The spontaneous formation of a vortex structure in a type II superconductor-ferromagnet bilayer

The conditions for the formation of a vortex structure in a thin superconducting film under the action of a stray field of stripe domain structure of a uniaxial ferromagnet are determined. The critical magnetization of the magnetic material is calculated, above which the mixed state of the superconductor becomes energetically favored over the Meissner phase. It is shown that the critical magnetization decreases monotonically with decreasing thickness of the superconducting film and is of the order of ten gauss in typical actual situations. The critical-current anisotropy in a superconducting film with an induced vortex structure is discussed qualitatively.     

Phase transitions in uniaxial ferromagnetic film covered by superconducting layers

The phase diagram and the single-domain uniform state for a uniaxial ferromagnetic film with the superconducting layers covering one or both sides of a ferromagnet are investigated. The superconductor is supposed to be a second-order one and the interaction between the magnetic sub-system and with the conductivity electrons in a superconductor is purely electromagnetic and the vortices in a superconductor are pinned. The critical thickness of the magnetic film for which the uniform state becomes absolutely stable is calculated when the external magnetic field is supposed to be in-plane of the film. It is shown that the critical thickness of the film from the magnetic material with the quality factor Q>1 monotonically decreases as the magnetic field increases in the range from zero value to the value of the transition field where the collinear phase transforms into the angular (canted) phase. Further the critical thickness increases with the increase of the field. The quasi-single-domain magnetic film states were considered when the film thickness was close to the critical one. It is shown that for a thin isolated magnetic film the domain period exponentially increases with the decrease of the film thickness. Such dependence, however for the film with double-side superconducting cover and close to the transition into the single domain state becomes logarithmic and for the film covered by superconductor only on the one side varies as the power series. The single-domain state existence and the asymptotic behaviour of the domain structure is explained by the features of the asymptotic behaviour of the domain walls within the system. As for isolated magnetic film and for a film with the superconductor cover layers the transition from the collinear phase to the inhomogeneous state is the second-order phase transition and the transition from the uniform angular phase to the inhomogeneous phase is the first-order transition.     

Influence of the film thickness and additional elements (Al,O, and N) on the properties of FeCo film structures

The magnetic properties and domain structure of FeCoAlON thin films with thicknesses varying from 55 to 550 nm have been studied, and conditions favoring preparation of FeCoAlON films with uniaxial anisotropy in the direction normal to the film plane, which is required for designing “perpendicular” super-high-density information recording, have been established. In FeCoAlON films with a thickness up to 300 nm, the domain structure consists of cross-linked domain walls, because strong demagnetizing field suppresses formation of stripe domains. After the film thickness has reached 320 nm, cross-linked domain walls transform into stripe domains, with uniaxial anisotropy in the film plane disappearing, to become replaced by uniaxial anisotropy in the direction normal to the film plane, which can be assigned to magnetoelastic stresses induced by nitrogen atoms filling up interstitial space in the (110) plane. A further increase in the film thickness (up to 550 nm) leads to a rotational anisotropy due to the increase of nitrogen concentration in interstitials and the increase of magnetoelastic stresses.     

The origin of noncollinear anisotropies and asymmetric magnetization reversal in FM/AFM bilayer system

The effects of the magnitude of the uniaxial anisotropy of a ferromagnet and the cooling field on the noncollinearity between uniaxial anisotropy and induced unidirectional anisotropy in a ferromagnet/antiferromagnet bilayer system are investigated. A diagram of noncollinear anisotropies and relative negative (positive) exchange bias field dependence upon cooling field and uniaxial anisotropy of the ferromagnet is obtained. The numerical result shows that the emergence of noncollinear anisotropies originates from the action of the cooling field and uniaxial anisotropy of the ferromagnet. The noncollinearity strongly depends on the magnitude of cooling field and uniaxial anisotropy of the ferromagnet. Moreover, the effect of noncollinear anisotropies and applied field on asymmetric magnetization reversal is also investigated. Amazingly, when the magnetic field is applied collinearly with unidirectional anisotropy, the hysteresis loop of ferromagnet/antiferromagnet bilayers is always symmetric even if there are noncollinear anisotropies. Our results indicate that the asymmetry of the hysteresis loop only originates from the noncollinearity between the induced unidirectional anisotropy and the applied field, rather than from the noncollinearity between the uniaxial and unidirectional anisotropies.     

