On features of magnetization self-organization in 1D stochastic ferromagnetic systems

The magnetic structure of a polycrystalline nanowire at the weak or missing magnetostatic interaction exhibits the special self-organization of magnetization. As is known, the magnetization structure forming in a random crystallographic anisotropy field has a characteristic length range, which involves tens and hundreds of crystallites. This leads to the occurrence of stochastic domains. The induced uniform anisotropy of magnetostatic nature or the texture co-directed with the crystallite anisotropy axes masks the picture of stochastic domains. Nevertheless, as we show, the information on stochastic domains remains in the magnetization structure. The experimental techniques for obtaining information on the magnetic properties of stochastic domains are proposed.     

Magnetostatic energy and stripe domain structure in a ferromagnetic plate of finite width with in-plane anisotropy

The magnetostatic energy and domain structure (DS) in a long ferromagnetic plate of a finite width with in-plane anisotropy are calculated for the case of the domain magnetization vectors lying in the plane of the plate. The situation where the DS period is much shorter than the width but is considerably larger than the thickness of the plate is analyzed in detail. The equilibrium DS period and the width ratio of two adjacent domains are determined as functions of an external magnetic field parallel to the plane of the plate by minimizing the energy. The DS period is found to be proportional to the plate width and the domain wall energy and inversely proportional to the squared saturation magnetization. While the width of the favorable domains (with the magnetization parallel to the field) grows with increasing field, the unfavorable domains, rather than disappearing completely, form relatively narrow transition regions between the favorable domains, i.e., 360° domain walls.     

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.     

Magnetostatic Energy of Domain Walls in Uniaxial Films of Finite Sizes

Physics of the Solid State - The solution to the problem of calculating the magnetostatic interaction energy of domain walls in uniaxial magnetics with a uniform magnetization distribution inside...     

Cluster analysis of an Ising-Preisach interacting particle system

The paper deals with the analysis of clusters' size in diverse magnetization states of a system of ferromagnetic particles organized in a perfect 2D array with all the anisotropy axes perpendicular to the plane (perpendicular medium) following the evolution of the clusters in correlation with various parameters like applied field or interaction strength. We present numerical simulations for a two-level Ising-type model each magnetic entity being characterized by a Stoner-Wohlfarth nonlinear energy barrier and a rectangular hysteresis loop (Ising-Preisach hysteron). In the simulations we took into account, the long-range inter-particle magnetostatic interactions in an attempt to mimic as accurately as possible with a still simple model, materials like Bit-Patterned media that are now considered as good candidates for the magnetic memories of the future.     

Hysteresis of the characteristics of magnetostatic waves in ferrite films with stripe domains whose magnetization vectors are oriented close to the plane of the film

The propagation of zero-exchange spin waves (magnetostatic waves) is investigated in yttrium iron garnet films having a regular stripe domain structure with almost in-plane orientation of the domain magnetization vectors. The characteristics of the waves are studied for magnetizations of the film parallel and perpendicular to projections of the [111] crystallographic axes onto the plane of the film. It is established, in contrast with films having the domain magnetization vectors oriented close to the normal to the plane of the film, that both the propagation of magnetostatic waves and the variation of the parameters of the domain structure exhibit a distinctly pronounced hysteretic character as the magnetizing field is varied. The hysteresis of the amplitude-frequency response, equiphase, and dispersion curves of the magnetostatic waves is investigated. The authors examine how the hysteresis of these parameters is related to the hysteresis of the domain structure. The spectrum of magnetostatic waves is found to have an interval of wavelengths (wave numbers) that are not excited in the unsaturated film when the applied field is close to the saturation value, and this phenomenon as well exhibits hysteresis. Zh. éksp. Teor. Fiz. 114, 1430–1450 (October 1998)     

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.     

Role of exchange and magnetostatic interactions in the effect of thermal magnetization of fine-crystalline alloys of highly anisotropic magnetics

The theory of micromagnetism has been applied to a system consisting of plane-parallel layers of a monoaxial magnetic which differ by the orientation of easy magnetization axes to numerically investigate the effect of thermal magnetization which was simulated by varying the anisotropy constant. It has been revealed that the effect of thermal magnetization does not show up if the exchange interaction between the layers is disregarded. An enhancement of magnetostatic interaction, which was simulated by increasing the degree of noncomplanarity of the easy magnetization axes in the system layers results in a reduction of the effect. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 8–11, August, 2007.     

