One method of creating and annihilating skyrmions in confined geometries is to use Voltage-Controlled Magnetic Anisotropy (VCMA) [1, 2, 3]. Previous study shows that robust voltage controlled ferromagnetic reversal from up to down state in the soft layer of a perpendicular Magnetic Tunnel Junction (p-MTJ) can be achieved by creating and subsequently annihilating an intermediate skyrmion state [4] in the presence of room temperature thermal noise and anisotropy variation across grains [4]. However, when scaling to 20 nm, thermal noise can annihilate the skyrmions, for example, by randomly moving the core towards the boundary of the nanostructure. In this work, we study three p-MTJs of different dimensions, particularly lateral dimensions of 100nm, 50nm and 20 nm and investigate the change in switching behavior as the dimension is decreased. Particularly, our focus is to investigate to what extent skyrmion mediated switching scheme can be employed below ~50nm lateral dimensions in the presence of thermal perturbation.
The role of universal memory can be successfully satisfied by magnetic tunnel junctions (MTJs) where the writing mechanism is based on spin-transfer torque (STT). An improvement in the switching properties (lower switching current density maintaining the thermal stability) has been achieved in MTJs with interfacial perpendicular anisotropy (IPA) at the interface between CoFeB and MgO. In this paper, micromagnetic simulations point out the influence of IPA and saturation magnetization (MS) on the properties of fast magnetization reversal achieved in 5, 10 and 20 ns. Both cases of in-plane and o…
We study skyrmions in magnetic thin films with structural inversion asymmetry perpendicular to the film plane. We determine the magnetization texture of a single skyrmion and its dependence on the strength of the Dzyaloshinskii-Moriya interaction relative to the magnetostatic energy. Furthermore, we construct a phenomenological model that describes the interaction between the motion of skyrmions and electric currents to lowest order in spin-orbit coupling. We estimate the experimental verifiable velocities for current-driven motion of skyrmion textures based on available results obtained from …
We have investigated Surface Acoustic Wave (SAW) induced ferromagnetic resonance (FMR) assisted Spin Transfer Torque (STT) switching of perpendicular MTJ (p-MTJ) with inhomogeneities using micromagnetic simulations that include the effect of thermal noise. With suitable frequency excitation, the SAW can induce ferromagnetic resonance in magnetostrictive materials, and the magnetization can precesses in a cone with high deflection from the perpendicular direction. With incorporation of inhomogeneity via lateral anisotropy variation as well as room temperature thermal noise, the magnetization pr…
We studied interactions between propagating spin waves (SWs) and a single skyrmion in a perpendicularly magnetized CoFeB nanostripe where the magnetic layer is interfaced with W and MgO. Micromagnetic numerical calculations revealed that robust interactions between the incident SWs and the skyrmion give rise to considerable forward skyrmion motions for specific SW frequencies (e.g., here: fsw = 12 - 19 GHz). Additionally, it was found that there exists a sufficiently low threshold field amplitude, e.g., 0.1 kOe for the fsw = 15 GHz SWs. This frequency-dependent interaction originated from the …
Thin-film sub-5 nm magnetic skyrmions constitute an ultimate scaling alternative for future digital data storage. Skyrmions are robust non-collinear spin-textures that can be moved and manipulated by small electrical currents. We show here an innovative technique to detect isolated nanoskyrmions with a current-perpendicular-to-plane geometry, which has immediate implications for device concepts. We explore the physics behind such a mechanism by studying the atomistic electronic structure of the magnetic quasiparticles. We investigate how the isolated skyrmion local-density-of-states which tunn…
Magnetic skyrmions are particle-like chiral spin textures found in a magnetic film with out-of-planeanisotropy and are considered to be potential candidates as information carriers in next generationdata storage devices. Despite intense research into the nature of skyrmions and their dynamic prop-erties, there are several key challenges that still need to be addressed. In particular, the outstandingissues are the reproducible generation, stabilization and confinement of skyrmions at room tempera-ture. Here, we present a method for the capture of nanometer sized magnetic skyrmions in an arrayof…
A magnetic skyrmion isusually refers to a twisted spin texture surrounded by uniformly aligned out-of-plane spinsin the background of a uniformly magnetized state. The invariance of the magnetic skyrmion conserves its topological charge under any continuous transformations of the spin textures, leads to which represents the robustness of a magnetic skyrmion their texture against external perturbations, making it ideal to use skyrmions as . Such a behaviour is required for an ideal information carriers. To date, most magnetic skyrmion studies have been performedfocused on in perpendicularly mag…