Recovery of soft magnetic properties of FeNiSm films by Ta interlayer

The magnetic properties of FeNiSm thin films with different thicknesses, different Ta interlayer thicknesses and different numbers of Ta interlayers were investigated. The single layer FeNiSm shows in-plane uniaxial anisotropy at a thickness below critical value, but shows weak perpendicular anisotropy with a stripe domain structure at thickness above the critical value. Experiments indicate that one or more Ta interlayers inserted into thick FeNiSm films with weak perpendicular anisotropy were effective not only in canceling the perpendicular anisotropy, but also in recovering the in-plane uniaxial anisotropy. Blocking of the columnar growth of FeNi grains by the Ta interlayer is considered to be responsible for this spin reorientation phenomenon. Moreover, the magnetization reversal mechanism in FeNiSm films with uniaxial anisotropy can be ascribed to coherent rotation when the applied field is close to the hard axis and to domain-wall unpinning when the applied field is close to the easy axis. The dynamic magnetic properties of FeNiSm films with uniaxial anisotropy were investigated in the frequency range 0.1-5 GHz. The degradation of the soft magnetic properties of magnetic thin films due to the growth of columnar grains can be avoided by insertion of a Ta interlayer.     

Domain structure in magnetic films with a saturation magnetization higher than the anisotropy field

The domain structure (DS) of yttrium-iron garnet films with uniaxial anisotropy fields higher than ∼120 Oe was found to have a 3D character: there is a stripe domain structure of a certain type in the surface layer and a structure of another type in the film bulk. It was revealed that in the absence of an external magnetic field, the boundaries of both DSs are almost perpendicular, whereas with an increase in an external field applied in the film plane along the boundaries of the interior-volume DS, the boundaries of the surface DS are gradually reoriented along the external field. This phenomenon is theoretically explained on the basis of the micromagnetic model, which describes DS formation in ferrite films.     

Thickness dependence of magnetic domain formation in La0.6Sr0.4MnO3 epitaxial thin films studied by XMCD-PEEM

We have used photoelectron emission microscopy (PEEM) and X-ray magnetic circular dichroism (XMCD) to study the effect of thin film thickness on the magnetic domain formation in La_0.6Sr_0.4MnO₃ samples that were epitaxially grown on stepped SrTiO₃ (0 0 1) substrates. The magnetic image exhibited a stripe structure elongated along the step direction, irrespective of film thickness, suggesting that uniaxial magnetic anisotropy induced by step-and-terrace structures plays an important role in the magnetic domain formation. Additional domains evolved gradually with increasing film thickness. In these domains, the direction of magnetization differed from the step direction due to biaxial magneto-crystalline anisotropy. The evolution of additional magnetic domains with increasing film thickness implies that a competition exists between the two anisotropies in LSMO films.     

Influence of surface and bulk anisotropies on domain structures in a thin plate

The method of micromagnetic modeling is used to investigate the influence of the surface anisotropy of easy plane type on the domain structures in a thin uniaxial magnetic plate for different values of the bulk anisotropy constant. The easy magnetization direction is oriented perpendicularly to the plate plane. It is established that for low and high bulk anisotropy values, the surface anisotropy has no significant effect on the magnetization field M. For some intermediate values of the bulk anisotropy constant, the surface anisotropy can influence the structure of the domain boundaries and change qualitatively the domain structure of the sample.     

Theoretical investigation of ferromagnetic resonance in a ferromagnetic thin film with external stress anisotropy

We use the ferromagnetic resonance(FMR)method to study the properties of ferromagnetic thin film,in which external stress anisotropy,fourfold anisotropy and uniaxial anisotropy are considered.The analytical expressions of FMR frequency,linewidth and the imaginary part of magnetic susceptibility are obtained.Our results reveal that the FMR frequency and the imaginary part of magnetic susceptibility are distinctly enhanced,and the frequency linewidth or field linewidth are broadened due to a strong external stress anisotropy field.The hard-axis and easy-axis components of magnetization can be tuned significantly by controlling the intensity and direction of stress and the in-plane uniaxial anisotropy field.     

