Micromagnetic Simulations Research Articles

Parametric Excitation and Instabilities of Spin Waves Driven by Surface Acoustic Waves

AbstractThe parametric excitation of spin waves by coherent surface acoustic waves in metallic magnetic thin film structures is demonstrated experimentally using Brillouin light scattering spectroscopy. Complementary micromagnetic simulations and analytical modeling reveal that, depending on the experimental conditions, the spin‐wave instabilities originate from different phonon‐magnon and magnon‐magnon scattering processes. This opens novel ways to create micro‐scaled nonlinear magnonic systems for logic and data processing that profit from the efficient excitation of phonons using piezoelectricity.

Current-controlled periodic double-polarity reversals in a spin-torque vortex oscillator

Micromagnetic simulations are used to study a spin-torque vortex oscillator excited by an out-of-plane dc current. The vortex core gyration amplitude is confined between two orbits due to periodical vortex core polarity reversals. The upper limit corresponds to the orbit where the vortex core reaches its critical velocity triggering the first polarity reversal which is immediately followed by a second one. After this double polarity reversal, the vortex core is on a smaller orbit that defines the lower limit of the vortex core gyration amplitude. This double reversal process is a periodic phenomenon and its frequency, as well as the upper and lower limit of the vortex core gyration, is controlled by the input current density while the vortex chirality determines the apparition of this confinement regime. In this non-linear regime, the vortex core never reaches a stable orbit and thus, it can be of interest for neuromorphic application as a leaky integrate-and-fire neuron for example.

Microstructure, phase compositions, and coercivity evolution in micron-thick SmCo-based permanent magnetic films

Permanent magnetic thick films are increasingly used in Micro-Electro-Mechanical Systems (MEMS) devices, but the interplay between magnetic properties, microstructure, and film thickness remains underexplored. We deposited SmCo-based films with thicknesses ranging from 350 nm to 1300 nm using magnetron sputtering at room temperature, followed by in-situ annealing. Our study examined the evolution of microstructure, phase composition, magnetic properties, and domain structures as thickness increases. The films displayed dense, fibrous structures typical of the zone T-type region, with 3D morphologies forming a network structure and an arc-shaped surface that expands with thickness. At thinner levels (around 350 nm), an amorphous SmCo phase predominates, prone to oxidation, while at greater thicknesses, the SmCo5 phase dominates but maintains a grain size of 12–15 nm. Coercivity decreases significantly from 33 kOe to 8 kOe as thickness increases from 630 to 1300 nm due to the diminishing pinning effect and dominance of the reversal domain nucleation mechanism. Analysis using magnetic force microscopy and micromagnetic simulations indicates that this reduction in coercivity is mainly due to the decomposition of the SmCo5 phase and a reduction in magnetic domain size.

Impact of thickness and saturation direction over magnetostatic mode energies and profiles in Ni80Fe20 antidots

Abstract The magnetization dynamics of square arrays of circular antidots fabricated on Si(001) substrates using deep ultraviolet lithography with a 248 nm exposing wavelength have been studied. The effects of thickness (40 nm and 80 nm) and the in-plane direction of the applied magnetic field on the magnetostatic mode energies were investigated through ferromagnetic resonance experiments and micromagnetic simulations for both thicknesses. The experimental results and the simulations allowed the determination of nature of the magnetostatic modes nature measured at angles of 0° and 45° between the applied magnetic field and the axis of the square array. Notably, in this geometry, the main modes do not disapear when the sample is rotated; instead, the localization of the modes follow the rotation of the applied field, with a variation in measured intensity directly related to the surface area occupied by the localized mode.

Spin transfer torque and field driven 360° domain wall to bimeron conversion

In this work, using micromagnetic simulations we study the mechanism involved in the conversion of a 360° domain wall into stable pairs of bimeron (Q = +1) and antibimeron (Q = -1) in a ferromagnetic background when it is subjected to Zhang Li type of spin transfer torque. We show that the time scales associated with the conversion process can be significantly reduced by applying out of plane bias field. In particular, choosing a constant inclination angle and increasing the intensity of bias field aids in reducing the energy barrier required to stabilize the spin textures. Similarly, for a constant bias field intensity, varying the inclination angle between 0° to 40° reveals that the time required to stabilize the first bimeron is reduced by ∼ 3 ns. Further, tailoring the strength of in-plane current density as well as effective uniaxial anisotropy leads to faster conversion of domain wall to bimerons.

