Transverse Domain Wall Research Articles

Vortex Domain Wall Thermal Pinning and Depinning in a Constricted Magnetic Nanowire for Storage Memory Nanodevices.

In this study, we investigate the thermal pinning and depinning behaviors of vortex domain walls (VDWs) in constricted magnetic nanowires, with a focus on potential applications in storage memory nanodevices. Using micromagnetic simulations and spin transfer torque, we examine the impacts of device temperature on VDW transformation into a transverse domain wall (TDW), mobility, and thermal strength pinning at the constricted area. We explore how thermal fluctuations influence the stability and mobility of domain walls within stepped nanowires. The thermal structural stability of VDWs and their pinning were investigated considering the effects of the stepped area depth (d) and its length (λ). Our findings indicate that the thermal stability of VDWs in magnetic stepped nanowires increases with decreasing the depth of the stepped area (d) and increasing nanowire thickness (th). For th ≥ 50 nm, the stability is maintained at temperatures ≥ 1200 K. In the stepped area, VDW thermal pinning strength increases with increasing d and decreasing λ. For values of d ≥ 100 nm, VDWs depin from the stepped area at temperatures ≥ 1000 K. Our results reveal that thermal effects significantly influence the pinning strength at constricted sites, impacting the overall performance and reliability of magnetic memory devices. These insights are crucial for optimizing the design and functionality of next-generation nanodevices. The stepped design offers numerous advantages, including simple fabrication using a single electron beam lithography exposure step on the resist. Additionally, adjusting λ and d allows for precise control over the pinning strength by modifying the dimensions of the stepped areas.

Depinning of domain walls in a notched ferromagnetic nanostrip: role of inertial and nonlinear damping effects

Abstract In this work, we investigate theoretically the static and kinetic depinning field of a domain wall in a notched magnetic nanostrip under the generalized framework of the Landau–Lifshitz-Gilbert equation, which combines inertial and nonlinear viscous-dry friction damping effects. We assume a head-to-head transverse domain wall configuration and analyzed its motion subject to a time-varying external magnetic field. To deduce the equation ruling the spatio-temporal evoution of the magnetic domain wall, we adopt the Schryer and Walker trial function approach. The results show that static and kinetic depinning fields increase as the dry friction dissipation increases. Moreover, viscous dissipation exhibits a weak dependence on the kinetic depinning field and saturated domain wall velocity, while inertial damping due to the relaxation time of angular momentum significantly impacts the kinetic depinning field, depinning time, and breakdown velocity. Our numerical results are in good qualitative agreement with the recent observations reported in the literature.

Discerning the magnetization reversal mechanism and magnetic interactions in arrays of FeNi nanowires

FeNi nanowires (NWs), 40 nm in diameter, were grown by electrodeposition. Compositional analysis showed Fe anomalous co-deposition, with different trends across the different potentials and electrolytes used. Those trends were explained within a modified Bocris-Drazic-Despic chemical reactions model, highlighting the importance of the electrochemical theory in understanding Fe-Ni electrodeposited systems. Structural characterization showed a change from a body-centred cubic structure for Fe-rich NWs to face-centred cubic at mid and low Fe content. Magnetic hysteresis measurements showed a range of coercivities from 20 mT for Fe-rich to 100 mT for Ni-rich NWs. Angular measurements allowed to determine that the magnetization reversal mechanism was dominated by transverse domain wall reversal. The analysis also hinted at the non-shape anisotropy acting as a demagnetizing force. First-order reversal curves (FORCs) showed that arrays with a high absolute value for the non-shape anisotropy had higher magnetic interactions, and vice versa. The non-shape anisotropy is dominated by the magnetostatic interactions between NWs, causing a weakening of the magnetic hardness. In combination with the coercivity angular measurements, the FORC analysis explained the shift in easy axis preference depending on NW chemical composition observed in the hysteresis loops of the samples.

