Asymmetric pinning of vortex domain walls in magnetic films in regions with lowered saturation magnetization

The asymmetric pinning of vortex domain walls in a region with a lowered saturation magnetization has been investigated in ferromagnetic films with the in-plane anisotropy. Numerical micromagnetic simulation within the two-dimensional model of the magnetization distribution has been used. The wall structure and the depinning fields in different directions have been investigated depending on the dimensions of the region with lowered saturation magnetization and the film thickness. The physical factors that determine the obtained regularities have been established.     

Velocity of motion of domain walls with vortex structure in multilayer ferromagnetic films

A two-dimensional model of the magnetization distribution has been applied to investigating the influence of the layered structure of a ferromagnetic film in which the layers differ in saturation magnetization M _S on the velocity of the motion of domain walls with a vortex distribution of magnetization. Films with uniaxial planar magnetic anisotropy have been analyzed. It is established that, in three-layer films with values of M _S in the near-surface layers that exceed those of the internal layer in a wide range of the external field, the velocity of motion of the domain wall is higher than in a homogeneous film with the same average saturation magnetization.     

Magnetic anisotropy of Co/Cu/Co nanocrystalline films upon magnetic annealing

The magnetic anisotropy of Co/Cu/Co films with the thickness of the copper spacer corresponding to the antiferromagnetic and ferromagnetic indirect exchange coupling between Co layers has been studied. The films deposited on naturally oxidized (111) Si single crystals were produced by magnetron sputtering. The films were annealed at 240°C. Such an annealing virtually neither changes the grain size nor leads to the mixing of layers; i.e., no disturbance of the coupling type between the cobalt layers takes place. Changes in the surface and induced magnetic anisotropy and in the effective energy of indirect exchange coupling have been studied upon annealing in the presence and absence of a magnetic field. It has been found that the shape of surface inhomogeneities in the films changes upon annealing in the magnetic field applied along the film plane, which substantially affects, the surface anisotropy. In the films characterized by antiferromagnetic coupling, the easy axis of magnetization is induced only in the magnetic fields exceeding the saturation field. The induced-anisotropy constant estimated theoretically agrees well with those determined experimentally.     

Simulation of three-dimensional micromagnetic structures in magnetically uniaxial films with in-plane anisotropy. Dynamics and structural reconstructions

Transition processes in nonequilibrium micromagnetic structures that represent regions of various types of asymmetrical vortex domain walls with closely spaced transition structural elements, including vertical Bloch lines (VBLs), singular points, and clusters consisting of VBLs and singular points, have been studied by the method of three-dimensional numerical simulation of the magnetization behavior. The realization of various scenarios of dynamic behavior, including the annihilation of transition elements accompanied by the liberation of energy and the initiation of wave processes, has been shown to be possible. The simulation was performed for the case of magnetically uniaxial ferromagnetic films with an easy axis parallel to their surface with exact allowance for the inhomogeneous exchange, magnetoanisotropic, and magnetostatic interactions.     

Structure and dynamic properties of asymmetric vortexlike domain walls in inhomogeneous magnetic films with an in-plane anisotropy: I. Equilibrium structures. Nonlinear dynamics in two-layered films

Within the framework of a two-dimensional distribution of magnetization and exact allowance for the basic interactions, including dipole-dipole one, the static properties and nonlinear dynamic behavior of vortexlike domain walls in multilayer magnetically uniaxial films with an in-plane anisotropy have been studied. It has been shown that in such films, just as in single-layer ones, there exist asymmetric vortexlike walls; however, in this case the wall vortices prove to be moved toward the layers with a higher magnetization or toward the layers with a lower anisotropy. At some thicknesses of the layers and magnetization differences in them, the asymmetric Néel walls prove to be unstable. New scenarios of the dynamic transformation of the structure of the walls in multilayer films have been established, which in some cases differ significantly from the appropriate scenarios in the single-layer films.     

