The nature of spin wave modes excited by spin-polarized direct current in a spin-torque auto-oscillator based on a magnetic nanocontact was studied by a micromagnetic simulation in the case when the external bias magnetic field was rotated from the in-plane to perpendicular-to-plane orientation. In qualitative agreement with the weakly-nonlinear analytical theory it was found, that at a certain critical angle, an abrupt switching from the self-localized nonlinear "bullet" mode to a propagating quasi-linear Slonczewski mode takes place, and is accompanied by an upward jump in generated microwave frequency. It was, also, found that the analytical theory overestimates the magnitude of a critical magnetization angle, corresponding to the mode switching, and that the magnitude of the frequency jump caused by the mode switching is inversely proportional to the nanocontact radius.
This letter studies the dynamical behavior of spin-Hall nanoscillators from a micromagnetic point of view. The model parameters have been identified by reproducing recent experimental data quantitatively. Our results indicate that a strongly localized mode is observed for in-plane bias fields such as in the experiments, while predict the excitation of an asymmetric propagating mode for large enough out-of plane bias field similarly to what observed in spin-torque nanocontact oscillators. Our findings show that spin-Hall nanoscillators can find application as spin-wave emitters for magnonic app…
We study bubble domain wall dynamics using micromagnetic simulations in perpendicularly magnetized ultra-thin films with disorder and Dzyaloshinskii-Moriya interaction. Disorder is incorporated into the material as grains with randomly distributed sizes and varying exchange constant at the edges. As expected, magnetic bubbles expand asymmetrically along the axis of the in-plane field under the simultaneous application of out-of-plane and in-plane fields. Remarkably, the shape of the bubble has a ripple-like part which causes a kink-like (steep decrease) feature in the velocity versus in-plane …
A new methodology for micromagnetic simulations of magnetic nanocomposites is presented. The methodology is especially suitable for simulations of two-phase composites consisting of magnetically hard inclusions in a soft magnetic matrix phase. The proposed technique allows to avoid the unnecessary discretization of the 'hard' inclusions (these are normally in a single-domain state), but enables an arbitrary fine discretization of the 'soft' phase. The method is applied to the determination of the equilibrium magnetization state of an iron-based nanocomposite from the Nanoperm (FeZrBCu) family …
Manipulation of magnetic domain walls can be used to improve the capabilities of the next generation of memory and sensing devices. Materials of recent interest for such devices include heterostructures of ultrathin ferromagnets sandwiched between a heavy metal and an oxide, where spin-orbit coupling and broken inversion symmetry give rise to the Dzyaloshinskii-Moriya interaction (DMI), stabilizing chiral domain walls. The efficiency of the motion of these chiral domain walls may be controlled using in-plane magnetic fields. This property has been used for measurement of DMI strength. While mi…
An atomic level micromagnetic model of granular recording media is developed and applied to examine external field-induced grain switching at elevated temperatures which captures non-uniform reversal modes. The results are compared with traditional methods which employ the Landau-Lifshitz-Gilbert equations based on uniformly magnetized grains with assigned intrinsic temperature profiles for $M(T)$ and $K(T)$. Using nominal parameters corresponding to high-anisotropy FePt-type media envisioned for Energy Assisted Magnetic Recording, our results demonstrate that atomic-level reversal slightly re…
Recent studies on heterostructures of ultrathin ferromagnets sandwiched between a heavy metal layer and an oxide have highlighted the importance of spin-orbit coupling (SOC) and broken inversion symmetry in domain wall (DW) motion. Specifically, chiral DWs are stabilized in these systems due to the Dzyaloshinskii-Moriya interaction (DMI). SOC can also lead to enhanced current induced DW motion, with the spin Hall effect (SHE) suggested as the dominant mechanism for this observation. The efficiency of SHE driven DW motion depends on the internal magnetic structure of the DW, which could be cont…
The recent development of a micromagnetic simulation methodology - suitable for multiphase magnetic nanocomposites - permits the computation of the magnetic microstructure and of the associated magnetic small-angle neutron scattering (SANS) cross section of these materials. In this review article we summarize results on the micromagnetic simulation of magnetic SANS from two-phase nanocomposites. The decisive advantage of this approach resides in the possibility to srutinize the individual magnetization Fourier contributions to the total magnetic SANS cross section, rather than their sum, which…
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 …
We present results of micromagnetic simulations of thin ferromagnetic nano hemispheroidal shells with sizes ranging from 1 to 50 nm (inside dimensions). Depending on the geometrical and magnetic parameters of the hemispheroidal shell, there exist four different magnetic phases: easy axis, easy plane, onion and vortex. The profile for the vortex magnetization distribution is analyzed and the limitations and applicability of different vortex ansatzes are discussed. In addition, we investigate the total energy density for each of the magnetic distributions as a function of the hemispheroidal shel…
