other have been presented. The ferromagnetic resonance spectra and the mode composition of resonant oscillations of the system have been investigated under the conditions of magnetostatic and exchange interactions between the microstrips. It has been shown that the magnetostatic interaction leads to the possibility of the excitation of in-phase and out-of-phase coupled oscillations of the magnetization of the microstrips. In the systems of exchange-coupled microstrips, there are intense resonances due to oscillations of the domain walls. The transformation of the ferromagnetic resonance spectrum and the change in the mode composition of resonant oscillations in different equilibrium configurations of the magnetization of the system have been discussed, as well as the conditions for the excitation of oscillations of different types depending on the direction of the microwave magnetic field.     

Magnetic ordering in granular system

The conditions of the formation of different magnetic structures with ferromagnetic (FM) and antiferromagnetic (AFM) ordering in granular materials containing a subsystem of ferromagnetic granules are considered within the phenomenological approach. It is supposed that the magnetostatic field and the exchange interaction between conduction electrons and magnetic ions are responsible for the formation of magnetic structure.     

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.     

Magnetostatic modes in coupled antiferromagnet/ferromagnet bilayers

We study the influence of interface effects on the magnetostatic modes propagating in a coupled ferromagnetic/antiferromagnetic bilayer. We assume that the magnetic layers are thick enough to be described by the bulk parameters and they are coupled through the interaction between the magnetic moments located at the interface. We use a phenomenological approach taking into account the presence of different magnetic layers in the system to calculate the modified dynamical response of each material. We use the corrected magnetic permeability of the layers to obtain a correlation between the interface characteristics and the physical behavior of the magnetic excitations propagating in the system.     

Ignoring your neighbors: moment correlations dominated by indirect or distant interactions in an ordered nanomagnet array

We have studied the moment correlations within triangular lattice arrays of single-domain coaligned nanoscale ferromagnetic islands. Independent variation of lattice spacing along and perpendicular to the island axis tunes the magnetostatic interactions between islands through a broad range of relative strengths. For certain lattice parameters, the sign of the correlations between near-neighbor island moments is opposite to that favored by the pairwise interaction. This finding, supported by analysis of the total correlation in terms of direct and convoluted indirect contributions across multiple pairwise interactions, indicates that indirect interactions and/or those mediated by further neighbors can be tuned to be dominant, with implications for the wide range of systems composed of interacting nanomagnets.     

非线性静磁表面波的传播特性

将文献[4]的理论结果加以推广,用微扰理论导出了微波场作用下铁磁材料的动态非线性磁化强度的各阶近似表达式。严格分析了在波矢k与外偏置磁场H₀成任意角度时非线性静磁表面波的传播特性。证明了静磁表面波在任何传播方向上都不能演化为静磁孤子。 关键词：     

Numerical calculation of the magnetic field and magnetic moment of ferromagnetic bodies with a complex spatial configuration

A method for numerical calculation of the magnetic field and magnetic moment of 3D ferromagnetic objects is described using the method of finite volume and absorbing boundary conditions. The magnetic moments and magnetic field of some ferromagnetic systems imitating various objects are calculated. It is shown that the configuration of ferromagnetic structures consisting of various combinations of rods determines their magnetic moments.     

Magnetization reversal of elliptic Co/Si/Co nanodisks in the field of a magnetic-force microscope probe

The processes of local magnetization reversal of elliptic Co/Si/Co nanodisks under the action of a nonuniform magnetic field of a magnetic-force microscope (MFM) probe have been investigated. The specific features of the distribution of the phase MFM contrast from particles with ferromagnetic and antiferromagnetic configurations of the magnetic moments in neighboring Co layers have been discussed. It has been shown experimentally that, under the action of the probe field, there occur orientational transitions of two types: transitions from the ferromagnetic configuration to the antiferromagnetic configuration due to the reorientation of the magnetization of the upper layer and transitions in the antiferromagnetic configuration with a change in the orientation of the magnetic moment in both ferromagnetic layers. The presented results of micromagnetic simulation of the processes of transformation of the magnetization in such particles under the action of the MFM probe field explain the main regularities of the magnetization reversal processes.     

