Simulations of magnetic microstructure in thin film elements used for programmable motion of magnetic particles

The results of two-dimensional micromagnetic modeling of magnetization patterns in Permalloy ellipses under the influence of rotating constant-amplitude magnetic fields are discussed. Ellipses of two different lateral sizes have been studied, 0.5 μm×1.5 μm and 1 μm×3 μm. The amplitude of the rotating magnetic field was varied between simulations with the condition that it must be large enough to saturate or nearly saturate the ellipse with the field applied along the long axis of the ellipse. For the smaller ellipse size it is found that the magnetization pattern forms an S state and the direction of the net magnetization lags behind the direction of the applied field. At a critical angle of the rotating magnetic field the direction of the magnetization switches by a large angle to a new S state. Both the critical angle and the angle interval of the switch depend on field amplitude. For this new state, it is instead the applied field direction that lags behind the magnetization direction. The transient magnetization patterns correspond to multi-domain patterns including two vortices, but this state never exists for the equilibrated magnetization patterns. The behavior of the larger ellipse in rotating field is different. With the field applied along the long-axis of the ellipse, the magnetization of the ellipse is nearly saturated with a vortex close to each apex of the ellipse. As the field is rotated, this magnetization pattern remains and the net-magnetization direction lags behind the direction of the field until for a certain angle of the applied field an equilibrium multi-domain state is created. Comparisons are made with corresponding experimental results obtained by performing in-field magnetic force microscopy on Permalloy ellipses.     

Dipolar coupling effect in magnetic bilayer system

Equilibrium micromagnetic structures in a bilayer system composed of two thin cobalt films separated by a non magnetic spacer are systematically analysed. These 2D magnetization distributions are obtained by numerical computations according to different set of magnetic and geometric parameters. The coupling effect due to the dipolar long range interaction (or stray-field effect) between the two Co layers is studied through the evolution of the magnetic pattern in the stack with or without an applied field and compared to a continuous film of same thickness. Special attention is paid to the hysteresis process in a bilayer. Even though the general aspect of the magnetization distribution looks like a Landau-Lifshitz structure, the absence of any core in the vortex of the magnetic structure is analysed in relation to a possible disappearence of (topological) hysteresis. Received 12 December 2001     

Dynamics of solenoidal magnetic structures in soft magnetic thin-film elements

We report on the dynamics of magnetic domain structure conversions exhibited by soft magnetic thin-film elements of elementary geometrical shape (square, disc, triangle) when exposed to a strong external magnetic field. Starting from flux closure vortex patterns, the magnetic structures evolve towards an in-plane saturated state under the influence of an external field. This irreversible and nucleation-free magnetization process occurs on the time scale of picoseconds. The details of this conversion are investigated by means of a time-resolved micromagnetic finite element modeling. We find a sensitive dependence of the temporal evolution of the magnetic structure on the value of the damping parameter in Gilbert's equation of motion. In the case of high damping, domain wall motion dominates the process, while lower damping leads to the formation of a 360° wall which collapses by emitting magnetization waves. It is shown that the mobility of vortices is generally much lower than that of domain walls. The calculations indicate that at a low damping, a magnetic vortex can act almost as a source for concentric waves in ferromagnetic thin-film elements.     

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.     

Effect of the number of nanodisks in two-dimensional arrays on magnetization reversal processes

The magnetic properties of nanodisks packed into square arrays with various numbers of elements in the face have been studied. It has been shown that the vortex nucleation field oscillates with increasing number of nanodisks; the oscillation behavior depends on the nanodisk thickness. The synchronism of the vortex state formation varies with increasing number of nanodisks. The effect of the magnetostatic interaction of nanodisks on the critical fields of magnetization reversal has been estimated for the cases of vortex and single-domain states.     