Skyrmions have attracted significant interest due to their topological spin structures and fascinating physical features. The skyrmion phase arises in materials with Dzyaloshinskii-Moriya (DM) interaction at interfaces or in volume of non-centrosymmetric materials. However, although skyrmions were generated experimentally, one critical intrinsic relationship between fabrication, microstructures, magnetization and the existence of skyrmions remains to be established. Here, two series of CoFeB ultrathin films with controlled atomic scale structures are employed to reveal this relationship. By in…
We investigate the field-induced crossover between two types of isolated skyrmions that exist within the conical phase of cubic helimagnets and orient themselves either along or perpendicular to the field. Such a crossover takes place for the same value of the field, at which the closely packed skyrmion lattice was predicted to stabilize in the A-phase region. The clusters and a skyrmion lattice comprised by the skyrmions perpendicular to the field, however, are unfavorable and lose their stability as compared with the skyrmions parallel to the field. We also followed transformation of perpend…
Skyrmions are emerging topological spin structures that are potentially revolutionary for future data storage and spintronics applications. The existence and stability of skyrmions in magnetic materials is usually associated to the presence of the Dzyaloshinskii-Moriya interaction (DMI) in bulk magnets or in magnetic thin films lacking inversion symmetry. While some methods have already been proposed to generate isolated skyrmions in thin films with DMI, a thorough study of the conditions under which the skyrmions will remain stable in order to be manipulated in an integrated spintronic device…
The understanding of the dynamical properties of skyrmion is a fundamental aspect for the realization of a competitive skyrmion based technology beyond CMOS. Most of the theoretical approaches are based on the approximation of a rigid skyrmion. However, thermal fluctuations can drive a continuous change of the skyrmion size via the excitation of thermal modes. Here, by taking advantage of the Hilbert-Huang transform, we demonstrate that at least two thermal modes can be excited which are non-stationary in time. In addition, one limit of the rigid skyrmion approximation is that this hypothesis …
Skyrmions dynamics in the approximation of point-particle skyrmions is considered in the multiferroic insulators, where the spiral magnetic structure is accompanied by finite electric dipole moment. The skyrmion motion is studied in the gradients of perpendicular magnetic and electric fields. The nonuniform magnetic field with a fixed gradient magnitude leads to the spiral motion, where skyrmion circulates in the plane perpendicular to the direction of magnetic field. The frequency of circulation is fixed by the derivative of the external magnetic field and the magnitude of the dipole moment. …
The observation of perpendicular magnetic anisotropy (PMA) at MgO/Fe interfaces boosted the development of spintronic devices based on ultrathin ferromagnetic layers. Yet, magnetization reversal in the standard magnetic tunnel junctions (MTJs) with competing PMA and in-plane anisotropies remains unclear. Here we report on the field induced nonvolatile broken symmetry magnetization reorientation transition from the in-plane to the perpendicular (out of plane) state at temperatures below 50K. The samples were 10 nm thick Fe in MgO/Fe(100)/MgO as stacking components of V/MgO/Fe/MgO/Fe/Co double b…
Thermal-magnetic noise at ferromagnetic resonance (T-FMR) can be used to measure magnetic perpendicular anisotropy of nanoscale magnetic tunnel junctions (MTJs). For this purpose, T-FMR measurements were conducted with an external magnetic field up to 14 kOe applied perpendicular to the film surface of MgO-based MTJs under a dc bias. The observed frequency-field relationship suggests that a 20 A CoFeB free layer has an effective demagnetization field much smaller than the intrinsic bulk value of CoFeB, with 4PiMeff = (6.1 +/- 0.3) kOe. This value is consistent with the saturation field obtaine…
Using micromagnetic simulations we demonstrate core reversal of a fixed magnetic skyrmion by modulating the perpendicular magnetic anisotropy of a nanomagnet with an electric field. We can switch reversibly between two skyrmion states and two ferromagnetic states, i.e. skyrmion states with the magnetization of the core pointing down/up and periphery pointing up/down, and ferromagnetic states with magnetization pointing up/down, by sequential increase and decrease of the perpendicular magnetic anisotropy. The switching between these states is explained by the fact that the spin texture correspo…
We study the combined effects of spin transfer torque, voltage modulation of interlayer exchange coupling and magnetic anisotropy on the switching behavior of perpendicular magnetic tunnel junctions (p-MTJs). In asymmetric p-MTJs, a linear-in-voltage dependence of interlayer exchange coupling enables the effective perpendicular anisotropy barrier to be lowered for both voltage polarities. This mechanism is shown to reduce the critical switching current and effective activation energy. Finally, we analyze the possibility of having switching via interlayer exchange coupling only.