The effect of friction on nonlinear oscillations of interacting domain walls in an external periodic field

The effect of dissipation on nonlinear oscillations in a system of domain walls experiencing an external harmonic field is studied numerically. The problem is formulated for uniaxial ferromagnet films, with the easy magnetic axis being perpendicular to the surface and with the harmonic field being aligned with the axis. Account is taken of the dynamic redistribution of magnetic poles on the film surface, which enables one to derive, in a natural way, an expression for a restoring force acting on the domain walls. The force is a nonlinear function of domain-wall displacement from the equilibrium position. It is found that the domain walls may execute complicated steady-state quasi-periodic oscillations and long-term chaotic oscillations. Attractors in the phase space of the system are determined.     

Pinning of vortices by the domain structure in a two-layered type II superconductor-ferromagnet system

The effectiveness of magnetic pinning of vortices in a layered system formed by a uniaxial ferromagnet and type II superconductor is considered. It is shown that, irrespective of the saturation magnetization of the ferromagnet, the energy of pinning at the domain structure does not exceed, in order of magnitude, the energy of artificial pinning at a column-type defect. The limitation of pinning energy is caused by the interaction of external vortices with a spontaneous vortex lattice formed in the superconducting film when the magnetization of the ferromagnetic film exceeds the critical value.     

The effect of stripe domain structure on dynamic permeability of thin ferromagnetic films with out-of-plane uniaxial anisotropy

The permeability is calculated for a thin ferromagnetic film with the stripe domain structure and out-of-plane uniaxial magnetic anisotropy. Analytical expressions for the frequency dependence of components of permeability tensor are derived with the use of the Smit–Beljers method, with the thickness of domain walls and the domain wall motion being neglected. The effect of the domain width and the angle between the anisotropy axis and the film plane on the frequency dependence of the permeability is analyzed. General equations relating the static permeability components and the ferromagnetic resonance frequencies are found. The results of the approach are applied to the derivation of the constraint for the microwave permeability of thin ferromagnetic films. The analysis of the constraint as a function of the axis deviation angle, the domain aspect ratio and the damping parameter allows the conditions to be found for maximal microwave permeability. The results obtained may be useful in connection with the problem of developing high-permeable microwave magnetic materials.     

Uniaxial magnetocrystalline anisotropy of metal/semiconductor interfaces: Fe/ZnSe(001)

A theoretical study of the magnetic moments and the in-plane magnetic anisotropy of an interface between a cubic ferromagnet and a cubic semiconductor, Fe/ZnSe(001), is presented. Theory confirms the observed, much debated, uniaxial anisotropy of the iron film. This result is important since the calculations are for perfect interfaces with squarelike environments, proving that the fourfolded symmetry of the interface Fe atoms is broken beyond the nearest neighboring semiconducting layer, effects that are usually assumed small. It is demonstrated how the uniaxial anisotropy is produced by the directional covalent bonds at the interface, even without atomic relaxations.     

A Geometric Interpretation of the Effective Uniaxial Anisotropy Field in Magnetic Films

It is shown that the effective uniaxial anisotropy field that is usually applied in thin magnetic films (TMFs), which is noncollinear to the magnetization vector, is insufficient for deeper understanding of these processes, although it explains many physical processes in films. The analysis of the magnetization discontinuity in films under certain conditions yields the component of the effective uniaxial anisotropy field collinear to the magnetization vector. This component explains the magnetization discontinuity and allows one to speak of the total effective uniaxial anisotropy field in TMFs.     

Domain structure of (011) crystalline garnet ferrite plates

The domain structure in (011) crystalline garnet ferrite plates is studied with allowance for induced uniaxial anisotropy and two-constant cubic anisotropy. It is shown that the inclusion of the second constant of cubic anisotropy greatly affects the orientational phase diagram and also the topology of magnetic inhomogeneities in a given magnet. It is found, in particular, that 180°non-Bloch domain walls may appear in a certain range of combined anisotropy constants, causing a continuous change in the wall orientation.     