We investigate the spin dynamics including Gilbert damping in the ferromagnetic nanowire arrays. We have measured the ferromagnetic resonance of ferromagnetic nanowire arrays using vector-network analyzer ferromagnetic resonance (VNA-FMR) and analyzed the results with the micromagnetic simulations. We find excellent agreement between the experimental VNA-FMR spectra and micromagnetic simulations result for various applied magnetic fields. We find that the demagnetization factor for longitudinal conditions, Nz (Ny) increases (decreases) as decreasing the nanowire width in the micromagnetic simu…
We have used numerical micromagnetics for the calculation of the magnetic (small-angle) neutron scattering cross section of nanocomposites. The novel aspect of our approach consists in the possibility to study the applied-field dependence of the individual contributions to the total magnetic scattering. Such a micromagnetic tool ideally complements neutron experiments in which one generally measures only a weighted sum of the Fourier components of the magnetization. The procedure furnishes unique and fundamental information regarding the magnetic microstructure and corresponding magnetic scatt…
Magnetic cylindrical nanowires are very fascinating objects where the curved geometry allows many novel magnetic effects and a variety of non-trivial magnetic structures. Micromagnetic modelling plays an important role in revealing the magnetization distribution in magnetic nanowires, often not accessible by imaging methods with sufficient details. Here we review the magnetic properties of the shape anisotropy-dominated nanowires and the nanowires with competing shape and magnetocrystalline anisotropies, as revealed by micromagnetic modelling. We discuss the variety of magnetic walls and magne…
Micromagnetic instabilities and non-uniform magnetization states play a significant role in spin transfer induced switching of nanometer scale magnetic elements. Here we model domain wall mediated switching dynamics in perpendicularly magnetized magnetic tunnel junction nanopillars. We show that domain wall surface tension always leads to magnetization oscillations and instabilities associated with the disk shape of the junction. A collective coordinate model is developed that captures aspects of these instabilities and illustrates their physical origin. Model results are compared to those of …
In this paper we present detailed numerical simulation studies on the synchronization of two spin-torque nanooscillators (STNO) in the quasi-1D geometry: magnetization oscillations are induced in a thin NiFe nanostripe by a spin polarized current injected via square-shaped CoFe nanomagnets on the top of this stripe. In a sufficiently large out-of-plane field, a propagating oscillation mode appears in such a system. Due to the absence of the geometrically caused wave decay in 1D systems, this mode is expected to enable a long-distance synchronization between STNOs. Indeed, our simulations predi…
We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the streng…
We report here the results of micromagnetic simulations of square artificial spin ice (ASI) systems with defects. The defects are introduced by misaligning of a nanomagnet at the vertex. In these defective systems, we are able to stabilize emergent monopole-like state by applying a small external field. We observe a systematic change of dipolar energies of the systems with varying misalignment angle. The fields at which the emergent monopoles are created vary linearly with the dipolar energies of the systems. Our results clearly show that the magnetization reversal of the ASI systems is intric…
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…
In this Article we discuss a micromagnetic modelling approach to describe the ultrafast spin-transfer torque excitation of coherent and incoherent magnons on the nanoscale. Implementing the action of a femtosecond spin current pulse entering an orthogonally magnetized thin ferromagnetic film, we reproduce recent experimental results and reveal the factors responsible for the unequal excitation efficiency of various spin waves. Our findings are in an excellent agreement with the results of an analytical description of spin-wave excitation based on classical kinetic equations. Furthermore, we su…
We analyze the micromagnetics of short longitudinal modulations of a high-magnetization material in cylindrical nanowires made of a soft-magnetic material of lower magnetization such as permalloy, combining magnetic microscopy, analytical modeling, and micromagnetic simulations. The mismatch of magnetization induces curling of magnetization around the axis in the modulations, in an attempt to screen the interfacial magnetic charges. The curling angle increases with modulation length, until a plateau is reached with nearly full charge screening for a specific length scale~$Δ_\mathrm{mod}$, larg…
We report the observation and micromagnetic analysis of current-driven magnetization switching in nanoscale ring-shaped magnetic tunnel junctions. When the electric current density exceeds a critical value of the order of $6\times 10^{6}$A/cm$^2$, the magnetization of the two magnetic rings can be switched back and forth between parallel and antiparallel onion states. Theoretical analysis and micromagnetic simulation show that the dominant mechanism for the observed current-driven switching is the spin torque rather than the current-induced circular Oersted field.