Asymmetrically shaped hysteresis loop in exchange-biased FeNi/FeMn film

The magnetization reversal of the bilayer polycrystalline FeNi(50 Å)/FeMn(50 Å) film sputtered in a magnetic field has been studied by magnetic and magneto-optical techniques. The external magnetic fields were applied along the easy or hard magnetization axis of the ferromagnetic permalloy layer. The asymmetry of hysteresis loop has been found. Appreciable asymmetry and the exchange bias were observed only in the field applied along the easy axis. The specific features of magnetization reversal were explained within the phenomenological model that involves high-order exchange anisotropy and misalignment of the easy axes of the antiferromagnetic and ferromagnetic layers. It has been shown that the film can exist in one of three equilibrium magnetic states in the field applied along the easy axis. The transitions between these states occur as first-order phase transitions. The observed hysteresis loop asymmetry is related to the existence of the metastable state.     

Magnetic properties of field-annealed FeCo thin films

Fe₅₀Co₅₀ thin films with thickness of 30 and 4 nm have been produced by rf sputtering on glass substrates, and their surface has been observed with atomic force microscopy (AFM) and magnetic force microscopy (MFM); MFM images reveal a non-null component of the magnetization perpendicular to the film plane. Selected samples have been annealed in vacuum at temperatures of 300 and 350 °C for times between 20 and 120 min, under a static magnetic field of 100 Oe. DC hysteresis loops have been measured with an alternating gradient force magnetometer (AGFM) along the direction of the field applied during annealing and orthogonally to it. Samples with a thickness of 4 nm display lower coercive fields with respect to the 30 nm thick ones. Longer annealing times affect the development of a harder magnetic phase more oriented off the film plane. The field applied during annealing induces a moderate magnetic anisotropy only on 30 nm thick films.     

Arrangement effects of triangular defects on magnetization reversal process in a permalloy dot

The arrangement effects of triangular defects on the magnetization configurations and switching process of a permalloy disk are investigated by micromagnetic simulations. For the case of one defect, the vortex is nucleated via the S state (W state) as the direction of the triangular defect is parallel (perpendicular) to the orientation of the external field. For the case of two defects, two types of switching processes are found dependent on their arrangement. For the two triangular defects with the same direction, the reversal occurs via formation, pinning, depinning and annihilation of the vortex state, however, for the two triangular defects with the opposite directions, the reversal is realized by formation and annihilation of the double-vortex state. The nucleation field for the disk with a triangular defect is more sensitive to the defect position than the case of a circular (square) defect, and it shows different variation trends for different triangular directions. The chirality of the vortex state nucleated in the reversal process can be controlled by the triangular defect.     

Needle-like domain structure in Co films deposited on Mo (1 1 0)

Magnetization reversal processes and domain structures have been studied in Mo(1 1 0)/Co(0 0 0 1)/Au(1 1 1) structures grown by molecular beam epitaxy on monocrystalline (11–20) sapphire substrates. Wedge-shaped samples with different Co thickness gradients relative to the Mo [0 0 1] direction were fabricated. Observation of the domain structure was performed at room temperature using Kerr microscopy in a Co thickness range varying from 5 to 50 nm, where the magnetization is oriented in the plane of the sample. A Co thickness-dependent coercivity field was determined through analysis of the domain wall position during the reversal process. A preferential orientation of magnetic domain walls was found, with the domains being needle-like. The orientation, as well as the size of the needles, depends on the Co thickness and the orientation of the magnetic field applied in the sample plane.     

A quantitative analysis of magnetic vortices in Permalloy nanoparticles characterized by electron holography

The present work investigates experimentally curling magnetic configurations locally observed in almost dispersed Permalloy nanoparticles in the remanent state. Magnetic analysis is performed in a field emission TEM using off-axis electron holography. Particularly, electron holography is used to characterize the magnetic microstructure of Fe₃₀Ni₇₀ nanoparticles, whose average diameter (50 nm) is expected to be close to the critical size for a curling magnetic structure (vortex) formation. The vortex core diameter D_core and the bulk magnetic profile of the vortex are measured and compared with a “rigid vortex” micromagnetic model. The connection between vortex structure and the characteristic micromagnetic length of the system deduced from magnetization curve measurements is discussed.     

