Magnetization of two-dimensional superconductors with defects

A new method is developed for numerical simulation of the magnetization of layered superconductors with defects that is based on the Monte Carlo algorithm. The minimization of the free energy functional of a two-dimensional vortex system enables one to obtain equilibrium configurations of vortex density and calculate the magnetization of a superconductor with arbitrary distribution of defects in a wide temperature range. Magnetization curves are obtained for the first time for a defective superconductor under conditions of cyclic variation of the external magnetic field for different temperatures. The magnetic induction profiles and the magnetic flux distribution inside a superconductor are calculated, which support the validity of Bean’s model. It is demonstrated that the process of magnetization reversal is accompanied by the emergence of an annihilation wave, i.e., the motion of a zone with zero magnetic induction at the leading front of the incoming magnetic flux.     

Magnetic vortex driven by non-uniform injection of spin-polarized current in nano-scale spin valves

We demonstrate that a current pulse of a non-uniform spin-polarized current density in a nanomagnet can drive, apart from magnetization reversal a static magnetic vortex. This vortex configuration can be achieved in low shape anisotropy spin valves of elliptical cross-sectional area. These non-uniform configurations exist also in presence of either ion mill damages below the nano-aperture or thermal effects at low temperature. We performed a numerical experiment of spin-torque driven ferromagnetic resonance in a magnetic vortex configuration, our results predict a frequency response with a few maxima and minima related to small oscillation of the vortex state around its equilibrium configuration.     

Magnetization reversal measurements in mesoscopic amorphous magnets by magneto-optical Kerr effect

A magneto-optical setup based on the transverse Kerr effect has been designed to study the magnetization reversal processes by vector magnetometry in arrays of magnetic nanostructures with a reduced total volume. This system allows the measurement of both the parallel and perpendicular to the field components of the magnetization. It has been used to analyze the behavior of amorphous Co _x Si_1-x lines fabricated by electron beam lithography that present a very well defined shape induced uniaxial anisotropy. When the field is applied near to the hard direction, coherent rotation processes are found to occur with a collapse of this reversal mode at fields very close to the hard axis that allows to estimate the very low anisotropy dispersion of these samples. The analysis of the vector hysteresis loops reveals that the magnetization switches via an incoherent process that starts prior to the Stoner-Wohlfarth instability and that can be described in terms of a localized curling-like reversal mode.Received: 16 June 2004, Published online: 24 September 2004PACS: 75.75. + a Magnetic properties of nanostructures - 75.60.Jk Magnetization reversal mechanisms - 75.50.Kj Amorphous and quasicrystalline magnetic materials     

Role of anisotropy on the domain wall properties of ferromagnetic nanotubes

In this paper we investigate the role of magneto-crystalline anisotropy on the domain wall (DW) properties of tubular magnetic nanostructures. Based on a theoretical model and micromagnetic simulations, we show that either cubic or uniaxial magneto-crystalline anisotropies have some influence on the domain wall properties (wall size, propagation velocity and energy barrier) and then on the overall magnetization reversal mechanism. Besides the characterization of the transverse and vortex domain wall sizes for different anisotropies, we predict an anisotropy dependent transition between the occurrence of transverse and vortex domain walls in tubular nanowires. We also discuss the dynamics of the vortex DW propagation gradually increasing the uniaxial anisotropy constant and we found that the average velocity is considerably reduced. Our results show that different anisotropies can be considered in real samples in order to manipulate the domain wall behavior and the magnetization reversal process.     

Kinetics of magnetization reversal in a heterophase nanomagnet with spatially modulated anisotropy

