Collective Coordinate Descriptions of Magnetic Domain Wall Motion in Perpendicularly Magnetized Nanostructures under the Application of In-plane Fields
S. Ali Nasseri, Eduardo Martinez, Gianfranco Durin
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 micromagnetic simulations are able to accurately predict domain wall motion under in-plane fields in these materials, collective coordinate models such as the $q-ϕ$ and $q-ϕ-χ$ models fail to reproduce the micromagnetic results. In this theoretical work, we present a set of extended collective coordinate models including canting in the domains, which better reproduce micromagnetic results, and helps us better understand the effect of in-plane fields on magnetic domain walls. These models are used in conjunction with micromagnetic simulations to identify critical points observed in the motion of the domain walls driven by out-of-plane magnetic fields, and electric current under magnetic in-plane fields. Our new models and results help in the development of future domain wall based devices based on perpendicularly magnetized materials.
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…
Perpendicularly magnetized nanowires exhibit distinct domain wall types depending on the geometry. Wide wires contain Bloch walls, narrow wires Néel walls. Here, the transition region is investigated by direct imaging of the wall structure using high-resolution spin-polarized scanning electron microscopy. An achiral intermediate wall type is discovered that is unpredicted by established theoretical models. With the help of micromagnetic simulations, the formation of this novel wall type is explained.
The oscillation properties of a spin torque oscillator consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer are studied based on an analysis of the energy balance between spin torque and damping. The critical value of an external magnetic field applied normal to the film plane is found, below which the controllable range of the oscillation frequency by the current is suppressed. The value of the critical field depends on the magnetic anisotropy, the saturation magnetization, and the spin torque parameter.
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We demonstrate efficient current induced spin orbit torque switching in perpendicularly magnetized epitaxial MgO(001)//Pd/Co2FeAl/MgO heterostructures grown by magnetron sputtering. The advantage of such heterostructures for spin orbit torque MRAM devices is that they allow a unique combination of critical ingredients: i) low resistivity required for reduced electric energy consumption during writing, ii) high TMR ratio required for efficient reading and iii) strong perpendicular magnetic anisotropy for increased thermal stability.
We study the theoretical conditions to excite a stable self-oscillation in a spin torque oscillator with an in-plane magnetized free layer and a perpendicularly magnetized pinned layer in the presence of magnetic field pointing in an arbitrary direction. The linearized Landau-Lifshitz-Gilbert (LLG) equation is found to be inapplicable to evaluate the threshold between the stable and self-oscillation states because the critical current density estimated from the linearized equation is considerably larger than that found in the numerical simulation. We derive a theoretical formula of the thresho…
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.
We present a study of the temperature dependence of the switching fields in Co/Ni-based perpendicularly magnetized spin-valves. While magnetization reversal of all-perpendicular Co/Ni spin valves at ambient temperatures is typically marked by a single sharp step change in resistance, low temperature measurements can reveal a series of resistance steps, consistent with non-uniform magnetization configurations. We propose a model that consists of domain nucleation, propagation and annihilation to explain the temperature dependence of the switching fields. Interestingly, low temperature (<30 K) s…
We report on the time-resolved investigation of current- and field-induced domain wall motion in perpendicularly magnetized microwires exhibiting asymmetric exchange interaction by means of scanning transmission x-ray microscopy using a time step of 200 ps. Dynamical domain wall velocities on the order of 50-100 m s$^{-1}$ were observed. The improvement in the temporal resolution allowed us to observe the absence of incubation times for the motion of the domain wall, together with indications for a negligible inertia. Furthermore, we observed that, for short current and magnetic field pulses, …
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 …
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Pulsed spin-torque switching has been studied using single-shot time-resolved electrical measurements in perpendicularly magnetized magnetic tunnel junctions as a function of pulse amplitude and junction size in 50 to 100 nm diameter circular junctions. The mean switching time depends inversely on pulse amplitude for all junctions studied. However, the switching dynamics is found to be strongly dependent on junction size and pulse amplitude. In 50 nm diameter junctions the switching onset is stochastic but the switching once started, is fast; after being initiated it takes less than 2 ns to sw…
Standing spin wave mode frequencies and linewidths in partially disordered perpendicular magnetized arrays of sub-micron Permalloy discs are measured using broadband ferromagnetic resonance and compared to analytical results from a single, isolated disc. The measured mode structure qualitatively reproduces the structure expected from the theory. Fitted demagnetizing parameters decrease with increasing array disorder. The frequency difference between the first and second radial modes is found to be higher in the measured array systems than predicted by theory for an isolated disc. The relative …