Chirality‐Dependent Dynamics and Pinning of Transverse Domain Wall in Constricted Nanowires

Magnetic nanowires with domain walls (DWs) are among the most promising future storage devices. In applications involving DWs, controlling their displacement within the device and the pinning strength and their magnetic structure are crucial parameters. In this article, the dynamics of the transverse domain wall (TW) and its pinning in magnetic nanowires are investigated using micromagnetic simulation. The spin‐transfer torque is used to drive the DW at different positions within a magnetic nanowire with a Z junction of length (λ) and depth (d). In this study, four different structures, namely, head‐to‐head transverse domain wall (HTW) and tail‐to‐tail transverse domain wall (TTW) with up and down magnetization configurations for each case, are focused on. It is found that a TW with a down chirality can be displaced faster than a TW with an up chirality with a velocity reaching 400 m s−1. In the simulation results, it is shown that both HTW and TTW have higher depinning current density for the up magnetization configuration compared to the down case. For the same chirality, it is shown that HTW has a greater pinning strength than TTW.

Strain‐controlled dynamics of transverse domain walls in hybrid piezoelectric–magnetostrictive heterostructures: An asymptotic approach

AbstractThe present work deals with an analytical study of the statical and dynamical behavior of transverse magnetic domain walls in hybrid bilayer piezoelectric/magnetostrictive heterostructures under the combined influence of spin‐polarized electric currents, transverse, and axial applied magnetic fields. The magnetostrictive material is considered to be isotropic and linearly elastic. We perform the investigation within the framework of the one‐dimensional Landau–Lifshitz–Gilbert equation. By employing the regular perturbation asymptotic expansion approach, we derive the explicit analytical expression of the most significant dynamic features, namely, traveling wave profile, DW velocity, and displacement under the influence of small and moderate transverse magnetic fields. Finally, we illustrate numerically the analytical results and delineate the domain wall motion for metallic and semiconductor ferromagnets.

Surface Roughness Effects on Magnetic Properties and Switching Mechanism in Iron Nanowires

Nanowires fabricated with experimental techniques are never perfect and possess structural imperfections. The effect of the resulting surface roughness on magnetic properties of iron nanowires has been simulated here with the use of numerical technique involving atomistic-resolved software Vampire. A two-regime or a power-law decrease in the coercive field has been found for the roughness amplitude up to 30% of the perfect radius of the wire. The roughness of the surface of the side face of cylindrical wire makes the ends of the cylinder inequivalent as far as the switching mechanism is concerned. As a result, the switching becomes dominated by a transverse domain wall arising at one specific end only. Both the coercive field and the switching mechanism are essential in designing magnetic devices, e.g., for memory storage.

Geometry effects on the domain wall width in bent nanowires

Spintronic devices using domain walls (DWs) as information carriers require stable high speeds and a clear understanding of their dynamics. The latter strongly depends on the geometry of the magnetic element hosting the DW. This work aims to determine the effects of the geometry on the width of a transverse DW nucleated in a bent magnetic nanowire with a rectangular cross-section. Our results show that a geometry-induced effective anisotropy is responsible for shrinking or stretching the DW width, depending on the direction along which the DW center points (DW phase).

Transverse domain wall dynamics in hybrid piezoelectric/ferromagnetic devices

This work investigates the static and dynamic features of transverse domain walls in a magnetostrictive, linear elastic isotropic ferromagnetic material under the action of magnetic field (axial and transverse) and electric current. The investigation is done in the framework of the extended Landau–Lifshitz–Gilbert equation by taking into account the effects of stresses induced by a piezoelectric actuator and Rashba spin‐orbit torque caused by structural inversion asymmetry. First, we obtain the expression of magnetization orientation into the two faraway domains, then characterize the static magnetization profile under the action of magnetoelastic and transverse magnetic fields. Next, we introduce a trial function (Schryer and Walker type). After that, by adopting the small angle approximation formalism, we derive the explicit expression of key quantities such as propagating transverse domain wall profile, excitation angle, transverse domain wall velocity, mobility, and displacement. Finally, we present the numerical illustrations of derived analytical results and find that they are in qualitatively good agreement with the recent numerical simulations and experimental observations.