An enhancement of the spin-orbit effects arising on an interface between a ferromagnet (FM) and a heavy metal (HM) is possible through the strong breaking of the structural inversion symmetry in the layered films. Here we show that the introduction of an ultrathin W interlayer between Co and Ru in Ru/Co/Ru films enables to preserve perpendicular magnetic anisotropy (PMA) and simultaneously induce a large interfacial Dzyaloshinskii-Moriya interaction (iDMI). We find that the Ru/Co/W/Ru films have PMA up to 0.35 nm of the nominal thickness of W (tW). The study of the spin-wave propagation in the…
We study the spectral characteristics of spin current nano-oscillators based on the Pt/[Co/Ni] magnetic multilayer with perpendicular magnetic anisotropy. By varying the applied magnetic field and current, both localized and propagating spin wave modes of the oscillation are achieved. At small fields, we observe an abrupt onset of the modulation sidebands. We use micromagnetic simulations to identify this state as a dynamical magnetic skyrmion stabilized in the active device region by spin current injection, whose current-induced dynamics is accompanied by the gyrotropic motion of the core due…
In the present work, using micromagnetic simulation, we show that the magnetic coupling effect plays a very important role in the process of creation of skyrmions in a coupled system of spin-torque nano-oscillators (STNO). First, we have determined the magnetic ground state in an isolated STNO for different values of perpendicular uniaxial anisotropy (PUA) and Dzyaloshinskii-Moriya interaction (DMI). Next, we have applied a perpendicular pulse polarized current density (J) and found that it is possible to create a metastable Néel skyrmion from a disk whose ground state is a single magnetic dom…
Recent work [1,2] suggests that ferromagnetic reversal with spin transfer torque (STT) requires more current in a system in the presence of DMI than switching a typical ferromagnet of the same dimensions and perpendicular magnetic anisotropy (PMA). However, DMI promotes stabilization of skyrmions and we report that when the perpendicular anisotropy is modulated (reduced) for both the skyrmion and ferromagnet, it takes much smaller current to reverse the fixed skyrmion than to reverse the ferromagnet in the same time, or the skyrmion reverses much faster than the ferromagnet at similar levels o…
We present an analytical theory to describe three-dimensional magnetic textures in perpendicularly magnetized magnetic multilayers that arise in the presence of magnetostatic interactions and the Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that domain walls in multilayers develop a complex twisted structure, which persists even for films with strong DMI. The origin of this twist is surface-volume stray field interactions that manifest as a depth-dependent effective field whose form mimics the DMI effective field. We find that the wall twist has a minor impact on the equilibrium sky…
GaMnAs-based magnetic tunnel junction (MTJ) devices are characterized by in-plane and perpendicular-toplane magnetotransport at low temperatures. Perpendicular-to-plane transport reveals the typical tunneling magnetotransport (TMR) signal. Interestingly, a similar TMR signature is observed in the in-plane transport signal. Here, low-ohmic shunting of the MTJ by the top contact results in significant perpendicular-to-plane current paths. This effect allows the determination of TMR ratios of MTJs based on a simplified in-plane measurement. However, the same effect can lead to an inaccurate deter…
We developed a cryogenic temperature deposition process for high-performance CoFeB/MgO/CoFeB magnetic tunnel junctions (MTJs) on 300 mm thermally oxidized silicon wafers. The effect of the deposition temperature of the CoFeB layers on the nanostructure, magnetic and magneto-transport properties of the MTJs were investigated in detail. When CoFeB was deposited at 100 K, the MTJs exhibited a perpendicular magnetic anisotropy (PMA) of 214 uJ/m2 and a voltage-controlled magnetic anisotropy (VCMA) coefficient of -45 fJ/Vm, corresponding to 1.4- and 1.7-fold enhancements in PMA and VCMA, respectivel…
We find numerically skyrmionic textures with skyrmion number Q=0 in ferromagnets with the Dzyaloshinskii-Moriya interaction and perpendicular anisotropy. These have the form of a skyrmion-antiskyrmion pair and may be called chiral droplets. They are stable in an infinite film as well as in disc-shaped magnetic elements. Droplets are found for values of the parameters close to the transition from the ferromagnetic to the spiral phase. We study their motion under spin-transfer torque. They move in the direction of the spin flow and, thus, their dynamics are drastically different than the Hall dy…
We discuss models for massless Dirac fermions being subject to a perpendicular magnetic field in spherical geometry. These models are analogues of Haldane`s spherical construction for massful charge carriers. The single particle states constructed here are easily implemented in existing numerical code for many-body problems in conventional quantum Hall systems. Moreover, the many-body states of fully filled sublevels in the subspace of lowest Landau level index are skyrmions with respect to the layer spin.