The magnetization reversal in 330 nm triangular prismatic magnetic nanoelements with variable magnetocrystalline anisotropy similar to that of partially chemically ordered FePt is studied using micromagnetic simulations employing Finite Element discretizations. Several magnetic properties including the evaluation of the magnetic skyrmion number $S$ are computed in order to characterize magnetic configurations exhibiting vortex-like formations. Magnetic vortices and skyrmions are revealed in different systems generated by the variation of the magnitude and relative orientation of the magnetocry…
Magnetic disks or dots of soft magnetic material of sub-micron dimensions may have as the lowest energy magnetic configuration a single-domain structure, with magnetization either perpendicular of parallel to the plane, or else may form magnetic vortices. The properties of these vortices may be used to encode data bits, in magnetic memory applications. In the present work the OOMMF code was used to compute by micromagnetic simulation the energy and the magnetization of circular and elliptical nanodots of permalloy. For the elliptical magnetic dots the analysis was made for variable thickness a…
Magnetic vortex is topologically nontrivial and commonly found in ferromagnetic nanodisks. So far, three classes spin-wave eigenmodes, i.e., gyrotropic, azimuthal and radial modes, have been identified in ferromagnetic nanodisks. Here, using micromagnetic simulation and analytical calculation, we reveal twisted spin-wave modes in a thick permalloy (Ni0.8Fe0.2) nanodisk. The twisted spin-waves carry topological charges, which sign depends on the core polarity of the magnetic vortex in the nanodisk. By applying rotating magnetic fields at one end of the sample, we observe continuous generation o…
Here we describe the development of the MALTS software which is a generalised tool that simulates Lorentz Transmission Electron Microscopy (LTEM) contrast of thin magnetic nanostructures. Complex magnetic nanostructures typically have multiple stable domain structures. MALTS works in conjunction with the open access micromagnetic software Object Oriented Micromagnetic Framework or MuMax. Magnetically stable trial magnetisation states of the object of interest are input into MALTS and simulated LTEM images are output. MALTS computes the magnetic and electric phases accrued by the transmitted el…
We investigate the effect of curvature on the energy and stability of domain wall configurations in curved cylindrical nanotubes and nanowires. We use micromagnetic simulations to calculate the phase diagram for the transverse wall (TW) and vortex wall (VW) states in tubes, finding the ground state configuration and the metastability region where both types of walls can exist. The introduction of curvature shifts the range for which the TW is the ground state domain wall to higher diameters, and increases the range of metastability. We interpret this behavior to be primarily due to the curvatu…
Cylindrical nanowires made of soft magnetic materials, in contrast to thin strips, may host domain walls of two distinct topologies. Unexpectedly, we evidence experimentally the dynamic transformation of topology upon wall motion above a field threshold. Micromagnetic simulations highlight the underlying precessional dynamics for one way of the transformation, involving the nucleation of a Bloch-point singularity, however, fail to reproduce the reverse process. This rare discrepancy between micromagnetic simulations and experiments raises fascinating questions in material and computer science.
