On the effective magnetization and uniaxial anisotropy of permalloy films

The values of the effective magnetization and uniaxial induced anisotropy were measured on permalloy films, vacuum deposited on unheated glass slides, by the method of local ferromagnetic resonance. The double resonance curves of these films indicate the existence of two magnetically different components; to both components there correspond different values of the effective magnetization and uniaxial anisotropy. These quantities have different local and time variations for each component. The results of measurement agree with the recently proposed model of the stratification of thin ferromagnetic films.The authors thank J. Kaczér and F. Kroupa for valuable discussions.     

Determination of the in-plane anisotropy field in hexagonal systems via rotational magnetization: Theoretical model and Monte Carlo simulations

The magnetic anisotropy field in thin films with in-plane uniaxial anisotropy can be deduced from the VSM magnetization curves measured in magnetic fields of constant magnitudes. This offers a new possibility of applying rotational magnetization curves to determine the first- and second-order anisotropy constant in these films. In this paper we report a theoretical derivation of rotational magnetization curve in hexagonal crystal system with easy-plane anisotropy based on the principle of the minimum total energy. This model is applied to calculate and analyze the rotational magnetization process for magnetic spherical particles with hexagonal easy-plane anisotropy when rotating the external magnetic field in the basal plane. The theoretical calculations are consistent with Monte Carlo simulation results. It is found that to well reproduce experimental curves, the effect of coercive force on the magnetization reversal process should be fully considered when the intensity of the external field is much weaker than that of the anisotropy field. Our research proves that the rotational magnetization curve from VSM measurement provides an effective access to analyze the in-plane anisotropy constant K ₃ in hexagonal compounds, and the suitable experimental condition to measure K ₃ is met when the ratio of the magnitude of the external field to that of the anisotropy field is around 0.2. Supported by the National Natural Science Foundation of China (Grant Nos. 90505007 and 10774061) Recommended by LI FaShen     

Magnetization curves of randomly oriented ferromagnetic single-domain nanoparticles with combined symmetry of magnetic anisotropy

The magnetization curves of randomly oriented nanoparticles with combined symmetry of magnetic anisotropy were studied. The composite mode of the Stoner–Wolfarth model has been used. In terms of this model each nanoparticle is characterized by random cubic crystalline magnetic anisotropy and by random uniaxial magnetic anisotropy. The series of simulated magnetization curves have been obtained. Each curve corresponds to different contributions of cubic and uniaxial magnetic anisotropy energy to the full energy of an individual nanoparticle k_u. Within this series we discuss the values of remnant magnetization, coercive force, both initial and maximal susceptibilities as the function of k_u. It is found that the magnetic properties are not monotonous functions of k_u. We discuss the possibility of comparing the calculated magnetization curves with the experimental curves in order to obtain new information on the magnetic constant.     

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.     

小尺寸正方形铁磁薄膜边界效应对磁化翻转过程的影响

用自旋动力学方法系统地研究磁偶极相互作用表现的边界效应对小尺寸正方形铁磁薄膜的磁化翻转过程的影响.在确定的磁偶极相互作用强度下,针对不同的单轴各向异性强度和不同的磁化角(外磁场与易轴间的夹角),具体给出矫顽场与磁化角及单轴各向异性强度之间的依赖关系和-些有代表性的磁滞回线,并给出磁化翻转过程中-些有代表性的微观磁结构.模拟结果表明:磁偶极相互作用表现的边界钉扎作用与单轴各向异性场之间的竞争决定磁滞回线的形状和矫顽场的大小,从而在不同磁化角情况下会导致不同的矫顽场机理.本文提出可有效地描述正方形铁磁性薄膜复杂微观磁畴结构的形成与演变的五磁畴模型.这种五磁畴模型既能直接揭示单轴各向异性正方形铁磁薄膜的几何特性和物理特性,也方便于磁化翻转过程的分析.     

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.     

Magnetization and magnetocrystalline anisotropy in YCo4B compound

Easy and hard magnetization curves of YCo₄B compound have been measured in the temperature range from 1.5 to 300 K. It was found that the uniaxial magnetic anisotropy field decreases with decreasing temperature, and the magnetic anisotropy changes from the easy c-axis to the easy cone at approximately 150 K. The easy and hard magnetization curves did not cross up to 6 T. High field susceptibility of the compound for magnetic field parallel to the alignment direction seems different from that for a field perpendicular to the alignment direction. A jump was observed along the easy magnetization curve at 1.5 and 77 K. The critical field of the jump is about 1.5 T at 1.5 K and 1.2 T at 77 K. The jump was shown to be reversible at 1.5 K by down hill measurement.     

