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.     

Domain formation in films of magnetic nanoparticles with a random distribution of anisotropy axes

A theoretical model describing the magnetization distribution in a system of closely packed ferromagnetic grains with a random distribution of easy magnetization axes is constructed. It is demonstrated that, in this system, the domain structure with domains characterized by a random distribution of magnetization axes is formed even if the magnetostatic energy is negligible and can be ignored. The domain size increases linearly with an increase in the ratio of the exchange energy of the interaction between grains to the anisotropy energy of a single grain. The inclusion of the magnetostatic energy only insignificantly changes the domain size but leads to the formation of a vortex magnetization distribution inside the domains. The behavior of the system is numerically simulated by the Monte Carlo method. The results of the simulation confirm the conclusions drawn from the theoretical model.     

Effect of anisotropy and dipole interaction on long-range order magnetic structures generated by Dzyaloshinskii–Moriya interaction

Self-organized long-range order structures, such as stripe domains and magnetic skyrmion lattices, are formed by the competition between ferromagnetic exchange interaction and Dzyaloshinskii–Moriya (DM) interaction. We investigated the properties of the magnetic structures generated by a DM interaction under the influence of anisotropy or magnetic dipole interaction, by performing Monte-Carlo simulated annealing. We constructed phase maps in external-field and anisotropy space to study the effect of anisotropy or dipole interaction on the phase boundaries between the magnetic structures. The simulation results show that the phase boundaries are sensitive to perpendicular anisotropy and that the skyrmion lattice region in phase space is extended under easy-plane anisotropy. The effect of the long-range dipole interaction was studied and was found to stabilize the skyrmion lattice phase and reduce the size of the magnetic structures.     

Carrier mediated ferromagnetism on the surface of a topological insulator

We study the effect of magnetic doping at the surface of a three dimensional topological insulator (TI) on emergence of ferromagnetic ordering at the TI-surface assuming the exchange coupling between the Dirac fermions and the dilute magnetic ions. We show that this coupling results in an uniaxial magnetic anisotropy with out-of-plane magnetization direction. It is found that the system under consideration is unstable with respect to a spontaneous uniform magnetization along the easy axis, which is accompanied by opening a gap in a spectrum of the Dirac surface states. In the framework of a mean-field approach, we study the possibility of ferromagnetic order on the magnetically doped surface of TI at different temperatures and positions of the chemical potential.     

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.     

Magnetization curve and magnetic correlations in a nanochain of ferromagnetic grains with random anisotropy

The magnetization curve and magnetization correlation function are calculated for a ferromagnetic chain of single-domain nanoparticles with a randomly oriented anisotropy axis for different ratios between the exchange correlation and anisotropy energies. It is shown that the coercive force decreases as the exchange correlations increase. For strong exchange correlations, the magnetization curve is described by the following three successive magnetization processes as the applied field is increased: (i) nonuniform rotation of the magnetization of stochastic domains, (ii) collapse of the magnetic solitons, and (iii) nonuniform rotation of exchange-correlated magnetization vectors of the nanoparticles. For high fields, the calculated correlation function of the transverse magnetization components coincides with that predicted from linear theory. At low and zero fields, the main parameters of the correlation function (the variance and correlation radius) tend to certain finite values rather than diverge (as is the case in linear theory). The irreversible variation in the magnetization at low fields (the hysteresis loop) and the hysteresis of the main parameters of the correlation function are calculated.     

Equilibrium magnetic properties of dipolar interacting ferromagnetic nanoparticles

We use Monte Carlo simulations to study the influence of dipolar interaction on the equilibrium magnetic properties of monodisperse single-domain ferromagnetic nanoparticles. Low field magnetizations simulated in zero field cooling (ZFC)/field cooling (FC) procedures and field-dependent magnetization curves above the blocking temperatures show strong dependence on the concentration and the spatial arrangement (cubic or random) of the magnetic particles. The field-dependent magnetizations can not be simply described by the T^* model at relative low temperatures due to the interplay between anisotropy and dipolar interactions, as well as the spatial arrangement effect.     

Field cooling induced changes in the antiferromagnetic structure of NiO films

The magnetic anisotropy in antiferromagnetic 500 A thick NiO films, before and after the establishment of an exchange bias field with Co84Fe16 ferromagnetic layers, was measured using magnetic linear dichroism in soft x-ray absorption. Both <111> textured NiO and untextured NiO films show exchange-bias induced in-plane magnetic anisotropy of nearly equal magnitude and with the Ni moment axis being nearly parallel to the exchange bias field direction. These results represent the first observation of the key step in the exchange biasing process, namely, repopulation of the antiferromagnetic domains whose magnetization axis is closest to the exchange bias field direction.     

Magnetization and magnetic susceptibility of the Ising ferromagnetic/antiferromagnetic superlattice

A linear cluster mean-field approximation is used to study the magnetic properties of the Ising ferromagnetic/antiferromagnetic superlattice, which is composed of a spin-1/2 ferromagnetic monolayer and a spin-1 antiferromagnetic monolayer with a single-ion anisotropy alternatively. By using the transfer matrix method, we calculate the magnetization and the initial magnetic susceptibility as functions of temperature for different interlayer coupling, single-ion anisotropy. We summarize the changing behaviors of the spin structure in ferromagnetic and antiferromagnetic layers and the characteristics of the corresponding magnetic susceptibilities, give the transition temperature as a function of the interlayer exchange coupling for different single-ion anisotropy, and analyze the features of the magnetization and the magnetic susceptibility.     