Magnetization reversal modes in a thin-film NiFeCuMo ferromagnet (FM) with periodically varying in-plane anisotropy are studied by the magneto-optical indicator film (MOIF) technique. The uni-directional anisotropy in FM regions exchange-coupled to a FeMn antiferromagnet (AFM) film in the form of square mesh stripes is alternated by the uniaxial anisotropy in the FM regions inside this mesh. It is shown that the boundaries formed along the edges of these stripes, which separate FM regions with different anisotropy, crucially influence the kinetics of domain-structure transformation in both types of FM regions. It is established that the lateral exchange anisotropy in the ferromagnet, which is determined by the stabilization of the spin distribution in the FM layer along the FM-(FM/AFM) interface, leads to the asymmetry of the magnetization reversal in FM regions bordered with an FM/AFM structure. Anisotropy of the mobility of 180-degree “charged” and “uncharged” domain walls situated, respectively, perpendicular and parallel to the unidirectional anisotropy axis is revealed. The difference observed between the mobilities of charged and uncharged domain walls is attributed to the difference in the spin distribution in these walls with respect to the unidirectional anisotropy axis and is a key factor for the difference between the magnetization reversal kinetics in horizontal and vertical exchange-biased FM stripes. Drastic differences are revealed in the asymmetry of magnetization reversal processes in mutually perpendicular narrow stripes of FM/AFM structures. Possible mechanisms of magnetization reversal in low-dimensional FM-(FM/AFM) heterostructures are discussed with regard to the effect of domain walls localized on the edges of AFM layers.     

Magnetization reversal processes in layered high-temperature superconductors with ferromagnetic impurities

The self-consistent interaction of a vortex system of a high-temperature superconductor and ferromagnetic impurities, including single impurities and their clusters, has been considered in the model of a layered high-temperature superconductor. For different temperatures and concentrations of ferromagnetic impurities, the magnetization reversal loops have been calculated by the Monte Carlo method taking into account an ensemble of ferromagnetic particles with different orientations of their easy magnetization axes with respect to the direction of an external magnetic field and for different magnetic anisotropy energies. It has been demonstrated that there is a nonlinear interaction of the high-temperature superconductor with ferromagnetic impurities, in which the initially thermodynamically reversible character of the magnetization reversal of the ferromagnetic ensemble can become irreversible. For a periodic lattice of clusters of ferromagnetic impurities, the magnetization curves of the high-temperature superconductor have been calculated for different sizes and configurations of the clusters. It has been revealed that, when extended defects are oriented parallel to the direction of the entrance of vortices in the sample, the length of the defects does not affect the remanent magnetization. It has been shown that the inclusion of the interaction between the magnetic moments inside the impurity cluster leads to a decrease in the magnetization reversal loop, the coercivity, and, accordingly, the energy loss due to magnetization reversal.     

Remanence in high-density recording media

The uniaxial anisotropy of independent single domain ferromagnetic grains in high density CoCrPtTa longitudinal recording media was derived from remanence measurements. The distribution of the uniaxial anisotropy axis directions was estimated from a measurement of the Kerr rotation in a perpendicular field. The dispersion of anisotropy fields was estimated from the remanence measurements after application of pulse fields in the film plane. Application of an external field to 45° from the film plane results in sharp magnetization reversal with a minimum writing field.     

In-plane current-induced magnetization reversal of Pd/CoZr/MgO magnetic multilayers

High critical current density ($> 10^{6}$ A/cm$^{2})$ is one of major obstacles to realize practical applications of the current-driven magnetization reversal devices. In this work, we successfully prepared Pd/CoZr(3.5 nm)/MgO thin films with large perpendicular magnetic anisotropy and demonstrated a way of reducing the critical current density with a low out-of-plane magnetic field in the Pd/CoZr/MgO stack. Under the assistance of an out-of-plane magnetic field, the magnetization can be fully reversed with a current density of about 10$^{4}$ A/cm$^{2}$. The magnetization reversal is attributed to the combined effect of the out-of-plane magnetic field and the current-induced spin-orbital torque. It is found that the current-driven magnetization reversal is highly relevant to the temperature owing to the varied spin-orbital torque, and the current-driven magnetization reversal will be more efficient in low-temperature range, while the magnetic field is helpful for the magnetization reversal in high-temperature range.     

