Universal magnetic domain wall dynamics in the presence of weak disorder

The motion of elastic interfaces in disordered media is a broad topic relevant to many branches of physics. Field-driven magnetic domain wall motion in ultrathin ferromagnetic Pt/Co/Pt films can be well interpreted within the framework of theories developed to describe elastic interface dynamics in the presence of weak disorder. Indeed, the three theoretically predicted dynamic regimes of creep, depinning, and flow have all been directly evidenced in this model experimental system. We discuss these dynamic regimes and demonstrate how field-driven creep can be controlled not only by temperature and pinning, but also via interactions with magnetic entities located inside or outside the magnetic layer. Consequences of confinement effects in nano-devices are briefly reviewed, as some recent results on domain wall motion driven by an electric current or assisted by an electric field. Finally new theoretical developments and perspectives are discussed.     

Experiments on the reflection of cold atoms from magnetic thin films

We report the results from a series of experiments in which ferromagnetic thin films were used as atom mirrors for laser-cooled rubidium atoms released from a magneto-optical trap. The thin films were made of cobalt and lanthanum calcium manganite (LCMO) with thicknesses between 20 and 300 nm. The magnetic domains in these thin films have a periodic structure where the spatial period is of the order of the thickness of the film, and the field decays exponentially above the film over a length scale comparable to the domain size. Thus, the neutral atoms reflect off these films from distances comparable to the thickness of the film, resulting in modification of the reflectivity due to the competition between the repulsive magnetic force and the attractive short-range forces such as van der Waals and Casimir forces. The smoothness of the atom mirror is also modified due to the proximity of the magnetic domains. The reflectivity is sensitive to the domain structure and size, which can be modified in LCMO by applying a modest external magnetic field. In this paper, we discuss the evaluation of the thin films as magnetic mirrors for atom optics, and the measurement of the van der Waals force with an accuracy of about 15%, using cobalt thin films. We also discuss some preliminary results on the temperature-dependent reflectivity for atoms near the ferromagnetic transition at 250 K in the LCMO film, and on the domain dynamics and relaxation.     

DC magnetization of ferromagnetic amorphous wires with local deformation

Experimental DC (VSM) and theoretical hysteresis loops of a ferromagnetic amorphous wire with a deformation in the middle or exposed to local magnetic fields are investigated. Hysteresis loops show two-stage Barkhausen jumps and staircase relaxation. With a local field at the same position, the loop drastically looses its shape and symmetry depending on the magnitude and the direction of the magnetic bias. A model to explain this behavior is proposed. The proposed model is based on the calculation of the magnetic moment distribution of the domain as a result of domain wall motion and nucleation in the inner core of a ferromagnetic wire and is in a good agreement with the experimental results.     

Domain wall motion in nanowires

We investigated the motion of domain walls in ferromagnetic cylindrical nanowires by solving the Landau–Lifshitz–Gilbert equation numerically for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole–dipole interactions, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. A transverse domain wall is observed for diameters smaller than the exchange length of the given system. In this case, the system effectively behaves one dimensionally and the domain wall velocity agrees with the result of Slonczewski for one-dimensional walls. For larger diameters, a crossover to a vortex wall sets in which enhances the domain wall velocity drastically. For a vortex wall the domain wall velocity is described by the Walker formula.     

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.     

Discontinuity in heat capacity of Fe0.5Co0.5(110) alloy thin films

In this work we calculate heat capacity of alloy thin films of FeCo on the surface of the plane (110), using three parameters, the concentration x(i), the lattice long range order parameter t(i) and the magnetic order parameter σ(i), being i the number of layers of the thin film. The formulations reported by Hill [1] in the context of small particles and Valenta's model [2] can be applied to the film structure when we treat a thin film as a system divided into subsystems equivalent to two-dimensional parallel layers. The FeCo bulk alloy is completely homogeneous while a thin film have spatial discontinuities in their surfaces. We consider three ferromagnetic thin films formed by 11, 15 and 19 layers in the Helmholtz's free energy, which is minimized applying their first partial derivatives with respect to chemical composition, long range order parameter and magnetic order parameter. We calculate internal energy and heat capacity as a function of temperature and we verify that have two jumps as are reported in literature for the bulk; there are many results of bulk or surface effects of FeCo, but no enough results about ferromagnetic FeCo thin films and this fact does this work interesting.     

Octupolar order in the multiple spin exchange model on a triangular lattice

We show how a gapless spin liquid with hidden octupolar order arises in an applied magnetic field, in a model applicable to thin films of 3He with competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions. Evidence is also presented for nematic--i.e., quadrupolar--correlations bordering on ferromagnetism in the absence of a magnetic field.     