Experimental determination of ultra-sharp stray field distribution from a magnetic vortex core structure

The fine magnetic stray field from a vortex structure of micron-sized permalloy (Ni₈₀Fe₂₀) elements has been studied by high-resolution magnetic force microscopy. By systematically studying the width of the stray field gradient distribution at different tip-to-sample distances, we show that the half-width at half-maximum (HWHM) of the signal from vortex core can be as narrow as ∼21 nm at a closest tip-to-sample distance of 23 nm, even including the convolution effect of the finite size of the magnetic tip. a weak circular reverse component is found around the center of the magnetic vortex in the measured magnetic force microscope (MFM) signals, which can be attributed to the reverse magnetization around the vortex core. Successive micromagnetic and MFM imaging simulations show good agreements with our experimental results on the width of the stray field distribution.     

Effects of size and interactions on the magnetic behaviour of elliptical (0 0 1)Fe nanoparticles

Arrays of elliptical particles with aspect ratio 1:3 and short axes 50, 100 and 150 nm were prepared by electron-beam lithography and ion-beam milling of epitaxial (0 0 1)Fe films of thicknesses 10 and 20 nm. The domain state of an individual particle imaged by magnetic force microscopy in zero field after demagnetization was observed to change from being bi-domain or multidomain (MD) to stable single domains (SD) as the lateral size and film thickness were decreased. The critical size for SD formation was found to be close to the actual lateral sizes of 100 nm×300 nm and 150 nm×450 nm for the thicknesses of 20 and 10 nm, respectively. Only in the 10 nm thick ellipses of lateral size 100 nm×300 nm, the magnetization reversal may take place through coherent rotation. For all other investigated samples, the experimental switching field is lower than what would be required for this process.     

MFM probe control of magnetic vortex chirality in elliptical Co nanoparticles

Magnetic force microscopy (MFM) methods were applied to investigate the peculiarities of magnetization distribution in elliptical 400×600×27 nm Co particles. Reversible transitions between the uniform and vortex states under inhomogeneous magnetic field of MFM probe were observed. Possibility to control the chirality of a magnetic vortex in these particles by MFM probe manipulation was shown.     

Kinetic theory of point vortices in two dimensions: analytical results and numerical simulations

We develop the kinetic theory of point vortices in two-dimensional hydrodynamics and illustrate the main results of the theory with numerical simulations. We first consider the evolution of the system “as a whole” and show that the evolution of the vorticity profile is due to resonances between different orbits of the point vortices. The evolution stops when the profile of angular velocity becomes monotonic even if the system has not reached the statistical equilibrium state (Boltzmann distribution). In that case, the system remains blocked in a quasi stationary state with a non standard distribution. We also study the relaxation of a test vortex in a steady bath of field vortices. The relaxation of the test vortex is described by a Fokker-Planck equation involving a diffusion term and a drift term. The diffusion coefficient, which is proportional to the density of field vortices and inversely proportional to the shear, usually decreases rapidly with the distance. The drift is proportional to the gradient of the density profile of the field vortices and is connected to the diffusion coefficient by a generalized Einstein relation. We study the evolution of the tail of the distribution function of the test vortex and show that it has a front structure. We also study how the temporal auto-correlation function of the position of the test vortex decreases with time and find that it usually exhibits an algebraic behavior with an exponent that we compute analytically. We mention analogies with other systems with long-range interactions.     

Dynamic origin of vortex core switching in soft magnetic nanodots

The magnetic vortex with in-plane curling magnetization and out-of-plane magnetization at the core is a unique ground state in nanoscale magnetic elements. This kind of magnetic vortex can be used, through its downward or upward core orientation, as a memory unit for information storage, and thus, controllable core switching deserves some special attention. Our analytical and micromagnetic calculations reveal that the origin of vortex core reversal is a gyrotropic field. This field is induced by vortex dynamic motion and is proportional to the velocity of the moving vortex. Our calculations elucidate the physical origin of the vortex core dynamic reversal, and, thereby, offer a key to effective manipulation of the vortex core orientation.     