Creation of transverse domain walls in permalloy nanowires using Lorentz transmission electron microscopy: progress, opportunities, and challenges

Creation of transverse domain walls in permalloy nanowires using Lorentz transmission electron microscopy: progress, opportunities, and challenges

Operating characteristics of domain walls in perpendicularly magnetized ferrimagnetic cylindrical nano-wires for three-dimensional magnetic memory

We observed field- and current-induced domain wall motion (DWM) in a ferrimagnetic cylindrical nano-wire using a micromagnetic simulation. Two types of domain walls, namely the Hedgehog Bloch point (HBP) and transverse domain wall (TDW), can be generated by controlling the initial state of these systems. In the case of the field-induced HBP motion, depinning and Walker breakdown were observed, whereas they did not appear in the field-induced TDW motion. According to the observation of current-induced DWM, we found that the domain wall mobility in ferrimagnetic cylindrical nano-wires is higher than that in conventional ferromagnetic cylindrical nano-wires owing to the small saturation magnetization. The current-induced HBP motion exhibits depinning, unlike the TDW motion, which corresponds to field-driven DWM. These differences are attributed to the symmetry of the magnetization in the domain walls. These results provide notable insight into the design of three-dimensional memory based on current-induced DWM.

Effect of thermal motion of transverse domain wall on thermodynamic states of cylindrical iron nanowire

The effect of thermal motion of a transverse domain wall (DW) on the thermodynamic states of a cylindrical iron nanowire (INW) is studied. It is shown that the contribution of the thermal motion of a transverse DW to the entropy and heat capacity of a cylindrical INW can be an actual value, along with the thermodynamic components of its electron, magnon, and phonon (Debye component) subsystems. The critical diameters corresponding to this phenomenon are determined; their magnitudes are lower as compared to the nickel nanowire (Shevchenko et al., 2020). The influence of the thermal motion of a transverse DW on the average magnetization of a cylindrical ferromagnetic nanowire is investigated—it is found out that the maximum magnitude of its relative average magnetization in weak magnetic fields (much lower than 2πM, where M is the magnetization of the nanowire) is ⩽1.2·10-2. It is shown that changes in M affect the temperature of a given thermodynamic state. For example, a reduction of the INW magnetization from M=1.7·103Gs to 102Gs results to a decrease in the temperature (for a given diameter) from 970K to 57K.

Simulation on spin wave transmission and domain wall dynamics in a permalloy nanostrip

Spin waves (SWs), the magnons, can potentially be used for fast and energy efficient information processing and the interaction of SWs with a magnetic domain wall (DW), which is quite complex, can play a key role in the development of magnonic devices. Manipulation of SW amplitude and phase is the key step in realization of spin wave devices. The SW transmission through DW is strongly dependent on the magnetization angle inside the DW and spatial movement of DW is coupled to this interaction. Magnonic spin transfer torque and linear momentum transfer of SW, collectively, control the motion of the DW and the rotation of magnetization inside the DW. In the present work, micromagnetic simulations were performed considering a ferromagnetic permalloy nanostrip with perpendicular magnetic anisotropy (PMA) using mumax3 platform to study SW transmission through DW. The correlation between rotation in magnetization tilt angle (δϕ) inside an initially Néel-type DW and SW-transmission ratio (TD) was investigated at different SW-frequencies ranging from 18 GHz to 28 GHz. Applied SW amplitude at each frequency was sufficiently large for transverse DW to show oscillatory motion along the length of the strip. The results showed that the dependence of TD on rotation in magnetization angle (δϕ) decreases as the frequency of SW is increased and it approaches a nearly isotropic behavior at higher frequencies.