磁涡旋极性翻转的局域能量

针对坡莫合金纳米圆盘中的单个磁涡旋结构,采用微磁学模拟研究了磁涡旋极性翻转过程中的局域能量密度.磁涡旋的极性翻转通过与初始涡旋极性相反的涡旋与反涡旋对的生成,以及随后发生的反涡旋与初始涡旋的湮没来实现.模拟结果显示当纳米圆盘样品中局域能量密度的最大值达到一临界值时,磁涡旋将会实现极性翻转,其中交换能起主导作用.基于涡旋极性翻转过程中出现的三涡旋态结构,应用刚性磁涡旋模型对局域交换能量密度进行了理论分析.通过刚性磁涡旋模型得到的磁涡旋极性翻转所需的局域交换能量密度的临界值与模拟结果符合得较好.     

Modelling of toroidal moment switching and dynamics in ferromagnetic nanorings

Switching between right and left vortex magnetization states in annular ferromagnetic nanostructures, was studied. The study was performed by numerically solving the modified Landau-Lifshitz equation with consideration of the effect of spin transfer and full-scale consideration of the magnetostatic field, exchange energy, and anisotropy energy. The dynamics of magnetization reversal of the ferromagnetic nanoring, caused by the electric current flowing perpendicularly to the object plane and penetrating the structure, was studied taking into account two mechanisms of the current effect on magnetization: by the Oersted field and spin transfer. It was found that the presence of the spin polarization both perpendicular and parallel to the nanoring plane decreases the critical current at which the object is switched by an order of magnitude. It was shown that the toroidal moment \(\vec T\) is a convenient characteristic for describing magnetization reversal processes in annular magnetic nanostructures.     

Avalanches and Self-Organized Criticality in superconductors

We review the use of superconductors as a playground for the experimental study of front roughening and avalanches. Using the magneto-optical technique, the spatial distribution of the vortex density in the sample is monitored as a function of time. The roughness and growth exponents corresponding to the vortex `landscape' are determined and compared to the exponents that characterize the avalanches in the framework of Self-Organized Criticality. For those situations where a thermo-magnetic instability arises, an analytical non-linear and non-local model is discussed, which is found to be consistent to great detail with the experimental results. On anisotropic substrates, the anisotropy regularizes the avalanches.     

Influence of induced anisotropy on the processes of magnetization reversal of cobalt circular nanodots

The magnetic structure and the processes of magnetization reversal of individual cobalt nanodots and arrays of cobalt nanodots have been studied using the magneto-optical Kerr effect and magnetic force microscopy. Arrays of nanodots have been prepared by ion etching from a continuous cobalt film. Magnetic anisotropy is induced during deposition of the cobalt films. The nanodots have the diameter d = 600 nm and the period varying from 1.5d to 3.0d. Magnetic force microscopy images have shown that the induced magnetic anisotropy affects the orientation of magnetization of noninteracting nanodots and the direction of displacement of the magnetic vortex center in the nanodots coupled by the dipole-dipole interaction.     

Investigation of micromagnetism and magnetic reversal of Ni nanoparticles using a magnetic force microscope

Isolated Ni nanoparticles were studied in situ by atomic and magnetic force microscopy in the presence of an additional external field up to 300 Oe. By comparing topographic and magnetic images, and also by computer modeling of magnetic images, it was established that particles smaller than 100 nm are single-domain and easily undergo magnetic reversal in the direction of the applied external magnetic field. For large magnetic particles, the external magnetic field enhances the magnetization uniformity and the direction of total magnetization of these particles is determined by their shape anisotropy. Characteristics of the magnetic images and magnetic reversal of particles larger than 150 nm are attributed to the formation of a vortex magnetization structure in these particles. Fiz. Tverd. Tela (St. Petersburg) 40, 1277–1283 (July 1998)     

Systematic study of magnetization reversal in square Fe nanodots of varying dimensions in different orientations

Ferromagnetic nanoparticles can be used for data storage, spintronics, and other applications. Especially vortex states are often suggested to be used to store information. Due to the shape anisotropy dominating in nanoparticles, magnetization reversal processes can be expected to depend not only on the dimensions, but also on the orientation with respect to the external magnetic field. While several papers evaluate magnetization dynamics, including vortex precessions, in round nanodots, square nanodots are less often investigated. Here we report on different magnetization reversal processes found in micromagnetic simulations of square Fe nanodots with lateral dimensions between 100 nm and 500 nm and thicknesses between 10 nm and 50 nm. Choosing magnetic field orientations parallel to one of the square edges and under 45^°, seven different reversal mechanisms were found, most of them including a single-vortex state, while in some cases two, three or more vortex-antivortex pairs were found. The ground state, i.e. the magnetic state at vanishing external magnetic field, was often a single-vortex state, making the nanodot with the respective dimensions suitable for data storage applications. The stability of this state, i.e. the field range over which it existed, depended strongly on the lateral dimensions and the dot thickness and was largest for small lateral dimensions and large thicknesses.     