Ferromagnetic resonance in a two-layer exchange-coupled ferromagnetic film with a combined uniaxial and cubic anisotropy in the layers

Dynamic properties of ferromagnetic two-layer exchange-coupled (100) films with a combined cubic and uniaxial magnetic anisotropy of layers have been studied numerously upon the magnetization along the [100], [010], and [011] directions. The allowance for cubic anisotropy substantially affects the dependence of the frequencies of the ferromagnetic resonance on the field strength. Repeated changes in the localization of the ferromagnetic-resonance modes between the layers of the film have been found to occur with an increase in the strength of the magnetic field. At a certain relationship between the constants of the combined anisotropy for the directions [010] and [011], an increase in the field leads to a shift of the maximum of the dynamic-susceptibility distribution toward the interlayer boundary without a change in the localization of the modes.     

Effect of magnetic surface anisotropy on domain wall structure in magnetic triaxial films

The influence of the presence of surface anisotropy on the micromagnetic structure of the domain wall in magnetic-triaxial films has been investigated. The investigation method is the numerical minimization of the energy functional of the domain wall used in the two-dimensional model of the distribution of magnetization. Films with different orientations of crystallographic axes with respect to the film surface have been considered. The effect of the surface anisotropy type and surface anisotropy constant K _S value on the stability of different types of domain walls has been found.     

Resonance properties of magnetically anisotropic films with various anisotropy dispersion

On the basis of a statistical model of noninteracting blocks, there is carried out an analysis of the specific features of the spectrum of ferromagnetic resonance in polycrystalline metallic magnetic films, which are connected with the presence of cubic crystallographic anisotropy and induced uniaxial magnetic anisotropy, and also with the presence of an angular dispersion of the crystallographic anisotropy. It is shown that the allowance for the angular dispersion of magnetic anisotropy leads to an asymmetry and a broadening of the integrated resonance curve and also to characteristic angular dependences of the resonance field and of the resonance linewidth.     

Magnetization reversal of Tb-Co/Fe19Ni81 films with a unidirectional anisotropy

Conditions have been found for the realization of induced in-plane uniaxial anisotropy of the amorphous Tb₃₁Co₆₉ films and of unidirectional anisotropy in the Permalloy layers in the composite two-layered Tb₃₁Co₆₉/Fe19Ni81 films. The mechanisms of magnetization reversal in such film structures have been studied in a temperature range of 5–300 K. It has been found that a decrease in temperature leads to a transformation of hysteresis loops, a significant increase in the field of unidirectional anisotropy, and a nonmonotonic change in the coercive force of the Permalloy layer. The regularities found are interpreted taking into account the variation in the properties of the amorphous layer Tb₃₁Co₆₉ with temperature under the assumption on a temperature-induced change in the localization of the interlayer magnetic boundary, which is formed upon a layer-by-layer magnetization reversal of the film structure.     

Effect of the shape anisotropy and configurational anisotropy on the magnetic structure of ferromagnetic nanodots

Processes of magnetization reversal of ordered square arrays of “nanodots” of different geometry coupled by dipole-dipole interaction that were formed by a focused beam of Ga⁺ ions from continuous polycrystalline Co films have been investigated. It has been established that the magnetic structure upon the magnetization reversal is mainly determined by the shape anisotropy of the nanodots. The round and square nanodots undergo magnetization reversal via a magnetic vortex, whereas the rectangular nanodots demonstrate a finite set of single-domain states depending on the orientations of the external magnetic field and easy axis of magnetization. It has been shown that the magnitude of the switching field of arrays of round and square nanodots and the distribution of switching fields in the system of rectangular nanodots upon magnetization reversal along the easy axis is substantially affected by the configurational anisotropy.     

Simulation of three-dimensional micromagnetic structures in magnetically uniaxial films with in-plane anisotropy: Static structures

The possible types of transition structures that can arise between the regions of vortex asymmetric domain walls that exist in magnetically uniaxial permalloy films with in-plane anisotropy have been studied by the method of three-dimensional computer simulation of the magnetization behavior. It has been established that, along with the previously found structures of vertical Bloch lines (VBLs), other types of structures can exist, namely, singular (Bloch) points and clusters that consist of VBLs and Bloch points. Spatial configurations and topological characteristics of transition structures have been calculated numerically.     