Dynamics of high-velocity domain wall motion and spin wave excitation in trilayer structures

Propagation of dipolar-coupled transverse domain walls in a permalloy/non-magnetic/permalloy trilayer was investigated using micromagnetic modeling. Circulating stray fields meant that the walls adopted a composite structure with behavior analogous to walls seen in nanotubes. Wall velocities were sensitive to the chirality of the stray field circulation, with velocities of the most favored chirality enhanced by 32% compared with velocities seen in the individual constituent layers just below their Walker breakdown field. Additionally, Walker breakdown was completely suppressed within the trilayer for both chiralities, despite occurring in the constituent layers when modelled in isolation, leading to a maximum of 317% velocity enhancement. Wall velocity saturated around 1100 m/s due to the Cherenkov-like emission of spin waves, comparable to the magnonic regime of nanotubes. By reproducing the advantageous domain wall dynamics of nanotubes within a planar system, we demonstrate that ultrafast magnetic switching may feasibly be realized within a lithographically produced system.

Edge defects inducing asymmetric transverse domain walls created in Ni80Fe20 nanowires

Polycrystalline permalloy nanowires (NWs) with different widths were studied by means of a Lorentz microscope associated with micro-magnetic simulations. Each NW was designed to create a single head-to-head transverse domain wall (DW). Edge defects at the long edges of those NWs were incrementally controlled. Therein, a single pixel at different positions along the NW edges was removed. The horizontal NWs were rotated with different angles, i.e. ±5°, ±10°, ±30° and ±45°, to produce a certain level of edge roughness. Some curved NWs with different widths were also designed, simulated and patterned. Lorentz images of those curved NWs were recorded. The asymmetric levels of such created walls were measured and correlated to our wall phase diagram. The obtained results showed that the edge defects created along either side of a NW strongly induce the asymmetric level of a transverse DW.

Controlling domain wall thermal stability switching in magnetic nanowires for storage memory nanodevices

The domain wall (DW) random switching in planar magnetic nanowires is one of the crucial problems for storage data applications. Hence, a micromagnetic simulation was used to investigate the transverse domain wall (TDW) nucleation in the thinner and narrower nanomagnetic devices and the vortex domain wall (VDW) nucleation for the thicker and wider nanowires due to the device temperature. The TDW thermal creation was examined based on magnetic properties such as uniaxial magnetic anisotropy energy (Ku) and saturation magnetization (Ms). The thermal stability of TDW switching in nanowires is strongly dependent on the improvement of magnetic properties, whereas the TDW thermal nucleation decreases by increasing Ku or Ms. In addition, the TDW and VDW thermal creation in storage nanodevices such as nanowires could be controlled by nanowire geometry manipulation like width and thickness. Reducing the nanowire width or increasing its thickness helps both domain wall types (TDW and VDW) switching to be more stable against nanodevice temperature. TDW thermal switching was found to be stable under a device temperature of up to 500 K, which is higher than the room temperature. However, the VDW shows higher thermal stability switching reaches up to 900 k, which are good candidates for storage applications. Furthermore, the TDW dynamics in nanowires were affected by device temperature, whereas the TDW moves faster by increasing nanodevice temperature. All these findings will help to maintain the storage memory in nanodevices from failure due to device temperature.

Spin-Torque-Triggered Magnetization Reversal in Magnetic Tunnel Junctions with Perpendicular Shape Anisotropy

The concept of perpendicular shape anisotropy spin-transfer torque magnetic random-access memory (PSA-STT-MRAM) consists in increasing the storage layer thickness to values comparable to the cell diameter, to induce a perpendicular shape anisotropy in the magnetic storage layer. Making use of that contribution, the downsize scalability of the STT-MRAM may be extended towards sub-20 nm technological nodes, thanks to a reinforcement of the thermal stability factor $\Delta$. Although the larger storage layer thickness improves $\Delta$, it is expected to negatively impact the writing current and switching time. Hence, optimization of the cell dimensions (diameter, thickness) is of utmost importance for attaining a sufficiently high $\Delta$ while keeping a moderate writing current. Micromagnetic simulations were carried out for different pillar thicknesses of fixed lateral size 20 nm. The switching time and the reversal mechanism were analysed as a function of the applied voltage and aspect-ratio (AR) of the storage layer. For AR $<$ 1, the magnetization reversal resembles a macrospin-like mechanism, while for AR $>$ 1 a non-coherent reversal is observed, characterized by the nucleation of a transverse domain wall at the ferromagnet/insulator interface which then propagates along the vertical axis of the pillar. It was further observed that the inverse of the switching time is linearly dependent on the applied voltage. This study was extended to sub-20 nm width with a value of $\Delta$ around 80. It was observed that the voltage necessary to reverse the magnetic layer increases as the lateral size is reduced, accompanied with a transition from macrospin-reversal to a buckling-like reversal at high aspect-ratios.