Magnetic materials hosting topological spin textures like magnetic skyrmion exhibit nontrivial Hall effect, namely, topological Hall effect (THE). In this study, we demonstrate the emergence of THE in thin films of half-metallic perovskite manganites. To stabilize magnetic skyrmions, we control the perpendicular magnetic anisotropy by imposing a compressive epitaxial strain as well as by introducing a small Ru doping. When the perpendicular magnetic anisotropy is tuned so that it is balanced with the magnetic dipolar interaction, the film exhibits a sizable THE in a magnetization reversal proc…
Spin-transfer ferromagnetic resonance (ST-FMR) in symmetric magnetic tunnel junctions (MTJs) with a varied thickness of the MgO tunnel barrier (0.75 nm < $t_{MgO}$ < 1.05 nm) is studied using the spin-torque diode effect. The application of an RF current into nanosized MTJs generates a DC mixing voltage across the device when the frequency is in resonance with the resistance oscillations arising from the spin transfer torque. Magnetization precession in the free and reference layers of the MTJs is analyzed by comparing ST-FMR signals with macrospin and micromagnetic simulations. From ST-FMR sp…
We report the observation of room-temperature magnetic skyrmions in Pt/Co/Os/Pt thin-film heterostructures and their response to electric currents. The magnetic properties are extremely sensitive to inserting thin Os layers between the Co-Pt interface resulting in reduced saturation magnetization, magnetic anisotropy and Curie temperature. The observed skyrmions exist in a narrow temperature, applied-field and layer-thickness range near the spin-reorientation transition from perpendicular to in-plane magnetic anisotropy. The skyrmions have an average diameter of 2.3μm and transport measurement…
We propose a two terminal nanomagnetic memory element based on magnetization reversal of a perpendicularly magnetized nanomagnet employing a unipolar voltage pulse that modifies the perpendicular anisotropy of the system. Our work demonstrates that the presence of Dzyaloshinskii-Moriya Interaction (DMI) can create alternative route for magnetization reversal that obviates the need for utilizing precessional magnetization dynamics as well as a bias magnetic field that are employed in traditional voltage control of magnetic anisotropy (VCMA) based switching of perpendicular magnetization. We sho…
We study the dynamics of skyrmions in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. An important link between topology and dynamics is established through the construction of unambiguous conservation laws obtained earlier in connection with magnetic bubbles and vortices. In particular, we study the motion of a topological skyrmion with skyrmion number $Q=1$ and a non-topological skyrmionium with $Q=0$ under the influence of an external field gradient. The $Q=1$ skyrmion undergoes Hall motion perpendicular to the direction of the field gradient with a drift velocity proportional to…
The nonlinear dynamic behavior of a magnetic skyrmion in circular nanodots was studied numerically by solving the Landau-Lifshitz-Gilbert equation with a classical spin model. We show that a skyrmion core reversal can be achieved within nanoseconds using a perpendicular oscillating magnetic field. Two symmetric switching processes that correspond to excitations of the breathing mode and the mixed mode (combination of the breathing mode and a radial spin-wave mode) are identified. For excitation of the breathing mode, the skyrmion core switches through nucleation of a new core from a transient …
We investigate the dependence of the Néel skyrmion size and stability on perpendicular magnetic field in ultrathin circular magnetic dots with out-of-plane anisotropy and interfacial Dzyaloshinskii-Moriya exchange interaction. Our results show the existence of two distinct dependencies of the skyrmion radius on the applied field and dot size. In the case of skyrmions stable at zero field, their radius strongly increases with the field applied parallel to the skyrmion core until skyrmion reaches the metastability region and this dependence slows down. More common metastable skyrmions demonstrat…