On the manifestation of effect of delayed acceleration of the transient process during 180° pulsed magnetization reversal of real ferrite–garnet films with planar anisotropy

The regime of 180° pulsed magnetization reversal of ferrite–garnet films with planar anisotropy in the region of external fields, in which the mechanism of uniform rotation of the magnetization operates, is investigated for the first time. An analysis of the numerical solutions of the Landau–Lifshitz equation and the calculated and experimentally obtained signals showed that the presence of biaxial anisotropy in real ferrite–garnet films leads to the fact that at finite duration of the remagnetizing pulse front the initial slow rotation at definite moment of time is sharply accelerated so that over an interval of ~0.7 ns the azimuthal angle changes from 45° to the equilibrium value (160°–170°). As a result, appearence of the nonlinear damped oscillations of magnetization with a fundamental harmonic period of ~1.5 ns become possible.     

Magnetic anisotropy and magnetization reversal of ultrathin iron films with in-plane magnetization on Si（111） substrates

The magnetic anisotropy and magnetization reversal of single crystal Fe films with thickness of 45 monolayer (ML) grown on Si(111) have been investigated by ferromagnetic resonance (FMR) and vibrating sample magnetometer (VSM). Owing to the significant modification of the energy surface in remanent state by slight misorientation from (111) plane and a uniaxial magnetic anisotropy, the azimuthal angular dependence of in-plane resonance field shows a six-fold symmetry with a weak uniaxial contribution, while the remanence of hysteresis loops displays a two-fold one. The competition between the first and second magnetocrystalline anisotropies may result in the switching of in-plane easy axis of the system. Combining the FMR and VSM measurements, the magnetization reversal mechanism has also been determined.     

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.     

黏性各向异性磁流体Kelvin-Helmholtz不稳定性:二维数值研究

利用corner transport upwind和constrained transport算法求解非理想磁流体动力学方程组,对匀强平行磁场作用下,黏性各向异性等离子体自由剪切层中的Kelvin-Helmholtz不稳定性进行了数值模拟.从流动结构、涡结构演化、磁场分布、横向磁压力、抗弯磁张力等角度对各向同性和各向异性黏性算例结果进行了讨论,分析了黏性各向异性对Kelvin-Helmholtz不稳定性的影响.结果表明,黏性各向异性比黏性各向同性更利于流动的稳定.其稳定性作用是由于磁感线方向上剪切速率降低导致界面卷起程度和圈数的降低,并使卷起结构中小涡产生增殖、合并,破坏了涡的常规增长,从而导致流动的稳定.黏性各向异性对横向磁压力的影响比对抗弯磁张力更大.     

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.     

Anatomy of field effects on magnetization dynamics and spin transfer noise

Spin transfer-related phenomena in nanomagnets have attracted extensive studies. In this paper we shall focus on analysis of individual and combined effects of the external, anisotropy, and demagnetization fields on magnetization dynamics and spin transfer noise. It is found that individual roles of the external, anisotropy, and demagnetization fields, as well as the combined roles of external plus anisotropy fields and anisotropy plus demagnetization fields, do not change the behavior of current induced magnetization switching. Such magnetization reversal procedures are of low noise. Our dynamics and power spectral density calculations show that it is the demagnetization field that plays a major role in inducing spin transfer noise: the demagnetization field itself or in combination with the anisotropy field will result in wave-like switching; moreover, the demagnetization field, together with the external field (not too small), will lead to precession and hence the system would be in noisy states. Our modeling work for an elliptical Py alloy is qualitatively consistent with Cornell's experiment and simulation [Science 307 (2005) 228].