The magnetization model of multilayered composite thin films: Beyond the effective-medium theories

Multilayered composites consisting of many thin ferromagnetic films with in-plane magnetic anisotropy separated by non-magnetic dielectric layers of different sizes are experimentally and theoretically investigated. Thin samples as well samples with transverse sizes comparable with longitudinal ones are used. The measured static magnetic properties of the bulk sample are found to be different from the properties of constituent thin films. This is an evidence for strong interactions between the magnetic layers in the sample, which interact at distances exceeding greatly the distance between adjacent magnetic layers. A theoretic model is developed taking into account magneto-dipole interactions between iron films in a multi-layer system. The model explains the anomalously high demagnetization field of the sample observed in the measurements.     

Domain wall creep in epitaxial ferroelectric Pb(Zr(0.2)Ti(0.08)O(3) thin films

Ferroelectric switching and nanoscale domain dynamics were investigated using atomic force microscopy on monocrystalline Pb(Zr(0.2)Ti(0.8))O(3) thin films. Measurements of domain size versus writing time reveal a two-step domain growth mechanism, in which initial nucleation is followed by radial domain wall motion perpendicular to the polarization direction. The electric field dependence of the domain wall velocity demonstrates that domain wall motion in ferroelectric thin films is a creep process, with the critical exponent mu close to 1. The dimensionality of the films suggests that disorder is at the origin of the observed creep behavior.     

涂覆聚甲基丙酸甲酯的磁性膜外磁场作用下的往复滑动摩擦行为研究

磁性材料被广泛应用于磁记录和磁润滑等领域,聚甲基丙烯酸甲酯因其良好的介电性,能够用作磁性材料的表面涂层.本文对外磁场作用下,外加载荷和磁场强度对往复滑动的聚甲基丙烯酸甲酯/磁性薄膜双膜系摩擦性能的影响开展了研究.实验结果表明:聚甲基丙烯酸甲酯/磁性双膜体系的摩擦性能随载荷和磁场强度改变而变化;但在干摩擦和硅油润滑两种模式下,磁场对其摩擦学性能的影响规律不同.理论分析了磁场作用下磁场诱发的磁性力与摩擦副物理性质变化对摩擦力和摩擦系数的影响,与实验结果符合良好.研究结果为磁性薄膜的界面介质设计与控制提供了依据.     

Precessional frequency of ferromagnetic elements: Influence of magnetic domain width

A model is presented that semi-quantitatively describes the dependence of precessional frequency on magnetic domain width in ferromagnetic thin film elements. With decreasing domain width an increase of precessional frequency at zero-bias field by a factor of about 1.5 is found experimentally and from the calculations. The modelled value of change of precessional frequency is in agreement with the experimental results. The simple model offers the opportunity to relate the drastic effects of domain structure on the dynamic magnetic properties of soft-magnetic thin films by a straightforward approach.     

Visualization of the Barkhausen effect by magnetic force microscopy

By visualization of the Barkhausen effect using magnetic force microscopy we are able to provide detailed information about the physical principles that govern the magnetization reversal of a granular ferromagnetic thin film with perpendicular anisotropy. Individual Barkhausen volumes are localized and distinguished as either newly nucleated or grown by domain wall propagation. The Gaussian size distribution of nucleated Barkhausen volumes indicates an uncorrelated random process, while grown Barkhausen volumes exhibit an inverse power law distribution, which points towards a critical behavior during domain wall motion.     

Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO3

Domains in ferroelectric films are usually smooth, stripelike, very thin compared with magnetic ones, and satisfy the Landau-Lifshitz-Kittel scaling law (width proportional to square root of film thickness). However, the ferroelectric domains in very thin films of multiferroic BiFeO3 have irregular domain walls characterized by a roughness exponent 0.5-0.6 and in-plane fractal Hausdorff dimension H||=1.4+/-0.1, and the domain size scales with an exponent 0.59+/-0.08 rather than 1/2. The domains are significantly larger than those of other ferroelectrics of the same thickness, and closer in size to those of magnetic materials, which is consistent with a strong magnetoelectric coupling at the walls. A general model is proposed for ferroelectrics, ferroelastics or ferromagnetic domains which relates the fractal dimension of the walls to domain size scaling.     

From bubble to Skyrmion: Dynamic transformation mediated by a strong magnetic tip

Skyrmions in thin metallic ferromagnetic films are stable due to competition between the RKKY interaction and uniaxial magnetic anisotropy. We study static nonlinear excitations in magnetic film in the presence of strong cylindrical magnetic tip of nanometer size. We mimic the RKKY interaction by the next-nearest-neighbors ferromagnetic and antiferromagnetic exchange interactions. We demonstrate analytically and numerically dissipative transformation of a bubble created by a strong magnetic tip into a stable Skyrmion.     