Magnetic skyrmions are topologically protected states that are very promising for the design of the next generation of ultralow-power electronic devices. In this letter, we propose a magnetic tunnel junction based spin-transfer torque diode with a magnetic skyrmion as ground state and a perpendicular polarizer patterned as nanocontact for a local injection of the current. The key result is the possibility to achieve sensitivities (i.e. detection voltage over input microwave power) larger than 2000V/W for optimized contact diameters. Our results can be very useful for the identification of a ne…
We have performed micromagnetic simulations to study the formation of skyrmions in ferromagnetic elements with different shapes having perpendicular anisotropy. The strength of Dzyaloshinskii-Moriya interaction (D) and uniaxial anisotropy (K) are varied to elucidate the regime in which skyrmion formation can take place. It is found that for a certain combination of D and K skyrmion formation does not happen. Further we also observed that for large D and small K values, finite size effect dominates which in turn hinders formation of typical N'eel (spherical) skyrmions. However the resulting mag…
Future spintronic devices based on skyrmions will require precise control of the skyrmion motion. We show that this goal can be achieved through the use of magnetic antidot arrays. With micromagnetic simulations and semi-analytical calculations based on Thiele equation, we demonstrate that an antidot array can guide the skyrmions in different directions depending on the parameters of the applied current pulse. Despite the fixed direction of the net driving current, due to the non-trivial interplay between the repulsive potential introduced by the antidots, the skyrmion Hall effect and the non-…
It has been reported in experiments that capping layers which enhance the perpendicular magnetic anisotropy (PMA) of magnetic tunnel junctions (MTJs) induce great impact on the tunnel magnetoresistance (TMR). To explore the essential influence caused by capping layers, we carry out ab initio calculations on TMR in the X(001)|CoFe(001)|MgO(001)|CoFe(001)|X(001) MTJ, where X represents the capping layer material which can be tungsten, tantalum or hafnium. We report TMR in different MTJs and demonstrate that tungsten is an ideal candidate for a giant TMR ratio. The transmission spectrum in Brillo…
We demonstrated that thick Permalloy films exhibiting a weak growth-induced perpendicular magnetic anisotropy can be employed as an ideal test system for the investigation of gyration dynamics in topologically trivial and non-trivial magnetic states ranging from an isolated magnetic skyrmion to more complex n$π$ spin configurations.
Magnetic skyrmions formed at temperatures around room temperature in square-based parallelepiped magnetic FePt nanoparticles with perpendicular magnetocrystalline anisotropy (MCA) were studied during the magnetization reversal using micromagnetic simulations. Finite Differences (FD) method were used for the solution of the Landau-Lifshitz-Gilbert equation. Magnetic configurations exhibiting Néel skyrmionic formations were detected. The magnetic skyrmions can be created in different systems generated by the variation of external field, side length and width of the squared-based parallelepiped m…
The measured melting curve $T_{m}(ν)$ between the crystal and liquid phases is analyzed using thermodynamics to extract the change of magnetization $ΔM$ as a function of the Landau level filling factor \ $ν,$ near $ν=1$. \ An explanation of $ΔM$($ν)$ is proposed \ in terms of Skyrmions. \ Near $ν=3$, a Wigner crystal is the most probable solid phase, experiments excluding Skyrmions.