Lamellar Zr-rich phase and its influence on coercivity for Sm(CoFeCuZr)z magnets

The precipitation-hardened Sm-Co permanent magnets relied on the pinning of nanocellular structures to achieve high coercivity, and have an irreplaceable position in high-temperature applications. In this article, by employing micromagnetic simulations and magnetic domain observations, the pinning behavior of lamellar phases (Z-phase) were investigated, which has not been well understood before. The results showed that the Z-phase can serve as a strong pinning position, but due to the parallel lamellar distribution, the magnetic domain walls can move around. Additionally, the effect of Z-phase on coercivity was achieved by changing the morphology of magnetic domain walls during magnetization reversal. For attractive pinning, the coercivity was reduced by the Z-phase, while for repulsive pinning, the Z-phase increased the coercivity when γZ＜0.54γH. Our findings can provide a novel understanding of the coercivity mechanism of precipitation-hardened Sm-Co permanent magnets.

Initialization-free multistate memristor: Synergy of spin–orbit torque and magnetic fields

Spin–orbit torque (SOT)-based perpendicularly magnetized memory devices with multistate memory have garnered significant interest due to their applicability in low-power in-memory analog computing. However, current methods are hindered by initialization problems, such as prolonged writing duration, and limitations, on the number of magnetic states. Consequently, a universal method for achieving multistate in perpendicular magnetic anisotropy (PMA)-based stacks remains elusive. Here, we propose a general experimental method for achieving multistate without any initialization step in SOT-driven magnetization switching by integrating an external out-of-plane magnetic field. Motivated by macrospin calculations coupled with micromagnetic simulations, which demonstrate the plausibility of magnetization state changes due to out-of-plane field integration, we experimentally verify multistate behavior in Pt/Co/Pt and W/Pt/Co/AlOx stacks. The occurrence of multistate behavior is attributed to intermediate domain states with Néel domain walls. We achieve repeatable 18 multistate configurations with a minimal reduction in retentivity through energy barrier measurements, paving the way for efficient analog computing.

High data rate spin-wave transmitter

Spin-wave devices have recently become a strong competitor in computing and information processing owing to their excellent energy efficiency. Researchers have explored magnons, the quanta of spin-waves, as an information carrier and significant progress has occurred in both excitation and computation. However, most transmission designs remain immature in terms of data rate and information complexity as they only utilize simple spin-wave pulses and suffer from signal distortion. In this work, using micromagnetic simulations, we demonstrate a spin-wave transmitter that operates reliably at a data rate of 4 Gbps over significant (multi-micron) distances with error rates as low as 10−14. Spin-wave amplitude is used to encode information. Carrier frequency and data rate are carefully chosen to restrict dispersion spreading, which is the main reason for signal distortion. We show that this device can be integrated into either pure-magnonic circuits or modern electronic networks. Our study reveals the potential for achieving an even higher data rate of 10 Gbps and also offers a comprehensive and logical methodology for performance tuning.

Skyrmion dynamics in attractive and repulsive local magnetic fields

The study of the behavior of magnetic skyrmions in local magnetic fields’ nanometric length-scale has gained increasing interest in recent years due to the theoretical proposal of magnetic skyrmion–superconducting vortex pairs as potential hosts for topologically protected bound states, which hold high promise for applications in quantum computing. From a magnetic interaction point-of-view, the key interest lies in understanding the skyrmion dynamics triggered by the magnetic energy landscape generated by the superconducting vortex. Here, we present a micromagnetic study of the dynamics of nanometric skyrmions inside a Gaussian magnetic field profile, which is used as a simplified version of the vortex magnetic flux. On the one hand, our calculations show that local non-linear magnetic fields can be very effective in controlling the dynamics of magnetic skyrmions; in particular, they offer the appealing possibility to manipulate skyrmions in a two dimensional space. On the other hand, they also show that the dynamics of a skyrmion in a local magnetic field can be manipulated via a uniform external magnetic field without any change in the magnetic field gradient. An analytical expression for the skyrmion velocity is given, and the corresponding microscopic dynamics are confirmed by the micromagnetic simulations. This work is expected to motivate more theoretical and experimental studies of the behavior of magnetic skyrmions in proximity to superconducting vortices.