Influence of induced uniaxial anisotropy on the domain structure and phase transitions of yttrium-iron garnet films

The effect of induced uniaxial anisotropy on the properties and parameters of the domain structure and phase transitions in yttrium-iron garnet (YIG) films is investigated. Based on the measurements and the derived formulas we determine the difference between the magnetization and the uniaxial anisotropy field for each of the films. We have also measured the parameters of the domain structures and phase transitions of the films for the magnetization parallel and perpendicular to the projections of the [111] crystallographic axes onto the plane of the film. We find that films of pure YIG films grown in (111) are characterized by the existence of some critical value of the uniaxial anisotropy field. It is found that for films in which the uniaxial anisotropy field is larger than this critical value and films in which it is less than this critical value, such parameters of the domain structures as the ratio of the width of the domains to the film thickness, the orientation of the magnetization of the domains, the orientation of the domain boundaries, and the magnitudes of the phase transition fields differ substantially. Fiz. Tverd. Tela (St. Petersburg) 41, 2034–2041 (November 1999)     

Optical measurement of magnetic anisotropy in thin garnet films

This paper describes an improved optical method for measuring locally the cubic and uniaxial magnetic anisotropy fields in thin garnet films. The derivative of the in-plane component of the magnetization is measured, using a double modulation technique which combines polarization modulation with field modulation. A simple graphical method is devised to calculateH _k andH _u from the extrema in this derivative curve. The results of measurements on magnetic garnet films obtained by different methods are compared. Local measurements of the anisotropy induced by substrate facet strain are described.     

Field-induced spin-reorientation transitions in magnetic superlattices with uniaxial anisotropy and biquadratic exchange

Phase transitions induced by an external field are investigated in magnetic multilayer systems with uniaxial anisotropy and biquadratic exchange. A magnetic field directed perpendicular to the plane of the layers changes the effective anisotropy and exchange constants, determining the orientation of the magnetization in the plane of the layers, and can give rise to spin-reorientation transitions. All possible types of such transitions are investigated for the case of uniaxial anisotropy, which differs substantially from the case of cubic anisotropy by the different renormalization of the effective anisotropy constants. Fiz. Tverd. Tela (St. Petersburg) 41, 461–463 (March 1999)     

Ferromagnetic resonance study of the effect of elastic stresses on the anisotropy of magnetic films

The distribution of the magnitude and direction of the uniaxial magnetic anisotropy field over the area of permalloy films obtained by thermal evaporation in vacuum was studied using a scanning ferromagnetic resonance spectrometer. The films were deposited on glass substrates subjected to bending stress in the presence of an in-plane static magnetic field. Depending on the character of the elastic-stress distribution over a local spot of a film, the uniaxial anisotropy induced by a magnetic field is either enhanced or completely compensated, which is accompanied by a significant change in the direction of the easy axis of magnetization. The observed effects are in good agreement with phenomenological calculations.     

Ferromagnetic resonance features in anisotropic magnetic films with a metastable state of magnetic moment

In experiments on single-domain magnetic films with uniaxial in-plane anisotropy, a new homogeneous ferromagnetic resonance peak was observed in a planar magnetic field oriented at an angle to the easy magnetization axis and directed opposite to the magnetization projection onto the field direction. The peak was observed in fields smaller than the magnetization reversal field of the film, and the origin of the peak was found to be related to the metastable state of the magnetic moment. A good agreement was obtained between phenomenological calculations and experimental data.     

Anisotropy and dynamic properties of Co2MnGe Heusler thin films

Co₂MnGe films of 30 and 50 nm in thickness were grown by RF-sputtering. Their magnetic anisotropies, dynamic properties and the different excited spin wave modes have been studied using conventional ferromagnetic resonance (FMR) and Microstrip line FMR (MS-FMR). From the in-plane and the out-of-plane resonance field values, the effective magnetization (4πM_eff) and the g-factor are deduced. These values are then used to fit the in-plane angular-dependence of the uniform precession mode and the field-dependence of the resonance frequency of the uniform mode and the first perpendicular standing spin wave to determine the in-plane uniaxial, the four-fold anisotropy fields, the exchange stiffness constant and the magnetization at saturation. The samples exhibit a clear predominant four-fold magnetic anisotropy besides a smaller uniaxial anisotropy. This uniaxial anisotropy is most probably induced by the growth conditions.     

Magnetic anisotropy of the VBO<Subscript>3</Subscript> and CrBO<Subscript>3</Subscript> transition-metal borates

Temperature and field dependences of the magnetization of VBO₃ and CrBO₃ single crystals with the magnetic field applied parallel and perpendicular to the (111) basal plane were measured. VBO₃ was found to have a considerable uniaxial anisotropy with a field H_a≈6.25 T. CrBO₃ was shown to exhibit not only uniaxial but also hexagonal anisotropy. The experimental anisotropy constants were estimated, and their temperature dependences are presented.     

An approach to Stoner and Wohlfarth's historical problem based on Fourier analysis

The long known angular delay δ of magnetization with respect to the field, for a magnetic object with uniaxial anisotropy, is treated by means of a Fourier analysis. This way analytical Fourier expansions are obtained for the curves of sin δ versus the angle γ between the field and the easy axis, and the corresponding harmonic coefficient tables have been numerically calculated. For both high and low values of the field, a close agreement with respect to the numerical iterative solution has been found.     