We report a significant Dzyaloshinskii-Moriya interaction (DMI) and perpendicular magnetic anisotropy (PMA) at interfaces comprising hexagonal boron nitride (h-BN) and Co. By comparing the behavior of these phenomena at graphene/Co and h-BN/Co interfaces, it is found that the DMI in latter increases as a function of Co thickness and beyond three monolayers stabilizes with one order of magnitude larger values compared to those at graphene/Co, where the DMI shows opposite decreasing behavior. At the same time, the PMA for both systems shows similar trends with larger values for graphene/Co and n…
From a theoretical perspective, we demonstrate that nanometric magnetic skyrmions are created by application of a circularly polarized microwave magnetic field to a thin-plate Dzyaloshinskii-Moriya ferromagnet with fabricated rectangular holes. This phenomenon is caused by an effective steady magnetic field perpendicular to the microwave-polarization plane induced by the rotating magnetic field and the intense interference of spin waves excited by this magnetic field due to the hole structure, which causes reversals of local magnetizations and results in the formation of skyrmions. Our proposa…
A model for a spin-torque nano-oscillator based on the self-sustained oscillation of a magnetic skyrmion is presented. The system involves a circular nanopillar geometry comprising an ultrathin film free magnetic layer with a strong Dzyaloshinkii-Moriya interaction and a polariser layer with a vortex-like spin configuration. It is shown that spin-transfer torques due to current flow perpendicular to the film plane leads to skyrmion gyration that arises from a competition between geometric confinement due to boundary edges and the vortex-like polarisation of the spin torques. A phenomenology fo…
It is predicted magnetic skyrmions can be controllably moved on surfaces using a focused laser beam. Here an absorbed power of the order 1 mW, focused to a spot-size of the order 10 $μ$m, results in a local temperature increase of around 50 K, and a local perpendicular strain of the order 10$^{-3}$ due to the thermo-elastic effect. For positive magneto-elastic coupling this generates a strong attractive force on skyrmions due to the magneto-elastic effect. The resultant motion is dependent on forces due to i) gradients in the local strain-induced magnetic anisotropy, ii) gradients in the effec…
We propose a new method to generate magnetic skyrmions through spin-wave focusing in chiral ferromagnets.A lens is constructed to focus spin waves by a curved interface between two ferromagnetic thin films with different perpendicular magnetic anisotropies. Based on the principle of identical magnonic path length, we derive the lens contour that can be either elliptical or hyperbolical depending on the magnon refractive index. Micromagnetic simulations are performed to verify the theoretical design. It is found that under proper condition magnetic skyrmions emerge near the focus point of the l…
We study the current-driven skyrmion expulsion from magnetic nanostrips using micromagnetic simulations and analytic calculations. We explore the threshold current density for the skyrmion expulsion, and show that this threshold is determined by the critical boundary force as well as the spin-torque parameters. We also find the dependence of the critical boundary force on the magnetic parameters; the critical boundary force decreases with increasing the exchange stiffness and perpendicular anisotropy constants, while it increases with increasing Dzyaloshinskii-Moriya interaction and saturation…
We report on the effect of the lateral confinement and a perpendicular magnetic field on isolated room-temperature magnetic skyrmions in sputtered Pt/Co/MgO nanotracks and nanodots. We show that the skyrmions size can be easily tuned by playing on the lateral dimensions of the nanostructures and by using external magnetic field amplitudes of a few mT, which allow to reach sub-100 nm diameters. Our XMCD-PEEM observations also highlight the important role of the pinning on the skyrmions size and stability under an out-of-plane magnetic field. Micromagnetic simulations reveal that the effect of l…
The well-known Hall effect describes the transverse deflection of charged particles (electrons or holes) in an electric-current carrying conductor under the influence of perpendicular magnetic fields, as a result of the Lorentz force. Similarly, it is intriguing to examine if quasi-particles without an electric charge, but with a topological charge, show related transverse motion. Chiral magnetic skyrmions with a well-defined spin topology resulting in a unit topological charge serve as good candidates to test this hypothesis. In spite of the recent progress made on investigating magnetic skyr…
We fabricate devices in which a magnetic nanopillar spin valve makes contact to a Co/Pt bilayer thin film with perpendicular magnetic anisotropy, in order to achieve local control of domains in the Co/Pt bilayer underneath the nanopillar. The goal is to develop the ability to nucleate, detect, and annihilate magnetic skyrmions in the Co/Pt using spin-polarized currents from the nanopillar. We demonstrate the ability to distinguish the local behavior of the Co/Pt film beneath the nanopillar from the extended film and show that the two can switch independently of each other. This allows us to is…
A generic theory about skyrmion crystal (SkX) formation in chiral magnetic thin films and its fascinating thermodynamic behaviours is presented. A chiral magnetic film can have many metastable states with an arbitrary skyrmion density up to a maximal value when a parameter $κ$, which measures the relative Dzyaloshinskii-Moriya interaction (DMI) strength, is large enough. The lowest energy state of an infinite film is a long zig-zagged ramified stripe skyrmion occupied the whole film in the absence of a magnetic field. Under an intermediate field perpendicular to the film, the lowest energy sta…
We present a comprehensive micromagnetic model of isolated axisymmetric skyrmions in magnetic multilayers with perpendicular anisotropy. Most notably, the essential role of the internal dipolar field is extensively considered with a minimum amount of assumptions on the magnetization profiles. The tri-dimensional structure of the multilayered skyrmions is modeled by their radial profiles in each layer. We first compare the results of the model against a full micromagnetic description in Cartesian coordinates. Our model combines information on both layer-dependent size and chirality of the skyrm…