Structure of two-dimensional domain walls in two-layer permalloy films with a nonmagnetic interlayer

Structure of domain walls in two-layer Permalloy films separated by a nonmagnetic interlayer has been studied by the numerical minimization of the functional of the total energy of the domain wall in terms of a two-dimensional model of the magnetization distribution with an exact allowance for basic interactions (including exchange, magnetoanisotropic, and dipole-dipole interactions). Differences between the structure of these walls and that of single-layer films of analogous thicknesses have been investigated. The total energy (and its exchange and dipole-dipole components) per unit area of the surface of domain walls in two-layer films has been calculated as functions of the thicknesses of the Permalloy layers and the interlayer. The dependence of the thickness of magnetic layers at which there occurs a transition from the walls of the same type as in single-layer films of the corresponding thickness to walls of another type on the thickness of the interlayer has also been constructed. A comparison of the curve of this dependence with the experimental data is carried out.     

On the vortex nature of the magnetization distribution in magnetic films

Fine features of the vortex structure of asymmetric domain walls have been studied on the basis of a numerical minimization of the functional of the energy of magnetic (uniaxial and triaxial) films with an exact allowance for the basic interactions, including dipole-dipole, within the framework of a two-dimensional model of magnetization distribution.     

Nonlinear dynamics of domain walls in three-layer magnetic films with nanosized layers

Nonstationary dynamics of domain walls in thin multilayer magnetic films with nanosized layers has been investigated using numerical solution of the nonlinear Landau-Lifshitz equation with exact consideration of all major interactions: exchange, magnetoanisotropic, and dipole-dipole (in continuum approximation). Scenarios have been established of nonlinear dynamic transformation of internal wall structure in three-layer films with layers with different saturation magnetization. It has been demonstrated that any velocities of nonstationary motion of the walls (average over the period, maximum over the period, preset at fixed fields) in layered films with the magnetizations of middle layers lower than the magnetization of outer layers are always higher than the velocities of one-layer films of the same thickness with the same average saturation magnetization as in multilayer films.     

Perpendicular magnetic anisotropy in nanocomposite Nd–Fe–B/FeCo bilayer films

Nd–Fe–B/FeCo bilayer films with Mo underlayers and overlayers have been investigated. All the samples have perpendicular anisotropy and the magnetization is found to increase with increasing FeCo layer thickness (d_FeCo) and the coercivity decreases with increasing d_FeCo. The maximum energy-product is 20 MGOe for d_FeCo = 5 nm. The enhancement of the remanence and energy products in the bilayer films is attributed to the exchange coupling between the magnetically soft and hard phases.     

Phase diagram of magnetic structures in Fe/Cr/Fe films with nanoscale geometric inhomogeneities of interfaces

Results of an analysis of magnetic structures (mutual orientations of the iron-layer magnetizations) in three-layered Fe/Cr/Fe films formed due to the exchange interactions inside the layers of iron and chromium and on the Fe/Cr interfaces are given. The analysis was performed under the following assumptions: (1) the iron layers are ferromagnetic, and the magnetic structure of chromium layers has the form of transverse linearly polarized spin-density waves; (2) the iron-chromium exchange interaction is considered as a weak disturbance as compared to the exchange interactions inside the iron and chromium layers; therefore, they were considered as first-order and second-order perturbation-theory corrections; (3) the relative value of these corrections depends on the degree of roughness of the Fe/Cr interfaces; it was assumed that the roughness has a nanometer scale. With such approximations, the mutual orientation of the magnetizations of iron layers can be parallel, antiparallel, or noncollinear. The limits of stability of these structures depending on the thickness of the chromium interlayer and on the ratio of the first-to-second-order corrections have been determined. The main attention was paid to the conditions of the loss of stability with respect to changes in the phase of the spin-density wave, which can result in jumps in the curves of magnetization and magnetization reversal of the Fe/Cr films.     