Exchange bias for ferromagnetic/antiferromagnetic bilayers with the uniaxial anisotropy being misaligned with the exchange anisotropy

Using the principle of minimal energy and S-W model, the exchange bias for ferromagnetic/antiferromagnetic bilayers has been investigated when the uniaxial anisotropy is misaligned with the exchange anisotropy. According to the relation between the energy of the bilayer and the orientation of ferromagnetic magnetization, it is found that the bilayer will be in the monostable state or bistable state when the external field is absent in the initial magnetization state. The monostable state or bistable state of the bilayer, which determines the angular dependence of exchange bias directly, is controlled by the competition between the exchange anisotropy and uniaxial anisotropy. When the applied field is parallel to the intrinsic easy axes and intrinsic hard axes, one of the switching fields of the hysteresis loop shows an abrupt change, while the other keep continuous by analyzing the magnetization reversal processes. Consequently, the exchange bias field and the coercivity will show a jump phenomenon. The numerical calculations indicate that both the magnitude and direction of the exchange anisotropy will significantly affect the angular dependence of exchange bias. The jump phenomenon of exchange bias is an intrinsic property of the bilayer, which is dependent on the interfacial exchange-coupling constant, the orientation of the exchange anisotropy, the thickness and uniaxial anisotropy constant of the ferromagnetic layer.     

交换偏置系统中的反铁磁磁化与自旋波

采用自由能变分法研究了铁磁/反铁磁双层膜系统在反铁磁层存在净磁化下的自旋波谱.本模型中铁磁薄层具有单轴磁晶各向异性和立方磁晶各向异性,反铁磁层仅具有单轴磁晶各向异性,但厚度有限,推导出了系统铁磁共振频率的表达式.结果表明：系统的自旋波谱分光学模和声学模两种,其中光学模仅在反铁磁层存在净磁化时得到激发.自旋波谱可按外磁场强度的变化情况分为强弱两支;区分强磁场和弱磁场的临界场依赖于铁磁/反铁磁间的交换作用,反铁磁层的磁化强度以及反铁磁层的厚度等.交换偏置场对光学模的影响明显于声学模,而反铁磁的净磁化和其厚度对系统的影响紧密联系,难以区分.但当反铁磁层净磁化很小可忽略时,系统只存在声学模激发. 关键词： 铁磁/反铁磁双层膜 反铁磁层净磁化 光学模 声学模     

Equilibrium states and quasi-static magnetization switching of a multilayer structure

The equilibrium orientations of magnetic moments that correspond to various values and directions of the biasing field are found in a set of magnetic films with cubic crystalline anisotropy and uniaxial induced anisotropy. The films are coupled by exchange interaction of the antiferromagnetic type. Field intervals are established where noncollinear and bistability states causing orientational phase transitions and hysteresis exist. Ninety degree magnetization switching (per switching cycle) of the magnetic moments of the films, as well as an orientational phase transition of bifurcation character, is discovered. Hysteresis loops for 180° in-plane magnetization switching are constructed.     

Hysteresis and rotational hysteresis of textured polycrystalline magnets

A system of magnetic particles with uniaxial anisotropy is considered. The orientation of the particles is described by a distribution function, representing the texture by a single integer n. In each particle, two elementary processes of the magnetization reversal of the particles are taken into account, the coherent rotation of the magnetization and the pinning of domain walls. In the framework of this model the hysteresis loops including minor loops and virgin curves and the rotational hysteresis are computed, where arbitrarv angles between the texture axis and the external field are taken into consideration.     

Interface biquadratic coupling and magnon scattering in exchange-biased ferromagnetic thin films grown on epitaxial FeF2

The magnetic anisotropy of ferromagnetic (FM) Ni, Co, and Fe polycrystalline thin films grown on antiferromagnetic (AF) FeF(2)(110) epitaxial layers was studied, as a function of temperature, using ferromagnetic resonance. In addition to an in-plane anisotropy in the FM induced by fluctuations in the AF short-range order, a perpendicular (biquadratic) magnetic anisotropy, with an out-of-plane component, was found which increased with decreasing temperature above the AF Neél temperature (T(N) = 78.4 K). This is a surprising result given that the AF's uniaxial anisotropy axis was in the plane of the sample, but is consistent with prior experimental and theoretical work. The resonance linewidth had a strong dependence on the direction of the external magnetic field with respect to in-plane FeF(2) crystallographic directions, consistent with interface magnon scattering due to defect-induced demagnetizing fields. Below T(N), the exchange bias field H(E) measured via FMR for the Ni sample was in good agreement with H(E) determined from magnetization measurements if the perpendicular out-of-plane anisotropy was taken into account. A low field resonance line normally observed at H ≈ 0, associated with domain formation during magnetization in ferromagnets, coincided with the exchange bias field for T < T(N), indicating domain formation with the in-plane FM magnetization perpendicular to the AF easy axis. Thus, biquadratic FM-AF coupling is important at temperatures below and above T(N).