Magnetostatic Green's functions for the description of spin waves in finite rectangular magnetic dots and stripes

We present derivation of the magnetostatic Green's functions used in calculations of spin-wave spectra of finite-size non-ellipsoidal (rectangular) magnetic elements. The elements (dots) are assumed to be single domain particles having uniform static magnetization. We consider the case of flat dots, when the in-plane dot size is much larger than the dot height (film thickness), and assume the uniform distribution of the variable magnetization along the dot height. The limiting cases of magnetic waveguides with rectangular cross-section and thin magnetic stripes are also considered. The developed method of tensorial Green's functions is used to solve the Maxwell equations in the magnetostatic limit, and to represent the Landau–Lifshitz equation of motion for the magnetization of a magnetic element in a closed integro-differential form.     

Magnetic domain configurations in exchange-coupled NiO/Co bilayer films

The magnetic domain configurations of exchange-coupled NiO/Co bilayers were investigated by magnetic force microscopy. These bilayers exhibit a well-defined uniaxial anisotropy resulting from the deposition at oblique incidence of the NiO layer. Two types of magnetic contrast are identified: (i) bipolar contrast due to 180° Néel walls in the parts of the walls which are parallel to the easy axis of magnetization, and (ii) monopolar contrast in the parts of the walls separating domains with meeting head-on magnetizations. These latter domain walls have a zigzag shape which represents a compromise between a decrease in the local density of magnetostatic energy and an increase in the wall length. The effect of the Co thickness of the shape on the domains is also discussed.     

Analysis of checkerboard pattern in ultrathin magnetic films

We discuss the magnetostatic energy of checkerboard domain structures in ultrathin magnetic films (of a few monolayer thickness) and in an atomic monolayer using simple magnetostatic considerations where the easy direction of magnetization is perpendicular to the film. The checkerboard domain size, D, the domain-wall width, ω, the ratio f of the uniaxial surface anisotropy, K_s, to the dipolar energy and the binding energy, (BE), have been calculated numerically with the variational parameter δ and the number of atomic layers, n_l, as parameters.     

Domain size and structure in exchange coupled [Co/Pt]/NiO/[Co/Pt] multilayers

We investigate the competing effects of interlayer exchange coupling and magnetostatic coupling in the magnetic heterostructure ([Co/Pt]/NiO/[Co/Pt]) with perpendicular magnetic anisotropy (PMA). This particular heterostructure is unique among coupled materials with PMA in directly exhibiting both ferromagnetic and antiferromagnetic coupling, oscillating between the two as a function of spacer layer thickness. By systematically tuning the coupling interactions via a wedge-shaped NiO spacer layer, we explore the energetics that dictate magnetic domain formation using high resolution magnetic force microscopy coupled with the magneto-optical Kerr effect. This technique probes the microscopic and macroscopic magnetic behavior as a continuous function of thickness and the interlayer exchange coupling, including the regions where interlayer coupling goes through zero. We see significant changes in domain structure based on the sign of coupling, and also show that magnetic domain size is directly related to the magnitude of the interlayer exchange coupling energy, which generally dominates over the magnetostatic interactions. When magnetostatic interactions become comparable to the interlayer exchange coupling, a delicate interplay between the differing energy contributions is apparent and energy scales are extracted. The results are of intense interest to the magnetic recording industry and also illustrate a relatively new avenue of undiscovered physics, primarily dealing with the delicate balance of energies in the formation of magnetic domains for coupled systems with PMA, defining limits on domain size as well as the interplay between roughness, domains and magnetic coupling.     

Modeling of irreversible switching and viscosity phenomena in perpendicular thin films

We have developed a simple numerical model for simulating domains as well as remanence and viscosity curves in the slow dynamics regime, for thin films characterized by perpendicular magnetization and irregular domain configurations due to strong disorder. The physical system is represented as constituted of identical switching units, described by proper switching field distributions and energy barrier laws for pinning and nucleation processes. The model also includes an effective field which accounts for magnetic forces proportional to magnetization, on average. Simulations of DCD curves show that when the reversal of magnetization is governed by pinning, the coercive field depends on the physical size of the film area on which the external field is applied. In the case of viscosity phenomena described by a linear energy barrier law associated with a single predominant reversal process (pinning or nucleation), universal viscosity curves can be generated by properly transforming the DCD curve of the system. We also demonstrate that a reduction of the maximum viscosity coefficient can coexist with a reduction of the energy barrier heights.     