Investigations of the spin-waves excited by the collision of domain walls in nanostrips

In a nanostrip, two kinds of spin waves (SWs) were produced by two possible collisions of transverse domain walls (DWs) under the driving magnetic fields. By micromagnetic simulations, we illustrated the difference between these two SWs. Interestingly, the SW induced by the collision of two DWs with same chirality shows a narrow frequency bandwidth in nanostrips with width ranging from 20 to 40 nm. Furthermore, its bandwidth is not only strongly dependent on the width of nanostrip, but also can be remarkably manipulated by the bias magnetic fields. We argue that this provides a valid method to excite SWs with a controllable bandwidth in nanostrips. .

Vortex Domain Wall Pinning Probability in Nanowires of Various Widths

We report the results of a micromagnetic simulation of vortex domain wall (VDW) dynamic pinning probability in 20-nm-thick planar permalloy wires with triangular notches and widths of 100, 200, and 300 nm. The notches have a fixed depth ratio of 30%, which is the depth divided by the wire width. Both the wire width and the applied field influenced the dynamic VDW pinning probability. The pinning probability decreased as the wire width increased. We observed a pinned domain wall (DW) structure around the notches and defined two types of pinning states, transverse DW pinning and VDW pinning. The 100-nm-wide wire had more transverse DW pinning–type events than did the 200- and 300-nm-wide wires. The 300-nm-wide wire had the lowest number of transverse DW pinning–type events. These results were caused by different wire widths having different DW energy densities and different pinning potential energy landscapes. When the applied field was larger than the Walker field, the wide wires easily led complex VDW motion.

Curvature-induced emergence of a second critical field for domain wall dynamics in bent nanostripes

We investigate the dynamics of a transverse domain wall (DW) in a bent nanostripe under an external field and spin-polarized current. Besides the standard Walker breakdown phenomenon, we show the emergence of a second Walker-like critical field, which depends on both the curvature of the nanostripe and its cross section geometry. At this field, DW can change its phase, i.e., can be re-oriented along another direction with respect to the nanostripe face. Additionally, we show that the amplitude and frequency of the DW oscillations above the Walker breakdown field also depend on the nanostripe geometry and can be controlled by external stimuli. Our results evidence that the inclusion of local curvatures in nanostripes is an important component for applications that demand an adequate control of the DW phase by the proper choice of external stimuli.

Effect of a local temperature region on the suppression of walker breakdown in a permalloy nanowire

Magnetic domain walls are potential data carriers in future spintronic devices and the application based on current-driven domain wall (DW) motion primarily relies on the effective control of the moving velocity of the DW and its structural stability. In this work, the propagation of the magnetic domain walls along a ferromagnetic nanowire with a localized temperature region is studied by micromagnetic simulation. The research indicates that the local temperature field can suppress the generation of Walker breakdown (WB) and make the transverse domain wall (TDW) move to a longer distance with a stable structure. The degree of suppression is the result of the joint influence of temperature difference (ΔT) and temperature region width (d). When both of the ΔT and the d are relatively large, the suppression effect is comparatively strong, while either of the ΔT and the d are small, the suppression effect is weak. The results reveal the local temperature field makes the exchange energy in the region reach a very high value rapidly, and the out-of-plane magnetic moment Mz of the DW keeps at a high level, which promotes the high-speed motion of the DW and suppresses the WB by destroying the periodic transition of the DW structure.