Topological information in artificial spin ice with random vacancies

In this work, we perform a numerical study on artificial spin ice systems formed by square arrays of ferromagnetic nano-islands. Inspired by topological studies, we consider absent nano-islands at random positions throughout the array. The system is described by a Hamiltonian that includes anisotropy energy as well as dipolar interaction among the islands in the Heisenberg spin model approach. The simulations were done in the framework of the Monte-Carlo method with the Metropolis algorithm. We focus on the effect of the vacancies on the magnetic vertices configurations. In particular, we calculate the distribution of all possible magnetic configurations of the vertices as a function of the percentage of vacancies. The absent nano-islands generate a loss of geometric frustration, and the system evolves faster than the system without vacancies to a lower energy state. However, the system shows the difficulty of reaching the ground state because the vacancies generate different sub-regions that evolve towards one of the two possible orientations of the magnetic moments with the minimum energy state. Furthermore, we show this system to be stable up to room temeperature when a state with local minimal energy is initially considered. Consequently, the system retains its information in a wide range of temperatures. The introduction of vacancies breaks with any translational symmetry and allows diversifications of the number of magnetic configurations with minimum energy. Therefore, this kind of systems can be used to store information.     

Magnetization reversal processes in layered high-temperature superconductors with ferromagnetic impurities

The self-consistent interaction of a vortex system of a high-temperature superconductor and ferromagnetic impurities, including single impurities and their clusters, has been considered in the model of a layered high-temperature superconductor. For different temperatures and concentrations of ferromagnetic impurities, the magnetization reversal loops have been calculated by the Monte Carlo method taking into account an ensemble of ferromagnetic particles with different orientations of their easy magnetization axes with respect to the direction of an external magnetic field and for different magnetic anisotropy energies. It has been demonstrated that there is a nonlinear interaction of the high-temperature superconductor with ferromagnetic impurities, in which the initially thermodynamically reversible character of the magnetization reversal of the ferromagnetic ensemble can become irreversible. For a periodic lattice of clusters of ferromagnetic impurities, the magnetization curves of the high-temperature superconductor have been calculated for different sizes and configurations of the clusters. It has been revealed that, when extended defects are oriented parallel to the direction of the entrance of vortices in the sample, the length of the defects does not affect the remanent magnetization. It has been shown that the inclusion of the interaction between the magnetic moments inside the impurity cluster leads to a decrease in the magnetization reversal loop, the coercivity, and, accordingly, the energy loss due to magnetization reversal.     

Direct imaging of asymmetric magnetization reversal in exchange-biased Fe/MnPd bilayers by x-ray photoemission electron microscopy

X-ray photoemission electron microscopy is used to probe the remnant magnetic domain structure in high quality, single-crystalline, exchange-biased Fe/MnPd bilayers. It is found that the induced unidirectional anisotropy strongly affects the overall magnetic domain structure. Real space images of the ferromagnetic domains provide direct evidence for an asymmetric magnetization reversal process after saturation along the ferromagnetic hard direction. The magnetization reversal occurs by moment rotation for decreasing fields while it proceeds by domain nucleation and growth for increasing fields. The observed domains are consistent with the crystallography of the bilayers and favor a configuration that minimizes the overall magnetostatic energy of the ferromagnetic layer.     

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.     

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.     

Surface dependence of the magnetic configurations of the ordered B2 FeCr alloy

Tight-binding linear muffin tin orbitals calculations with generalized gradient approximation were carried out for the magnetic configurations at the surface of the ferromagnetic ordered B2 FeCr alloys. For both (001) and (111) crystallographic phases, non ferromagnetic configurations are shown to be more stable than the ferromagnetic configuration of the bulk alloy. For (001) surface we display a c ground state for either Cr or Fe at the surface. For Cr top layer the magnetic moments are larger than in the bulk B2 FeCr while they are slightly enhanced for Fe top layer. For (111) surface an antiferromagnetic coupling between surface and subsurface is always obtained i.e. for either Fe or Cr at the surface. This change of coupling between Fe and Cr (from ferromagnetic to antiferromagnetic) is expected to be fundamental to any explanation of the experimental results obtained for the interface alloying at the Fe/Cr interfaces. Received 23 March 1998     

Interaction of a shear wave with a moving domain wall in a ferromagnetic crystal with allowance for the external magnetic field

The boundary-value problem of the magnetoelastic wave interaction with a moving domain wall in a ferromagnetic crystal is solved in the nonexchange magnetostatic approximation with allowance for the external magnetic field. It is shown that the difference introduced by magnetic field between the ferromagnetic resonance frequencies of the domains does not cause any noticeably departure of the refraction characteristics of reflected and transmitted waves from those observed at zero frequency mismatch. By contrast, the magnitudes of the transmission and reflection coefficients strongly depend on the external magnetic field and on the mobility of the domain wall. The dependence of the magnitude of the reflection coefficient on the external magnetic field at a fixed angle of shear wave incidence is found to possess two ferromagnetic resonance peaks. The positions and heights of the peaks may vary depending on the mobility of the domain wall.     

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.