Domain and wall structures in films with helical magnetization profile

We study soft magnetic bilayers having orthogonal, in-plane easy axes. The layers are thicker than the Bloch wall width linked to the anisotropy, so that a helical magnetization with a large angle exists across the sample thickness. The magnetic domains structure has been investigated at both sample surfaces, using magneto-optical microscopy. The domain structure is found to be similar to that of double films with biquadratic coupling. Two kinds of domain walls are identified, namely with a 90° and 180° rotation of the average magnetization. The detailed structure and energy of these walls are studied by micromagnetic calculations.     

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.     

Diffusion-annihilation and the kinetics of the Ising model in one dimension

The relationship between the one-dimensional kinetic Ising model at zero temperature and diffusion-annihilation in one dimension is studied. Explicit asymptotic results for the average domain size, average magnetization squared, and pair-correlation function are derived for the Ising model, for arbitrary initial magnetization. For the case of zero initial magnetization (m ₀=0, a number of recent exact results for diffusion-annihilation with random initial conditions are obtained. However, for the casem ₀ not equal to zero, the asymptotic behavior turns out to be different from diffusion-annihilation with random initial conditions and at a finite density. In addition, in contrast to the case of diffusion-annihilation, the domain-size distribution scaling functionh(x) is found to depend nontrivially on the initial magnetization. The origin of these differences is clarified and the existence of nontrivial correlations in the initial wall distribution for finite initial magnetization is found to be responsible for these differences. Results of Monte Carlo simulations for the domain size distribution function for different initial magnetizations are also presented.This paper is dedicated to George Weiss on the occasion of his 60th birthday.     

Statistics of irreversible displacements of domain walls in nanowires

The process of quasistatic displacement of domain walls is considered in a nanowire represented as a one-dimensional chain of ferromagnet crystallites. The domain wall pinning due to spatial fluctuations of the anisotropy axes is analyzed. Based on the theory of overshoots of random processes, we have calculated the distribution functions of the initial susceptibility and of the maximal force of interaction of the domain wall with inhomogeneities. These functions are found to be non-Gaussian. We have derived expressions for the magnetization curve and the coercive force, which depend on the length of the chain.     

Micromagnetism in a planar system with a random magnetic anisotropy and two-dimensional magnetic correlations

The hysteresis loops and the micromagnetic structure of a ferromagnetic nanolayer with a randomly oriented local easy magnetization axis and two-dimensional magnetization correlations are studied using a micromagnetic simulation. The properties and the micromagnetic structure of the nanolayer are determined by the competition between the anisotropy and exchange energies and by the dipole–dipole interaction energy. The magnetic microstructure can be described as an ensemble of stochastic magnetic domains and topological magnetization defects. Dipole–dipole interaction suppresses the formation of topological magnetization defects. The topological defects in the magnetic microstructure can cause a sharper change in the coercive force with the crystallite size than that predicted by the random magnetic anisotropy model.     

Effect of interparticle magnetostatic interaction on the magnetization reversal in neodymium-iron-boron alloys

A program for modeling the hysteretic behavior of permanent magnets based on Nd₂Fe₁₄B alloys and visualizing their domain structure was developed on the basis of a phenomenological approach to the elementary event of magnetization reversal of highly anisotropic uniaxial ferromagnets. It is shown that the magnetostatic interaction between microvolumes of the material leads to cooperative magnetization reversal of microvolumes with the formation of reverse-magnetization channels and interaction domains.     

Secondary super-structures in random copolymers

Secondary domain superstructures in correlated random block copolymers are considered theoretically using the concept of the second order parameter related to fluctuations of the local mean block length. It is shown that the size of secondary domains, , is much larger than the primary domain size, L: , while , where is a small parameter defining the composition asymmetry. Different secondary morphologies are characterized. It is also shown that separation of the system in two macroscopic phases with different primary morphologies predicted earlier using the free energy expansion up to ( is the usual order parameter related to local composition) is an artifact of this widely accepted theoretical model. Received 15 July 1998 and Received in final form 18 January 1999