The Origin of Magnetofossil Coercivity Components: Constraints From Coupled Experimental Observations and Micromagnetic Calculations

AbstractBiogenic magnetite crystals produced by magnetotactic bacteria (MTB) and associated magnetofossils in sediments are characterized by variable morphologies, grain sizes, and chain structures. Magnetofossils are widely used in paleomagnetic and paleoenvironmental studies, but the complex magnetofossil shapes and particle arrangements significantly affect magnetic properties, hampering their magnetic detection and proxy interpretation. Here we perform coupled experimental and micromagnetic modeling analyses of typical magnetofossil‐rich sediments, where the effects of magnetofossil crystal forms and microstructures on magnetic properties can be quantitatively separated. Since the in situ magnetofossil chain structures in sediments remain poorly known, we compare results from magnetic measurements and micromagnetic simulations based on realistic magnetofossil shapes and grain size distributions. Our results suggest that bullet‐shaped magnetofossils certainly contribute to the biogenic hard (BH) coercivity component with a minor contribution from elongated prismatic particles, and collapsed equidimensional grains to the biogenic soft (BS) component. Micromagnetic simulations with different collapse models of bullet‐shaped magnetofossils produce variable FORC (first‐order reversal curve) central‐ridge contributions with similar coercivity distributions. Sensitivity test suggests that samples containing different forms of magnetofossils can produce the BH coercivity component if the proportion of the bullet‐shaped particles is more than ∼2%. Magnetofossil assemblages with a higher proportion of bullet‐shaped particles have higher coercivities, squareness ratios, and larger BH contents. Our data shed new light on understanding the origin of magnetofossil coercivity components and the in situ magnetofossil microstructures in sediments, which is widely useful for interpreting magnetofossil proxy signals in geological records.

Dynamic properties of the magnetic skyrmion driven by electromagnetic waves with spin angular momentum and orbital angular momentum

Abstract We theoretically studied the dynamic properties of the skyrmion driven by electromagnetic (EM) waves with spin angular momentum (SAM) and orbital angular momentum (OAM) using micromagnetic simulations. First, the guiding centers of the skyrmion driven by EM waves with SAM, i.e., left-handed and right-handed circularly polarized EM waves, present circular trajectories, while present elliptical trajectories under linear EM waves driving due to the superposition of oppositely polarized wave components. Second, the trajectories of the skyrmion driven by EM waves with OAM demonstrate similar behavior to that driven by linearly polarized EM waves. Because the wave vector intensity varies with the phase for both linearly polarized EM waves and EM waves with OAM, the angular momentum is transferred to the skyrmion non-uniformly, while the angular momentum is transferred to the skyrmion uniformly for left-handed and right-handed circularly polarized EM driving. Third, the dynamic properties of the skyrmion driven by EM waves with both SAM and OAM are investigated. It is found that the dynamic trajectories exhibit more complex behavior due to the contributions or competition of SAM and OAM. We investigate the characteristics of intrinsic gyration modes and frequency-dependent trajectories. Our research may provide insight into the dynamic properties of skyrmion manipulated by EM waves with SAM or OAM and provide a method for controlling skyrmion in spintronic devices.

Magnetic properties of bamboo-like Ni-Zn-in nanowires using 3D-AAO templates

In this paper, using three-dimensional porous alumina (3D-AAO) as a template, Ni-Zn-In nanowires array with periodically changing diameters was successfully prepared by direct current electrodeposition method. The effect of deposition voltage on the morphology, crystal structure and magnetic properties of Ni-Zn-In ternary alloy nanowires was studied. The experimental results show that the diameters of the nanowires are 212 nm and 151 nm, and the periodic length is 800 nm, which matches the pore size of the phosphoric acid-etched 3D-AAO template. XRD results indicate that the crystal structure of Ni-Zn-In nanowires can be adjusted by the deposition voltage. The VSM results reveal that the Ni-Zn-In nanowires possess soft magnetic properties and significant magnetic anisotropy, with the easy magnetization direction parallel to the film. The nanowires deposited at −1.5 V exhibit the highest coercivity of 161 Oe and squareness of 0.045. Micromagnetic simulations show that the magnetization reversal mechanism of the Ni-Zn-In nanowires is localized nucleation mode.