Cylindrical magnetization model for glass-coated microwires with circular anisotropy: Statics

The static magnetization profile of glass-coated microwires with effective circular anisotropy is investigated using micromagnetics. In this family of microwires, the ferromagnetic nucleus with an amorphous character presents a magnetic structure composed of an inner region with axial domains and an outer region with circular domains, due to magnetoelastic anisotropy. A one-dimensional micromagnetic model is developed, taking into account both the exchange and magnetoelastic anisotropy energies, and solved quasi analytically. The total energy, magnetization profiles and magnetization curves are investigated as a function of radius and anisotropy constant of the nucleus. This work represents a fundamental study of the magnetization process in these amorphous microwires and provides guidelines for the production of microwires with tailored magnetic properties. En passant, the nucleation problem in an infinite cylinder, introduced by W.F. Brown, is revisited.     

Long-time relaxation of the magnetization and tunneling magnetoresistance of granular ferromagnets

Magnetic anisotropy and orientational variance as well as shape diversity of granules largely determine the magnetic properties of granular ferromagnetic metals. The model of magnetically anisotropic ellipsoidal granules explains the glassy nature of the magnetic state of such systems. The relaxation of the magnetization and the magnetoresistance of granular ferromagnetic metals is examined on the basis of this model.     

铁磁/反铁磁双层薄膜中应力各向异性研究

采用铁磁共振方法,研究了铁磁/反铁磁双层薄膜中交换各向异性和应力各向异性对其物理性质的影响.结果表明,单向各向异性来源于界面交换作用,应力各向异性对材料的磁化难易程度有较大影响.当外磁场方向与应力场方向平行时,应力场的存在将促进该方向的磁化.反之,应力场将会阻碍该方向的磁化.     

Random anisotropy studies in amorphous FeTmB

We have studied the magnetization of melt spun amorphous Fe_{80 −x}Tm_xB₂₀ alloys with 0 x 15 under magnetic fields up to 18 kOe, and have analyzed the results at different temperatures based on the random magnetic anisotropy model. Exchange interactions J_FeFe and J_FeTm evaluated by the fitting of M-T curves are discussed. The local random anisotropy K_L and the exchange constant A are found to decrease with increasing temperature. Experimental data show that the ferromagnetic correlation length R_f decreases with increasing Tm content.     

Evidence of domain wall scattering in thin films of granular CoFe-AgCu

Thin films of the giant magnetoresistive granular CoFe-AgCu system prepared by rf sputtering displayed a great variety of domain-like microstructures with a net out-of-plane component of the magnetization for ferromagnetic volume concentrations above about 0.25. Therefore, magnetic percolation takes place at ferromagnetic concentrations much lower than the physical percolation threshold. The out-of-plane structure of the as-deposited samples in magnetic virgin state consisted of a distribution of both quasi-circular domains and short stripes depending on the ferromagnetic content. Furthermore, these samples present high metastability and a variety of remanent in-plane and out-of-plane microstructures can be achieved as a function of the magnetic history. Besides, the evolution of the magnetic microstructure yields strong training effects on magnetotransport properties, due to the extra contribution of the electron scattering at the domain walls. All in all, the observed behavior is the result of a subtle correlation between perpendicular anisotropy produced by residual stresses, exchange interparticle interactions due to CoFe alloyed in the matrix, and dipolar interactions. Thus, as high structural evolution occurs through annealing, the features of randomly distributed ferromagnetic particles are recovered and, the out-of-plane domain structures and the training effects disappear. Received 30 September 1999     

铁磁/反铁磁双层膜系统中的磁畴动力学行为

比较了铁磁单层膜与铁磁/反铁磁双层膜结构中的磁畴演化行为, 发现由于反铁磁层膜对铁磁层膜的耦合作用使得系统的磁畴壁厚度、 磁畴壁等效质量、磁畴壁移动速度等发生了改变, 系统的矫顽场增强, 并出现了交换偏置场. 文章具体研究了反铁磁层耦合作用下其磁畴壁厚度、 等效质量以及磁畴壁移动速度等与反铁磁层的净磁化、 磁各向异性、界面耦合强度以及温度等的关系; 并研究了其对铁磁/反铁磁双层膜中的交换偏置场、矫顽场的影响. 进而 从磁畴结构的形成及其演化上揭示了铁磁/反铁磁双 层膜中出现交换偏置以及矫顽场增加的物理机制.     

Unified nonequilibrium dynamical theory for exchange bias and training effects

We have investigated the exchange bias and training effect in the ferromagnetic/antiferromagnetic (FM/AF) heterostructures using a unified Monte Carlo dynamical approach. The magnetization of the uncompensated AF layer is still open after the first field cycling is finished. Our simulated results show obvious shift of hysteresis loops (exchange bias) and cycling dependence of exchange bias (training effect) when the temperature is below 45~K. The exchange bias field decreases with decreasing cooling rate or increasing temperature and the number of the field cycling. Essentially, these two effects can be explained on the basis of the microscopical coexistence of both reversible and irreversible moment reversals of the AF domains. Our simulations are useful to understand the real magnetization dynamics of such magnetic heterostructures.     

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.     

Novel magnetization processes in ferrimagnetic multilayers with random anisotropy

We carried out a numerical study of magnetization processes in ferrimagnetic multilayers in the presence of pinning forces acting on one of the magnetic components. The multilayers consist of an alternation of two ferromagnetic materials (M and T) which are assumed antiferromagnetically coupled through the interfaces (as in Fe/Tb multilayers for instance). A random anisotropy field acts on the magnetization of material T. The reversal of the magnetization of the multilayers when the applied field is swept from positive saturation to negative saturation is characterized by a competition between coherent rotation and nucleation-propagation mechanisms. In this competition the rotational hysteresis induced by the random anisotropy on the magnetization of material T plays a crucial role. Very original features have been observed in the magnetization processes of these systems such as crossed hysteresis loops with a negative remanent magnetization. An overview of these magnetization processes below and above the compensation temperature is given in this paper.     

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.