Some comments on the Mindlin-Goodman method of solving vibrations problems with time dependent boundary conditions

Experimental evidence is presented for chaotic type non-periodic motions of a deterministic magnetoelastic oscillator. These motions are analogous to solutions in non-linear dynamic systems possessing what have been called “strange attractors”. In the experiments described below a ferromagnetic beam buckled between two magnets undergoes forced oscillations. Although the applied force is sinusoidal, nevertheless bounded, non-periodic, apparently chaotic motions result due to jumps between two or three stable equilibrium positions. A frequency analysis of the motion shows a broad spectrum of frequencies below the driving frequency. Also the distribution of zero crossing times shows a broad spectrum of times greater than the forcing period. The driving amplitude and frequency parameters required for these non-periodic motions are determined experimentally. A continuum model based on linear elastic and non-linear magnetic forces is developed and it is shown that this can be reduced to a single degree of freedom oscillator which exhibits chaotic solutions very similar to those observed experimentally. Thus, both experimental and theoretical evidence for the existence of a strange attractor in a deterministic dynamical system is presented.     

Microwave and static magnetic properties of multi-layered iron-based films

Thin ferromagnetic films with in-plane magnetic anisotropy are promising materials for obtaining high microwave permeability. To produce a bulk massive sample from thin films, multi-layer films made of a number of many thin films may be used. The paper reports on an experimental study of microwave and static magnetic properties of multi-layer iron-based films and composite samples made of these. The multi-layer films under study are deposited onto a mylar substrate by a magnetron-sputtering process performed in Ar atmosphere with controlled N₂ admixture. The sputtered iron layers are alternated with SiO₂ layers. The measured static and microwave magnetic properties of the bulk sample are found to differ from the properties of constituent films. This is an evidence for strong interactions between the magnetic layers in the sample, which interact at distances exceeding greatly the distance between adjacent magnetic layers. A theoretic model is developed to account for magneto-dipole interactions between iron films in a multi-layer system. The model explains the anomalously high demagnetization field of the sample observed in the measurements.     

Dense stripe domains in a nanocrystalline CoFeSiB thin film

We recently reported a possible antiferromagnetically coupled phase in a Co-rich CoFeSiB thin film, that had a partially nanocrystalline Co phase in an amorphous CoFeSiB matrix. Although an amorphous CoFeSiB film should show a ferromagnetic behavior, we observed an antiferromagnetic coupling associated with a nanocrystalline Co phase in the hysteresis-loop measurements of Co-rich CoFeSiB thin films. We ascribed the observed antiferromagnetic coupling to dense stripe domains consisting of periodically up and down domains perpendicular to the surface of the film. The configuration of the stripe domains was confirmed with magnetic force microscopy images. When a longitudinal magnetic field was applied, the size of the stripe domain was reduced. While for a transverse field, the domain structure became tilted and zigzagged, but no in-plane magnetic anisotropy was noted. When the magnetic field was increased to values above the saturation magnetic field, H_S = 2.5 kOe, the domain structure disappeared.     

Nonlinear dynamics of domain walls with cross-ties

The dynamic behavior of a domain wall with cross-ties is analyzed on the basis of micromagnetic simulation with exact allowance for all main (exchange, magnetoanisotropic, and magnetostatic) interactions in thin magnetically uniaxial ferromagnetic films with planar anisotropy. It is found that the peculiarities of motion of such domain walls are closely related to the behavior of topological defects in the magnetization distribution (generation, motion, and annihilation of vortex–antivortex pairs on the film surface and Bloch points). We observe three different regimes of motion (stationary, periodic, and turbulent regimes), each of which is realized in a certain range of fields oriented along the easy magnetization axis. It is shown that the experimentally observed dynamic bends of the walls with cross-ties are determined by the type of motion of vortices and antivortices. The velocities of domain walls in different regimes are calculated, and the dynamic configurations of the magnetization and existing dynamic transitions between them are investigated.     

消磁场对纳米铁磁线磁畴壁动力学行为的影响

为了实现基于磁畴壁运动的自旋电子学装置, 掌握磁畴壁动力学行为是重要争论之一.研究了在外磁场驱动下L-型纳米铁磁线磁畴壁的动力学行为. 通过微磁学模拟,在各种外磁场的驱动下考察了纳米铁磁线磁畴壁的动力学特性; 在较强外磁场的驱动下, 在不同厚度纳米线上考察了纳米线表面消磁场对磁畴壁动力学行为的影响. 为了进一步证实消磁场对磁畴壁动力学的影响, 在垂直于纳米线表面的外磁场辅助下分析了磁畴壁的动力学行为变化. 结果表明, 随着纳米线厚度和外驱动磁场强度的增加, 增强了纳米线表面的消磁场的形成, 使得磁畴壁内部自旋结构发生周期性变化, 导致磁畴壁在纳米线上传播时出现Walker崩溃现象. 在垂直于纳米线表面的外磁场辅助下, 发现辅助磁场可以调节消磁场的强度和方向. 这意味着利用辅助磁场可以有效地控制纳米铁磁线磁畴壁的动力学行为.