Control of spin–orbit torque-driven domain nucleation through geometry in chirally coupled magnetic tracks

The interfacial Dzyaloshinskii–Moriya interaction (DMI) can be exploited in magnetic thin films to realize lateral chirally coupled systems, providing a way to couple different sections of a magnetic racetrack and realize interconnected networks of magnetic logic gates. Here, we systematically investigate the interplay between spin–orbit torques, chiral coupling, and the device design in domain wall racetracks. We show that the current-induced domain nucleation process can be tuned between single-domain nucleation and repeated nucleation of alternate domains by changing the orientation of an in-plane patterned magnetic region within an out-of-plane magnetic racetrack. Furthermore, by combining experiments and micromagnetic simulations, we show that the combination of damping-like and field-like spin–orbit torques with DMI results in selective domain wall injection in one of two arms of a Y-shaped device depending on the current density. Such an element constitutes the basis of domain wall based demultiplexer, which is essential for distributing a single input to any one of the multiple outputs in logic circuits. Our results provide input for the design of reliable and multifunctional domain wall circuits based on chirally coupled interfaces.

Steerable current-driven emission of spin waves in magnetic vortex pairs.

The efficient excitation of spin waves is a key challenge in the realization of magnonic devices. We demonstrate current-driven generation of spin waves in antiferromagnetically coupled magnetic vortices. We use time-resolved x-ray microscopy to directly image the emission of spin waves upon the application of alternating currents flowing directly through the magnetic stack. Micromagnetic simulations allow us to identify the current-driven Oersted field as the main origin of excitation, in contrast to spin-transfer torques. In our case, these internal Oersted fields have an orders of magnitude higher spin-wave excitation efficiency than commonly used stripline antennas. For magnetostrictive materials, we furthermore demonstrate that the direction of magnon propagation can be steered by increasing the excitation amplitude, which modifies the underlying magnetization profile through an additional anisotropy. The demonstrated methods allow for the efficient and tunable excitation of spin waves, marking a substantial advance concerning the design of magnonic devices.

Construction of Chiral-Magnetic-Dielectric Trinity Structures with Different Magnetic Systems for Efficient Low-Frequency Microwave Absorption.

The fabrication of carbon nanocoil (CNC)-based chiral-dielectric-magnetic trinity composites holds great significance in low-frequency microwave absorption fields. However, it is not clear that how the different magnetic systems affect the magnetic and frequency responses of the composites. Herein, four types of magnetic metals, FeCo, CoNi, FeNi, and FeCoNi, are selected to be combined with the chiral templates respectively, resulting in four types of chiral-dielectric-magnetic composites with similar morphology. The CNC templates endow all the composites with excellent dielectric loss. Further permeability analysis and the micro-magnetic simulation confirm that the frequency response region can be well adjusted by changing the magnetic systems with specific magnetic resonance modes and magnetic domain motion. Due to the synergistic effect between magnetism, chirality, and dielectricity, the FeNi-based composites exhibit the best low-frequency microwave absorption performance. The minimum RL of -60.7 dB is achieved at 6.7 GHz with an ultra-low filling ratio of 10%, and the EAB value in low-frequency region is extended to 3.7 GHz. This study provides further guidelines for the design of the chiral-dielectric-magnetic trinity composites in low-frequency microwave absorption.

Energy-efficient picosecond spin-orbit torque magnetization switching in ferro- and ferrimagnetic films.

Electrical current pulses can be used to manipulate magnetization efficiently via spin-orbit torques. Pulse durations as short as a few picoseconds have been used to switch the magnetization of ferromagnetic films, reaching the terahertz regime. However, little is known about the reversal mechanisms and energy requirements in the ultrafast switching regime. In this work we quantify the energy cost for magnetization reversal over seven orders of magnitude in pulse duration, in both ferromagnetic and ferrimagnetic samples, bridging quasi-static spintronics and femtomagnetism. To this end, we develop a method to stretch picosecond pulses generated by a photoconductive switch by an order of magnitude. Thereby we can create current pulses from picoseconds to durations approaching the pulse width available with commercial instruments. We show that the energy cost for spin-orbit torque switching decreases by more than an order of magnitude in all samples when the pulse duration enters the picosecond range. We project an energy cost of 9 fJ for a 100 × 100 nm2 ferrimagnetic device. Micromagnetic and macrospin simulations unveil a transition from a non-coherent to a coherent magnetization reversal with a strong modification of the magnetization dynamical trajectories as pulse duration is reduced. Our results show the potential for high-speed magnetic spin-orbit torque memories and highlight alternative magnetization reversal pathways at fast timescales.

Strongly Interacting Nanoferrites for Magnetic Particle Imaging and Spatially Resolved Thermometry.

