It was shown by micromagnetic simulation that a current-driven in-plane magnetized magnetic nano-contact, besides a quasi-linear propagating ("Slonczewski") spin wave mode, can also support a nonlinear self-localized spin wave "bullet" mode that exists in a much wider range of bias currents. The frequency of the "bullet" mode lies below the spectrum of linear propagating spin waves, which makes this mode evanescent and determines its spatial localization. The threshold current for the excitation of the self-localized "bullet" is substantially lower than for the linear propagating mode, but finite-amplitude initial perturbations of magnetization are necessary to generate a "bullet" in our numerical simulations, where thermal fluctuations are neglected. Consequently, in these simulations the hysteretic switching between the propagating and localized spin wave modes is found when the bias current is varied.
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 microwav…
Spin wave spectra of perpendicularly magnetized disks with trilayers consisting of a 100 nm permalloy (Py) layer sandwiched by two Cu layers of 30 nm, are measured individually with a Magnetic Resonance Force Microscope (MRFM). It is demonstrated by 3D micromagnetic simulations that in disks having sub-micron size diameters, the lowest energy spin wave mode of the saturated state is not spatially uniform but rather is localized at the center of the Py/Cu interface in the region of a minimum demagnetizing field.
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 …
An analytical model was developped to describe the current induced DW dynamics of a Bloch DW in the presence of an external transverse magnetic field. The model takes into account the DW deformation and the magnetization tilting in the domain. The model is compared to the results of micromagnetic simulation and an excellent agreement is obtained. In the steady state regime, the model shows that the domain tilting does not change the DW mobility. An external or current induced transverse magnetic field such as the Oersted or Rashba field can prevent the Walker breakdown leading to a higher doma…
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…
Through detailed experimental studies of the angular dependence of spin wave excitations in nanocontact-based spin-torque oscillators, we demonstrate that two distinct spin wave modes can be excited, with different frequency, threshold currents and frequency tuneability. Using analytical theory and micromagnetic simulations we identify one mode as an exchange-dominated propagating spin wave, and the other as a self-localized nonlinear spin wave bullet. Wavelet-based analysis of the simulations indicates that the apparent simultaneous excitation of both modes results from rapid mode hopping ind…
Microwave spectroscopy of individual vortex-state magnetic nano-disks in a perpendicular bias magnetic field, $H$, is performed using a magnetic resonance force microscope (MRFM). It reveals the splitting induced by $H$ on the gyrotropic frequency of the vortex core rotation related to the existence of the two stable polarities of the core. This splitting enables spectroscopic detection of the core polarity. The bistability extends up to a large negative (antiparallel to the core) value of the bias magnetic field $H_r$, at which the core polarity is reversed. The difference between the frequen…
The effect of damping-like spin-orbit torque (DL SOT) on magnetic domain walls (DWs) in in-plane magnetised soft tracks is studied analytically and with micromagnetic simulations. We find that DL SOT drives vortex DWs, whereas transverse DWs, the other typical DW structure in soft tracks, propagate only if the Dzyaloshinskii-Moriya interaction (DMI) is present. The SOT drive can add to, and be more efficient than, spin-transfer torque (STT), and so may greatly benefit applications that require in-plane DWs. Our analysis based on the Thiele equation shows that the driving force arises from a cy…
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…
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…
The dynamics of individual magnetic skyrmions confined in ultrathin film dots is studied theoretically. The systems considered are transition metal ferromagnets possessing perpendicular magnetic anisotropy and particular attention is given to the dynamic response of the skyrmions to perpendicular driving fields. By using micromagnetics simulations, it is shown that breathing modes can hybridize with geometrically-quantized spin wave eigenmodes of the circular dots considered, leading to distinct features in the power spectrum that differ to the behavior expected for uniformly magnetized system…
It has been shown previously that the presence of a Dzyaloshinskii-Moriya interaction in perpendicularly magnetized thin films stabilizes Néel type domain walls. We demonstrate, using micromagnetic simulations and analytical modeling, that the presence of a uniaxial in-plane magnetic anisotropy can also lead to the formation of Néel walls in the absence of a Dzyaloshinskii-Moriya interaction. It is possible to abruptly switch between Bloch and Néel walls via a small modulation of both the in-plane, but also the perpendicular magnetic anisotropy. This opens up a route towards electric field con…
In this paper we study magnetization excitations induced in a thin extended film by a spin-polarized dc-current injected through a point contact in the current-perpendicular-to-plane (CPP) geometry. Using full-scale micromagnetic simulations, we demonstrate that in addition to the oscillations of the propagating wave type, there exist also two localized oscillation modes. The first localized mode has a relatively homogeneous magnetization structure of its kernel and corresponds to the so called 'bullet' predicted analytically by Slavin and Tiberkevich (Phys. Rev. Lett., 95 (2005) 237201). Magn…
Current-induced dynamics of twisted domain walls and skyrmions in ferromagnetic perpendicularly magnetized multilayers is studied through three-dimensional micromagnetic simulations and analytical modeling. It is shown that such systems generally exhibit a Walker breakdown-like phenomenon in the presence of current-induced damping-like spin-orbit torque. Above a critical current threshold, corresponding to typical velocities of the order tens of m/s, domain walls in some layers start to precess with frequencies in the gigahertz regime, which leads to oscillatory motion and a significant drop i…