We numerically and analytically investigate the voltage controlled spin wave (SW) propagations in a nanowire with locally manipulated perpendicular magnetic anisotropy (PMA) by applying an electric field. It is shown that the velocity and wavelength of the propagating SWs are tailored by the modified PMA, which can be locally controlled by the external electric field. First, we observe a phase shift when the propagating SWs pass through the area of locally modified PMA. By introducing phase control of the SWs, we finally propose a three terminal SW device. Constructive/destructive interference…
We present switching field distributions of spin-transfer assisted magnetization reversal in perpendicularly magnetized Co/Ni multilayer spin-valve nanopillars at room temperature. Switching field measurements of the Co/Ni free layer of spin-valve nanopillars with a 50 nm x 300 nm ellipse cross section were conducted as a function of current. The validity of a model that assumes a spin-current dependent effective barrier for thermally activated reversal is tested by measuring switching field distributions under applied direct currents. We show that the switching field distributions deviate sig…
We report the free layer switching field distributions of spin-valve nanopillars with perpendicular magnetization. While the distributions are consistent with a thermal activation model, they show a strong asymmetry between the parallel to antiparallel and the reverse transition, with energy barriers more than 50% higher for the parallel to antiparallel transitions. The inhomogeneous dipolar field from the polarizer is demonstrated to be at the origin of this symmetry breaking. Interestingly, the symmetry is restored for devices with a lithographically defined notch pair removed from the midpo…
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…
Ferromagnetic films of L10-ordered MnGa and MnAl that exhibit giant perpendicular magnetic anisotropy and great controllability in the magnetism and structural disorders show promise not only in the applications in magnetic recording, permanent magnets and spintronics, but also in controllable studies of disorder-relevant electrical transport phenomena. In this article, we review the intriguing experimental observations of the orbital two-channel Kondo effect and anomalous Hall effect in L10-ordered MnGa and MnAl thin films with perpendicular magnetic anisotropy. We also give a perspective wit…
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The thermal stability in nanostructured magnetic systems is an important issue for applications in information storage. From a theoretical and simulation perspective, an accurate prediction of thermally-activated transitions is a challenging problem because desired retention times are on the order of 10 years, while the characteristic time scale for precessional magnetization dynamics is of the order of nanoseconds. Here, we present a theoretical study of the thermal stability of magnetic elements in the form of perpendicularly-magnetized ferromagnetic disks using the forward flux sampling met…
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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 …
Ferrimagnets, which contain the advantages of both ferromagnets (detectable moments) and antiferromagnets (ultrafast spin dynamics), have recently attracted great attention. Here we report the optimization of epitaxial growth of a tetragonal perpendicularly magnetized ferrimagnet Mn2Ga on MgO. Electrical transport, magnetic properties and the anomalous Hall effect (AHE) were systematically studied. Furthermore, we successfully integrated high-quality epitaxial ferrimagnetic Mn2Ga thin films onto ferroelectric PMN-PT single crystals with a MgO buffer layer. It was found that the AHE of such a f…
A theoretical formula is derived for the threshold current to switch a perpendicular magnetization in a ferromagnet by the spin Hall effect. The numerical simulation of the Landau-Lifshitz-Gilbert equation indicates that magnetization switching is achieved when the steady-state solution of the magnetization in the presence of the current is outside an energetically unstable region. Based on the numerical result, an analytical theory deriving the threshold current is developed by focusing on the first-order perturbation to the unstable state. The analytical formula clarifies that the magnitude …
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Understanding the stability of thin film nanomagnets with perpendicular magnetic anisotropy (PMA) against thermally induced magnetization reversal is important when designing perpendicularly magnetized patterned media and magnetic random access memories. The leading-order dependence of magnetization reversal rates are governed by the energy barrier the system needs to surmount in order for reversal to proceed. In this paper we study the reversal dynamics of these systems and compute the relevant barriers using the string method of E, Vanden-Eijnden, and Ren. We find the reversal to be often sp…
Measurements of the ac magnetic susceptibility of perpendicularly magnetized Fe/2ML Ni/W(110) ultrathin films show a clear signature of the dynamics of domain growth and domain density changes in the striped domain pattern that this system supports. The susceptibility peak measured at different constant heating rates in the range 0.20 K/s < R < 0.70 K/s shifts to higher temperature as the heating rate is increased. Analysis using a relaxation model demonstrates quantitatively that the dynamics is driven by a non-equilibrium domain density at (nearly) zero field (i.e. by dipole interactions), a…