We measure the frequencies of spin waves in nm-thick perpendicularly magnetized FeCoB systems, and model the frequencies to deduce the exchange stiffness of this material in the ultrathin limit. For this, we embody the layers in magnetic tunnel junctions patterned into circular nanopillars of diameters ranging from 100 to 300 nm and we use magneto-resistance to determine which rf-current frequencies are efficient in populating the spin wave modes. Micromagnetic calculations indicate that the ultrathin nature of the layer and the large wave vectors used ensure that the spin wave frequencies are…
We perform 3D micromagnetic simulations of current-driven magnetization dynamics in nanoscale exchange biased spin-valves that take account of (i) back action of spin-transfer torque on the pinned layer, (ii) non-linear damping and (iii) random thermal torques. Our simulations demonstrate that all these factors significantly impact the current-driven dynamics and lead to a better agreement between theoretical predictions and experimental results. In particular, we observe that, at a non-zero temperature and a sub-critical current, the magnetization dynamics exhibits nonstationary behaviour in …
The current-induced motion of a domain wall in a semicircle nanowire with applied Zeeman field is investigated. Starting from a micromagnetic model we derive an analytical solution which characterizes the domain-wall motion as a harmonic oscillation. This solution relates the micromagnetic material parameters with the dynamical characteristics of a harmonic oscillator, i.e., domain-wall mass, resonance frequency, damping constant, and force acting on the wall. For wires with strong curvature the dipole moment of the wall as well as its geometry influence the eigenmodes of the oscillator. Based…
Magnetic nanowires (NW) are promising candidates for heat generation under AC-field application due to their large shape anisotropy. They may be used for catalysis, hyperthermia or water purification treatments. In the present work we theoretically evaluate the heat dissipated by a single magnetic nanowire, originated from the domain wall dynamics under the action of an AC-field. We compare the Permalloy NWs (which demagnetize via the transverse wall propagation) with the Co fcc NWs whose reversal mode is via a vortex domain wall. The average hysteresis loop areas -which are proportional to th…
We study the effect of the Dzyaloshinskii-Moriya interaction (DMI) on current-induced magnetic switching of a perpendicularly magnetized heavy-metal/ferromagnet/oxide trilayer both experimentally and through micromagnetic simulations. We report the generation of stable helical magnetization stripes for a sufficiently large DMI strength in the switching region, giving rise to intermediate states in the magnetization confirming the essential role of the DMI on switching processes. We compare the simulation and experimental results to a macrospin model, showing the need for a micromagnetic approa…
We study the excitation of spin waves in scaled magnetic waveguides using the magnetoelastic effect. In uniformly magnetized systems, normal strains parallel or perpendicular to the magnetization direction do not lead to spin wave excitation since the magnetoelastic torque is zero. Using micromagnetic simulations, we show that the nonuniformity of the magnetization in submicron waveguides due to the effect of the demagnetizing field leads to the excitation of spin waves for oscillating normal strains both parallel and perpendicular to the magnetization. The excitation by biaxial normal in-plan…
We investigate numerically the micromagnetic properties and the low-energy physics of an artificial square spin system in which the nanomagnets are physically connected at the lattice vertices. Micromagnetic simulations reveal that the energy stored at the vertex sites strongly depends on the type of magnetic domain wall formed by the four connected nanomagnets. As a consequence, the energy gap between the vertex types can be partially modified by varying the geometrical parameters of the nanomagnets, such as their width and thickness. Based on the energy levels given by the micromagnetic simu…
Strain-mediated thin film multiferroics comprising piezoelectric/ferromagnetic heterostructures enable the electrical manipulation of magnetization with much greater efficiency than other methods; however, the investigation of nanostructures fabricated from these materials is limited. Here we characterize ferromagnetic Ni nanostructures grown on a ferroelectric PMN-PT substrate using scanning electron microscopy with polarization analysis (SEMPA) and micromagnetic simulations. The magnetization of the Ni nanostructures can be controlled with a combination of sample geometry and applied electri…
Spinmotive force induced by domain wall motion in perpendicularly magnetized nanowires is numerically demonstrated. We show that using nanowires with large magnetic anisotropy can lead to a high stability of spinmotive force under strong magnetic fields. We observe spinmotive force in the order of tens of microvolt in a multilayered Co/Ni nanowire and in the order of several hundred microvolt in a FePt nanowire; the latter is two orders of magnitude greater than that in permalloy nanowires reported previously. The narrow structure and low mobility of a domain wall under magnetic fields in perp…
In this paper, we employ micromagnetic simulations to study non-adiabatic stochastic resonance (NASR) excited by spin-transfer torque in a super-paramagnetic free layer nanomagnet of a nanoscale spin valve. We find that NASR dynamics involves thermally activated transitions among two static states and a single dynamic state of the nanomagnet and can be well understood in the framework of Markov chain rate theory. Our simulations show that a direct voltage generated by the spin valve at the NASR frequency is at least one order of magnitude greater than the dc voltage generated off the NASR freq…
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…
Deterministic current-induced spin-orbit torque (SOT) switching of magnetization in a heavy transition metal/ferromagnetic metal/oxide magnetic heterostructure with the ferromagnetic layer being perpendicularly-magnetized typically requires an externally-applied in-plane field to break the switching symmetry. We show that by inserting an in-plane magnetized ferromagnetic layer CoFeB underneath the conventional W/CoFeB/MgO SOT heterostructure, deterministic SOT switching of the perpendicularly-magnetized top CoFeB layer can be realized without the need of in-plane bias field. Kerr imaging study…
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 …
We report here the results of two-dimensional electron gas based micro-Hall magnetometry measurements and micromagnetic simulations of dipolar coupled nanomagnets of Ni80Fe20 arranged in a double ring-like geometry. We observe that although magnetic force microscopy images exhibit single domain like magnetic states for the nanostructures, their reversal processes may undergo complex behavior. The details of such reversal behavior is observed as specific features in micro-Hall magnetometry data which compares well with the micromagnetic simulation data.