Substrate temperature dependence of chemical state and magnetoresistance characteristics of Co–TiO2 nanocomposite films

Co−TiO₂ nanocomposite films were prepared via magnetron sputtering at various substrate temperatures. The films comprise Co particles dispersed in an amorphous TiO₂ matrix and exhibit coexisting ferromagnetic and superparamagnetic properties. When the substrate temperature increases from room temperature to 400 °C, Co particles gradually grow, and the degree of Co oxidation significantly decreases. Consequently, the saturation magnetization increases from 0.13 to 0.43 T at the same Co content by increasing the substrate temperature from room temperature to 400 °C. At a high substrate temperature, conductive pathways form among some of the clustered Co particles. Thus, resistivity rapidly declines from 1600 to 76 μΩ·m. The magnetoresistive characteristic of Co−TiO₂ films is achieved even at resistivity of as low as 76 μΩ·m. These results reveal that the obtained nanocomposite films have low Co oxidation, high magnetization and magnetoresistance at room temperature.     

Structural, optical and magnetic properties of Eu-doped ZnO films

Polycrystalline Zn_1−xEu_xO (x = 0, 0.02, 0.05) films were deposited on silicon (1 0 0) substrates by radio-frequency magnetron sputtering. The structural, optical and magnetic properties of the films were investigated. The results from both the X-ray diffraction and photoluminescence spectra reveal that Eu³⁺ ions successfully substitute for Zn²⁺ ions in the ZnO lattice. The magnetic field and temperature dependence of magnetization curves demonstrate that the Zn_0.95Eu_0.05O films are ferromagnetic at room temperature. No impurity phase was found in Eu-doped films with X-ray diffraction, Raman spectroscopy and zero-field-cooled measurements. The ferromagnetism is attributed to the intrinsic property of Eu-doped ZnO films and could be interpreted by the bound-magnetic-polaron model.     

Tb doped CoNbZr soft magnetic films with high anisotropy field for applications in GHz frequency region

CoNbZr films for an adjustable magnetic anisotropy field H_k by doping with rare-earth of different atomic ratio Tb element were obtained in this work. The effect of Tb addition ranged from 0 to 4 at.% on the magnetic properties of the amorphous CoNbZr films was further investigated. The results show that the magnetic anisotropy field H_k increases sharply with the addition of Tb while the coercivity H_ch along the hard axis and H_ce along the easy axis change slightly with increasing Tb content in the films. As a consequence, CoNbZr film doped with 2 at.% of Tb exhibits excellent soft magnetic properties with a saturation magnetization 4πM_s of 8.9 kG, a hard axis coercivity H_ch of 1.79 Oe, a easy axis coercivity H_ce of 1.4 Oe and a magnetic anisotropy field H_k of 87 Oe. The measured ferromagnetic resonance frequency f_FMR of this film is 2.30 GHz. The real permeability μ′ is about 100, which is maintained up to 2 GHz. In addition, there is a broad band of the imaginary permeability μ″ over a large frequency band, indicating high losses. Therefore, Tb doped CoNbZr film is an excellent candidate for high frequency applications such as electromagnetic interference suppressors.     

Microstructure and thickness dependent magnetic properties of nanogranular Co-Zn-O thin films for microwave applications

Co-based granular thin films with in-plane anisotropy were deposited on Si substrate by magnetron sputtering. The films have a phase structure of Co nanocrystallites and amorphous Zn-O inter-granular phases. The Co nanograins with uniform size of 8-10 nm are evenly distributed in the amorphous matrix. This structure gives the films relatively high resistivities. The as-deposited films with thickness larger than 100 nm have low coercivity (<10 Oe) along both easy and hard directions. The dynamic properties in the frequency range up 5 GHz for the films with various thicknesses have been investigated. High values of permeability (μ′ up to 560 and μ″ up to 1000) and ferromagnetic resonance frequency (FMR) up to 4.1 GHz have been obtained in these films. The FMR frequency decreases with increasing thickness, because of the increases in real and imaginary permeabilities. The high frequency characteristics have complicated dependences on the resistivity, anisotropy field, and magnetization. The microwave properties of Co-Zn-O films can be adjusted in a relatively wide range by changing film thickness, which makes these films promising for absorber applications.