Magnetocaloric effect in DyCu2

The magnetocaloric effect of the rare-earth intermetallic compound DyCu₂ is explored through magnetization measurements. DyCu₂ is paramagnetic at the room temperature but becomes antiferromagnetic below 27 K (Neel temperature). Strong temperature and field dependence of magnetization in DyCu₂ at and around the Neel temperature lead to a large magnetocaloric effect. An appreciable magnetocaloric effect persists well above the Neel temperature probably because of the presence of short-range ferromagnetic correlations in the paramagnetic state of DyCu₂. This along with the absence of magnetic hysteresis lead to a large effective refrigerant capacity of 194 J/kg below 44 K, which makes the material important as a potential magnetic refrigerant for the cryogenic liquefier cycles.     

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.     

Effect of magnetic field on the TC and magnetic properties for the aligned MnBi compound

In the compound MnBi, a first-order transition from the paramagnetic to the ferromagnetic state can be triggered by an applied magnetic field and the Curie temperature increases nearly linearly with an increase in magnetic field by ∼2 K/T. Under a field of 10 T, T_C increases by 20 and 22 K during heating and cooling, respectively. Under certain conditions a reversible magnetic field or temperature induced transition between the paramagnetic and ferromagnetic states can occur. A magnetic and crystallographic H-T phase diagram for MnBi is given. Magnetic properties of MnBi compound aligned in a Bi matrix have been investigated. In the low temperature phase MnBi, a spin-reorientation takes place during which the magnetic moments rotate from being parallel to the c-axis towards the basal plane at ∼90 K. A measuring Dc magnetic field applied parallel to the c-axis of MnBi suppresses partly the spin-reorientation transition. Interestingly, the fabricated magnetic field increases the temperature of spin-reorientation transition T_s and the change in magnetization for MnBi. For the sample solidified under 0.5 T, the change in magnetization is ∼70% and T_s is ∼91 K.     

Perpendicular magnetic anisotropy of ultrathin FeCo alloy films on Pd(0 0 1) surface: First principles study

Using the full potential linearized augmented plane wave (FLAPW) method, thickness dependent magnetic anisotropy of ultrathin FeCo alloy films in the range of 1 monolayer (ML) to 5 ML coverage on Pd(0 0 1) surface has been explored. We have found that the FeCo alloy films have close to half metallic state and well-known surface enhancement in thin film magnetism is observed in Fe atom, whereas the Co has rather stable magnetic moment. However, the largest magnetic moment in Fe and Co is found at 1 ML thickness. Interestingly, it has been observed that the interface magnetic moments of Fe and Co are almost the same as those of surface elements. The similar trend exists in orbital magnetic moment. This indicates that the strong hybridization between interface FeCo alloy and Pd gives rise to the large magnetic moment. Theoretically calculated magnetic anisotropy shows that the 1 ML FeCo alloy has in-plane magnetization, but the spin reorientation transition (SRT) from in-plane to perpendicular magnetization is observed above 2 ML thickness with huge magnetic anisotropy energy. The maximum magnetic anisotropy energy for perpendicular magnetization is as large as 0.3 meV/atom at 3 ML film thickness with saturation magnetization of . Besides, the calculated X-ray magnetic circular dichroism (XMCD) has been presented.     

Micromagnetic simulations of 200-nm-diameter cobalt nanorings using a Reuleaux triangular geometry

Using micromagnetic simulations, we investigated the magnetic states and switching processes of Co nanorings with lateral dimensions of 200 nm. We propose a special geometry of nanorings that adopts different Reuleaux triangular shapes. Reuleaux's triangles (RT) combine both the equilateral triangle and circular geometries. We studied the magnetic spin configurations of individual nanorings by varying the thickness and geometry of the nanomagnets. Our results demonstrated that in most nanomagnets exhibiting a thickness of less than 4 nm, there exists an onion-type state, which precedes either a twisted, double twisted, or cardioid state, when studying the magnetization reversal process. The hysteresis loops and magnetic states found in these RTs are compared with circular nanorings.