We study the current-driven domain wall (DW) motion in cylindrical nanowires using micromagnetic simulations by implementing the Landau-Lifshitz-Gilbert equation with nonlocal spin-transfer torque in a finite difference micromagnetic package. We find that in the presence of DW Gaussian wave packets (spin waves) will be generated when the charge current is applied to the system suddenly. And this effect is excluded when using the local spin-transfer torque. The existence of spin waves emission indicates that transverse domain walls can not move arbitrarily fast in cylindrical nanowires although…
Spin Hall effect (SHE) induced reversal of perpendicular magnetization has attracted significant interest, due to its potential to lead to low power memory and logic devices. However, the switching requires an assisted in-plane magnetic field, which hampers its practical applications. Here, we introduce a novel approach for external-field-free spin Hall switching of a perpendicular nanomagnet by utilizing a local dipolar field arising from an adjacent in-plane magnetic layer. Robust switching of perpendicular CoFeB nanopillars in a dipole-coupled composite stack is experimentally demonstrated …
In this paper we present an overview of recent progress made in the understanding of the spin-torque induced magnetization dynamics in nanodevices using mesoscopic micromagnetic simulations. We first specify how a spin-torque term may be added to the usual Landau-Lifshitz-Gilbert equation of magnetization motion and detail its physical meaning. After a brief description of spin-torque driven dynamics in the macrospin approximation, we discuss the validity of this approximation for various experimentally relevant geometries. Next, we perform a detailed comparison between accurate experimental d…
Perpendicular shape anisotropy (PSA) offers a practical solution to downscale spin-transfer torque Magnetic Random-Access Memory (STT-MRAM) beyond the sub-20 nm technology node whilst retaining thermal stability of the storage layer magnetization. However, our understanding of the thermomagnetic behavior of PSA-STT-MRAM is often indirect, relying on magnetoresistance measurements and micromagnetic modelling. Here, the magnetism of a FeCoB / NiFe PSA-STT-MRAM nano-pillar is investigated using off-axis electron holography, providing spatially resolved magnetic information as a function of temper…
Micromagnetic Modeling of Surface Acoustic Wave Driven Dynamics: Interplay of Strain, Magnetorotation, and Magnetic Anisotropy
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Institut des Nanosciences de Paris（巴黎纳米科学研究所）；Université de Strasbourg（斯特拉斯堡大学）；Institut de Physique et Chimie des Matériaux de Strasbourg（斯特拉斯堡材料与物理化学研究所）
Geometrical frustration arised in spin ices leads to fascinating emergent physical properties. Nowadays there is a wide diversity of the artificial structures, mimicking spin ice at the nanoscale and demonstrating some new effects. Most of the nanoscaled spin ices are two dimensional. Ferromagnetic inverse opal-like structures (IOLS) are among inspiring examples of the three-dimensional system exhibiting spin ice behaviour. However detailed examination of its properties is not straightforward. Experimental technique which is able to unambiguously recover magnetization distribution in 3D mesosc…
We report experimental and analytical work on spin-transfer torque induced vortex dynamics in metallic nanopillars with in-plane magnetized layers. We study nanopillars with a diameter of 150 nm, containing two Fe layers with a thickness of 15 nm and 30 nm respectively, separated by a 6 nm Ag spacer. The sample geometry is such that it allows for the formation of magnetic vortices in the Fe disks. As confirmed by micromagnetic simulations, we are able to prepare states where one magnetic layer is homogeneously magnetized while the other contains a vortex. We experimentally show that in this co…