High-crystal-quality nanoferrites with short surface ligands (oleic acid) were recently shown to exhibit enhanced sensitivity and spatial resolution, likely due to chain formation (uniaxial assemblies of particles) for magnetic particle imaging (MPI). Here, we develop a simple one-pot thermal decomposition approach to produce ferrite (iron oxide) magnetic nano-objects (MNOs) that strongly interact magnetically and have good synthetic reproducibility. The ferrite MNOs were physically characterized by X-ray diffraction, Raman spectroscopy, transmission electron microscopy, and dynamic light scattering. The MNOs were magnetically characterized by magnetometry and magnetic particle spectroscopy (MPS) to study their interactions, dynamics, and suitability for spatially resolved magnetic thermometry. The MNOs were synthesized in a range of sizes between 12 nm and 27 nm, showing that MNOs below a minimum size do not exhibit dynamic interactions/significant increased response and that a larger field is required for chain formation as size increases. In addition to size effects, we explore the role of ligand length, environment (liquid vs solid), and concentration on the proposed chain formation. The experimental results were then correlated to micromagnetic simulations to gain further insight into the formation of chains. Compared to some existing MPI tracers, our ferrite MNOs exhibit enhanced signal (up to about 37×) and spatial resolution (up to about 9×) under certain limited (ferrite-MNO optimal) field and frequency conditions used. MPS as a function of temperature and drive field amplitude was performed, showing promise for spatially resolved thermometry. These results confirm the importance of tuning the frequency and amplitude of the drive field for optimal imaging/thermal performance.

Nonreciprocal damping of spin waves propagating in magnetic domain walls induced by Dzyaloshinskii-Moriya interaction

The nonreciprocity of spin waves refers to the phenomenon that spin waves propagating in opposite directions display different features. This phenomen becomes a fundamental requirement for implementing magnon logic architectures. The nonreciprocal transportion of spin waves induced by Dzyaloshinskii-Moriya interaction (DMI) has been studied extensively. It is characterized by a shift of spin-wave dispersion. Here we report another feature of the DMI-induced nonreciprocity, i.e., the nonreciprocal spin wave damping. We find that the spin waves propagating with opposite wave vectors in magnetic domain wall have different damping, which is frequency dependent and especially evident in low frequancy range. For spin waves with sufficient low frequencies (around 1 GHz), the damping nonreciprocity is so extreme that spin waves can transport only in one direction, thus realizing the spin-wave diode function. The theoretical predictions are validated by micromagnetic simulations. The findings in this work points out a new feature of DMI-induced spin wave nonreciprocity and may be exploited for designing novel magnonic devices.

Material Characterization Study of Magnetite Nanocrystals for RF Sensing.

Magnetite nanocrystals show promise for electrically small gigahertz frequency applications, which could lead to miniaturizing transformer cores and new sensing technologies. This work presents a rigorous radiofrequency characterization of these nanocrystals using vector network analyzer (VNA) ferromagnetic resonance (FMR) measurements. For the first time, two different average diameters of Fe3O4 nanocrystals are investigated (7.3 and 20.2 nm). When the VNA-FMR results were compared to micromagnetic simulations, the magnetic anisotropy (K 1) deviated from the ideal mean orientation value of K 1/2 to K 1/80 for the 7.3 nm nanocrystal. In contrast, the obtained magnetic anisotropy in 20.2 nm nanocrystals slightly deviated to K 1/11 due to less structural deformations. These findings resulted in a newly proposed methodology for an approximate simulation based on VNA-FMR measurements. In addition, this work estimates the approximate amount of nanocrystals needed to measure a useful VNA-FMR spectrum.

Exotic Spin Excitations in a Polar Magnet VOSe_{2}O_{5}.

Magnetic resonance dynamics has been studied for a polar magnet VOSe_{2}O_{5}, which hosts several nontrivial magnetic phases including Néel-type skyrmion lattice (SkL). In both cycloidal and SkL spin states, two excitation modes active to oscillating magnetic field B_{ν}⊥c and one mode active to B_{ν}∥c are identified. The subsequent micromagnetic simulations well reproduce the observed selection rules and relative resonance frequencies, which allows the unambiguous assignment of the spin oscillation manner for each mode. Interestingly, the IC-2 phase with a potential double-q character was found to host similar excitation modes as the SkL state. We also discovered the existence of the novel B' phase with four modes active to B_{ν}⊥c. The present results provide a fundamental basis for the comprehensive understanding of resonant spin dynamics in polar magnets, and highlight VOSe_{2}O_{5} as a unique material platform to host a rich variety of nontrivial spin excitations.