Proximity effect and spontaneous vortex phase in planar SF structures

The proximity effect in SF structures is examined. It is shown that, due to the oscillations of the induced superconducting order parameter in a ferromagnet, the critical temperature of an SF bilayer becomes minimal when the thickness of the ferromagnetic layer is close to a quarter of the period of spatial oscillations. It is found that the spontaneous vortex state arising in the superconductor due to the proximity of the magnetic domain structure of a ferromagnet brings about noticeable magnetoresistive effects.     

Angular control of multi-mode resonance frequencies in obliquely deposited CoZr thin films with rotatable stripe domains

We investigate the angular-dependent multi-mode resonance frequencies in CoZr magnetic thin films with a rotatable stripe domain structure.A variable range of multi-mode resonance frequencies from 1.86 GHz to 4.80 GHz is achieved by pre-magnetizing the CoZr films along different azimuth directions,which can be ascribed to the competition between the uniaxial anisotropy caused by the oblique deposition and the rotatable anisotropy induced by the rotatable stripe domain.Furthermore,the regulating range of resonance frequency for the CoZr film can be adjusted by changing the oblique deposition angle.Our results might be beneficial for the applications of magnetic thin films in microwave devices.     

Two-dimensional micromagnetic simulation of domain structures in films with combined anisotropy

The transformation of the domain structure of micrometer-thick films with variations in the induced uniaxial anisotropy constant with the easy magnetization axis perpendicular to the film surface has been investigated using numerical micromagnetic simulation in the framework of a two-dimensional model of the magnetization distribution. The case where the tetra-axial crystallographic anisotropy exists in the film with uniaxial magnetic anisotropy has been considered. The transformation of the open domain structure into the structure with a magnetic flux closed inside the sample has been investigated in detail, and new types of 109-degree and 90-degree vortex-like domain walls and periodic domain structures have been obtained.     

Piezo‐voltage control of magnetization orientation in a ferromagnetic semiconductor

The possibility to control magnetic properties via electrical fields is investigated in a piezoelectric actuator/ferromagnetic semiconductor thin film hybrid structure. Using anisotropic magnetoresistance techniques, the magnetic anisotropy and the magnetization orientation within the plane of the ferromagnetic film are measured quantitatively. The experiments reveal that the application of an electrical field to the piezoelectric actuator allows to continuously and reversibly rotate the magnetization orientation in the ferromagnet by about 70°. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

具有条纹磁畴结构的NiFe薄膜的制备与磁各向异性研究

具有条纹磁畴结构的磁性薄膜表现出面内转动磁各向异性,对于解决高频电子器件的方向性问题起着至关重要的作用.本文采用射频磁控溅射的方法,研究了NiFe薄膜的厚度、溅射功率密度、溅射气压等制备工艺参数对条纹磁畴结构、面内静态磁各向异性、面内转动磁各向异性、垂直磁各向异性的影响规律.研究发现,在功率密度15.6 W/cm~2与溅射气压2 mTorr(1 Torr=1.33322×102Pa)下生长的NiFe薄膜,表现出条纹磁畴的临界厚度在250 nm到300 nm之间.厚度为300 nm的薄膜比250 nm薄膜的垂直磁各向异性场增大近一倍,从而磁矩偏离膜面形成条纹磁畴结构,并表现出面内转动磁各向异性.高溅射功率密度可以降低薄膜出现条纹磁畴的临界厚度.在相同功率密度15.6 W/cm~2下生长300 nm的NiFe薄膜,随着溅射气压由2 mTorr增大到9 mTorr,NiFe薄膜的垂直磁各向异性场逐渐由1247.8 Oe(1 Oe=79.5775 A/m)增大到3248.0 Oe,面内转动磁各向异性场由72.5 Oe增大到141.9 Oe,条纹磁畴周期从0.53μm单调减小到0.24μm.NiFe薄膜的断面结构表明柱状晶的形成是表现出条纹磁畴结构的本质原因,高功率密度下低溅射气压有利于柱状晶结构的形成,表现出规整的条纹磁畴结构,高溅射气压会导致柱状晶纤细化,面内转动磁各向异性与面外垂直磁各向异性增强,条纹磁畴结构变得混乱.