We show on in-plane magnetized thin films that magnetization can be switched efficiently by 180 degrees using large amplitude Rayleigh waves travelling along the hard or easy magnetic axis. Large characteristic filament-like domains are formed in the latter case. Micromagnetic simulations clearly confirm that this multi-domain configuration is compatible with a resonant precessional mechanism. The reversed domains are in both geometries several hundreds of μm^2, much larger than has been shown using spin transfer torque- or field-driven precessional switching. We show that surface acoustic wav…
Spin wave scattering in the right angle ferromagnetic cross was measured. Shape anisotropy defined magnetization ground states at zero biasing magnetic fields. Scattering of the spin waves in the center of ferromagnetic cross is strongly dependent on the amplitude and angle of the biasing magnetic field. Micromagnetic simulations indicate that low in-plane biasing magnetic fields rotate the magnetization of the cross center while the arms stay axially magnetized due to the shape anisotropy. We discuss effect of biasing magnetic fields on the spin wave scattering and approaches to an effective …
The Talbot effect has been known in optics since XIX century and found various technological applications. In this paper, we demonstrate with the help of micromagnetic simulations this self-imaging phenomenon for spin waves propagating in a thin ferromagnetic film magnetized out-of-plane. We show that the main features of the obtained Talbot carpets for spin waves can be described, to a large extent, by the approximate analytical formulas yielded by the general analysis of the wave phenomena. Our results indicate a route to a feasible experimental realisation of the Talbot effect at low and hi…
Current induced domain wall (DW) motion in perpendicularly magnetized nanostripes in the presence of spin orbit torques is studied. We show using micromagnetic simulations that the direction of the current induced DW motion and the associated DW velocity depend on the relative values of the field like torque (FLT) and the Slonczewski like torques (SLT). The results are well explained by a collective coordinate model which is used to draw a phase diagram of the DW dynamics as a function of the FLT and the SLT. We show that a large increase in the DW velocity can be reached by a proper tuning of…
We study how the shape of the spinwave resonance lines in rf-voltage induced FMR can be used to extract the spinwave density of states and the damping within the precessing layer in nanoscale tunnel junctions that possess perpendicular anisotropy. We work with a field applied along the easy axis to preserve the uniaxial symmetry of the system. We describe the set-up to study the susceptibility contributions of the spin waves in the field-frequency space. We then identify the maximum device size above which the spinwaves can no longer be studied in isolation as the linewidths of their responses…
An analytical and numerical approach is developped to pinpoint the optimal experimental conditions to irreversibly switch magnetization using surface acoustic waves (SAWs). The layers are magnetized perpendicular to the plane and two switching mechanisms are considered. In precessional switching, a small in-plane field initially tilts the magnetization and the passage of the SAW modifies the magnetic anisotropy parameters through inverse magneto-striction, which triggers precession, and eventually reversal. Using the micromagnetic parameters of a fully characterized layer of the magnetic semic…
We report manipulation of the magnetic states of elliptical cobalt magnetostrictive nanomagnets (of nominal dimensions ~ 340 nm x 270 nm x 12 nm) delineated on bulk 128° Y-cut lithium niobate with Surface Acoustic Waves (SAWs) launched from interdigitated electrodes. Isolated nanomagnets that are initially magnetized to a single domain state with magnetization pointing along the major axis of the ellipse are driven into a vortex state by surface acoustic waves that modulate the stress anisotropy of these nanomagnets. The nanomagnets remain in the vortex state until they are reset by a strong m…
We present a micromagnetic study of the current-induced domain wall motion in perpendicularly magnetized Pt/Co/AlOx racetracks. We show that the domain wall velocity depends critically on the tilt angle of the wall relative to the current direction, which is determined by the combined action of the Dzyaloshinskii-Moriya interaction, damping-like, and field-like spin-orbit torques. The asymmetry of the domain wall velocity can be controlled by applying a bias-field perpendicular to the current direction as well as by the current amplitude. As the faster domain walls are expelled rapidly from th…
Spin wave frequency hysteresis in Ir/Co/Pt multilayers with Dzyaloshinskii-Moriya interaction
Faculty of Physics, University of Bialystok（比亚韦斯托克大学物理学院）；Faculty of Physics, Adam Mickiewicz University（亚当·密茨凯维奇大学物理学院）；Institute of Molecular Physics, Polish Academy of Sciences（波兰科学院分子物理研究所）
Detailed understanding of spin dynamics in magnetic nanomaterials is necessary for developing ultrafast, low-energy and high-density spintronic logic and memory. Here, we develop micromagnetic models and analytical solutions to elucidate the effect of increasing damping and uniaxial anisotropy on magnetic field pulse-assisted switching time, energy and field requirements of nanowires with perpendicular magnetic anisotropy and yttrium iron garnet-like spin transport properties. A nanowire is initially magnetized using an external magnetic field pulse (write) and self-relaxation. Next, magnetic …
We investigate fast-pulse switching of in-plane-magnetized magnetic tunnel junctions (MTJs) within 3-terminal devices in which spin-transfer torque is applied to the MTJ by the giant spin Hall effect. We measure reliable switching, with write error rates down to $10^{-5}$, using current pulses as short as just 2 ns in duration. This represents the fastest reliable switching reported to date for any spin-torque-driven magnetic memory geometry, and corresponds to a characteristic time scale that is significantly shorter than predicted possible within a macrospin model for in-plane MTJs subject t…
Spin waves are perturbations in the relative orientation of magnetic moments in a continuous magnetic system, which have been proposed as a new kind of information carrier for spin-based low power applications. For this purpose, a major obstacle to overcome is the energy-efficient excitation of coherent short wavelength spin waves and alternatives to excitation via the Oersted field of an alternating current need to be explored. Here we show, by means of micromagnetic simulations, how, in a perpendicularly magnetized thin strip, a domain wall pinned at a geometrical constriction emits spin wav…