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Current induced domain wall (DW) motion has been investigated in a 600-nm wide nanowire using multilayer film with a structure of Ta(5 nm)/Pd(5 nm)/[CoFe(0.4 nm)/Pd(1.2 nm)]$_{15}$/Ta(5 nm)in terms of anomalous Hall effect measurements. It is found that motion of DWs can be driven by a current density as low as 1.44$\times$10$^{11}$ A.m$^{-2}$. The effect of the Oersted field ($H_{Oe}$) and spin transfer torque field ($H_{ST}$), which are considered as effective fields for DW motion, has been quantitatively separated from the dependence of depinning fields on the current. The results show that…
We proposed a novel and simple multilayer structure to realize the deterministic switching of perpendicularly magnetized layers (Co in our work) by spin orbital torque from the spin Hall Effect in this paper. A pinned layer is introduced, antiferromagnetically coupled to the magnetic Co layer. We have confirmed the deterministic switching of perpendicularly magnetized layers from perspectives of switching loops, trajectories and switching properties under periodic spin currents through micromagnetic simulation. The antiferromagnetic interaction accounts for the deterministic switching exhibite…
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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…
We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level o…
We time-resolve the spin-transfer-torque-induced switching in perpendicularly magnetized tunnel junctions of diameters from 50 to 250 nm in the thermally activated regime. When the field and the spin-torque concur to favor the P to AP transition, the reversal yields monotonic resistance ramps that can be interpreted as a domain wall propagation through the device at velocities of 17 to 30 nm/ns; smaller cells switch hence faster. When the field hinders the P to AP transition, the switching is preceded by repetitive switching attempts, during which the resistance transiently increases until suc…
Tailoring Ultrathin Magnetic Multilayers at Terraced Topologically Insulating Interfaces for Perpendicularly Magnetized Domains
University of Leeds（利兹大学）；ISIS Neutron and Muon Source, STFC Rutherford Appleton Laboratory（STFC卢瑟福阿普尔顿实验室中子与μ子源）；Diamond Light Source（钻石光源）；Imperial College London（伦敦帝国理工学院）
Centro Atómico Bariloche（巴里洛切原子中心）；Instituto Balseiro, Universidad Nacional de Cuyo–CNEA（巴尔塞罗研究所，门多萨国立大学-国家原子能委员会）；Instituto de Nanociencia y Materiales de Aragón (INMA-CSIC)（阿拉贡纳米与材料研究所）；Universidad de Zaragoza（萨拉戈萨大学）
Magnetization dynamics are strongly influenced by damping. An effective damping constant αeff is often determined experimentally from the spectral linewidth of the free induction decay of the magnetization after the system is excited to its non-equilibrium state. Such an αeff, however, reflects both intrinsic damping as well as inhomogeneous broadening. In this paper we compare measurements of the magnetization dynamics in ultrathin non-epitaxial films having perpendicular magnetic anisotropy using two different techniques, time-resolved magneto optical Kerr effect (TRMOKE) and hybrid optical-…
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…
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 critical current of the self-oscillation of spin torque oscillator (STO) consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer was studied by solving the Landau-Lifshitz-Gilbert (LLG) equation. We found that the critical current diverged at certain field directions, indicating that the self-oscillation does not occur at these directions. It was also found that the sign of the critical current changed depending on the applied field direction.
Oscillation frequency of spin torque oscillator with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer is theoretically investigated by taking into account the field-like torque. It is shown that the field-like torque plays an important role in finding the balance between the energy supplied by the spin torque and the dissipation due to the damping, which results in a steady precession. The validity of the developed theory is confirmed by performing numerical simulations based on the Landau-Lifshitz-Gilbert equation.
The self-oscillation of the magnetization in a spin torque oscillator (STO) with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer in the absence of an applied magnetic field was studied by numerically solving the Landau-Lifshitz-Gilbert equation. It was pointed out that field-like torque was necessary to realize stable self-oscillation in this type of STO at zero field. The numerical simulation at finite temperature showed that the presence of the field-like torque led to a high power with a relatively high oscillation frequency.
Theoretical conditions to excite self-oscillation in a spin torque oscillator consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer are investigated by analytically solving the Landau-Lifshitz-Gilbert equation. The analytical relation between the current and oscillation frequency is derived. It is found that a large amplitude oscillation can be excited by applying a small field pointing to the direction anti-parallel to the magnetization of the pinned layer. The validity of the analytical results is confirmed by comparing with numerical simulation, showi…
We have measured spin transfer-induced dynamics in magnetic nanocontact devices having a perpendicularly magnetized Co/Ni free layer and an in-plane magnetized CoFe fixed layer. The frequencies and powers of the excitations agree well with the predictions of the single-domain model and indicate that the excited dynamics correspond to precessional orbits with angles ranging from zero to 90 degrees as the applied current is increased at a fixed field. From measurements of the onset current as a function of applied field strength we estimate the magnitude of the spin torque asymmetry parameter la…
