Walker Breakdown Research Articles

Chirality-dependent properties of domain walls in a U-shaped Permalloy nanostrip

Transverse domain walls (DWs) in a U-shaped ferromagnetic nanostrip possess many dynamic properties different from those in flat nanostrip. By breaking the top–bottom symmetry, the U-shaped strip endows DWs with chirality-dependent structures, mobilities and Walker breakdown fields. More interestingly, Walker breakdown in U-shaped nanostrip is hierarchy, with two different modes. Micromagnetic simulations predicted that DWs with different chiralities have different robustness and (anti)vortex dynamics in Walker breakdown. Our results provide a method for manipulating DW chirality.

Cherenkov-type three-dimensional breakdown behavior of the Bloch-point domain wall motion in the cylindrical nanowire

A three-dimensional breakdown behavior of the magnetic Bloch-point domain wall (BP-DW) propagation was investigated in a ferromagnetic nanowire with the variation of the external magnetic field by means of micromagnetic simulation. As magnetic field strength increases up to a threshold value, the BP-DW velocity approaches a critical phase velocity of the spontaneously emitting spin wave (SW), where a Cherenkov-type DW breakdown phenomenon is observed originating from an interaction between the spontaneously emitting SW and the BP-DW. It is found that the velocity of the BP-DW approaches a maximum value (∼2000 m/s) due to the intrinsic reversal time of a BP spin texture. This suggests that although cylindrical ferromagnetic nanowires might be free from the two-dimensional Walker breakdown phenomenon, there exists a Cherenkov-type three-dimensional breakdown behavior.

Asymmetric dynamic behaviors of magnetic domain wall in trapezoid-cross-section nanostrip**Project supported by the National Key R & D Program of China (Grant Nos. 2017YFB0903700 and 2017YFB0903702), YichangGovernment Fund (Grant No. A19-402-a05), the Korea Research Foundation (NRF) (Grant No. 2018R1A2B3009569), and Korea Basic Science Institute (KBSI) (Grant No. D39614).

Field-driven magnetic domain wall propagation in ferromagnetic nanostrips with trapezoidal cross section has been systematically investigated by means of micromagnetic simulation. Asymmetric dynamic behaviors of domain wall, depending on the propagation direction, were observed under an external magnetic field. When the domain walls propagate in the opposite direction along the long axis of the nanostrip, the Walker breakdown fields as well as the average velocities are different. The asymmetric landscape of demagnetization energies, which arises from the trapezoidal geometry, is the main origin of the asymmetric propagation behavior. Furthermore, a trapezoid-cross-section nanostrip will become a nanotube if it is rolled artificially along its long axis, and thus a two-dimensional transverse domain wall will become a three-dimensional one. Interestingly, it is found that the asymmetric behaviors observed in two-dimensional nanostrips with trapezoidal cross section are similar with some dynamic properties occurring in three-dimensional nanotubes.

Controlling domain wall oscillations in bent cylindrical magnetic wires

Magnetic cylindrical nanowires are promising candidates for future three-dimensional nanotechnology. Domain walls (DWs) in magnetic nanowires play the role of information carriers, and the development of applications requires proper description of their dynamics. Here we perform a detailed analytical and numerical analysis of the DW motion along a bent magnetic nanowire under the action of tangential magnetic fields. Our results show that the DW velocity, precession, and oscillation frequencies can be controlled by the interplay between the curvature and the external magnetic field. Small magnetic fields induce a DW motion without precession and oscillatory behavior, while higher magnetic fields yield a Walker breakdown regime, in which an oscillatory forward and backward DW motion is observed. Controlled DW motion under the Walker breakdown regime makes magnetic nanowires potential candidates for nanoscale microwave generation and sensing.

Anomalies in the dynamics of ferrimagnets near the angular momentum compensation point

In this paper, we elaborate analytical theory of domain wall dynamics close to the angular momentum compensation point based on non-linear dynamic equations derived from the effective Lagrangian of a ferrimagnet. In the framework of the proposed model, we explore dynamic processes in the Walker and post-Walker regimes. Analysis of the precession angle and domain wall’s velocity oscillations in post-Walker regime in a ferrimagnet is performed. We show that although spin oscillations quench the dynamics of domain walls near the Walker breakdown field, a further increase of the driving magnetic field increases domain wall speed and mobility. An anomalous behavior of domain wall dynamic properties near the angular momentum compensation point in ferrimagnets (unlimited enhancement of the domain velocity, vanishing of effective dynamic mass) is discussed.

Unveiling domain wall dynamics of ferrimagnets in thermal magnon currents: Competition of angular momentum transfer and entropic torque

Control of magnetic domain wall motion holds promise for efficient manipulation and transfer of magnetically stored information. Thermal magnon currents, generated by temperature gradients, can be used to move magnetic textures, from domain walls, to magnetic vortices and skyrmions. In the last years, theoretical studies have centered in ferro- and antiferromagnetic spin structures, where domain walls always move towards the hotter end of the thermal gradient. Here we perform numerical studies using atomistic spin dynamics simulations and complementary analytical calculations to derive an equation of motion for the domain wall velocity. We demonstrate that in ferrimagnets, domain wall motion under thermal magnon currents shows a much richer dynamics. Below the Walker breakdown, we find that the temperature gradient always pulls the domain wall towards the hot end by minimizating its free energy, in agreement with the observations for ferro- and antiferromagnets in the same regime. Above Walker breakdown, the ferrimagnetic domain wall can show the opposite, counterintuitive behavior of moving towards the cold end. We show that in this case, the motion to the hotter or the colder ends is driven by angular momentum transfer and therefore strongly related to the angular momentum compensation temperature, a unique property of ferrimagnets where the intrinsic angular momentum of the ferrimagnet is zero while the sublattice angular momentum remains finite. In particular, we find that below the compensation temperature the wall moves towards the cold end, whereas above it, towards the hot end. Moreover, we find that for ferrimagnets, there is a torque compensation temperature at which the domain wall dynamics shows similar characteristics to antiferromagnets, that is, quasi-inertia-free motion and the absence of Walker breakdown.

Cluster multipole dynamics in noncollinear antiferromagnets

In this paper, the authors study spin dynamics in the noncollinear antiferromagnet Mn3Sn. They derive an effective low-energy model based on the cluster multipole expansion of the magnetic structure and show that the cluster multipole degrees of freedom dominate its low-energy dynamics. They also show that Mn3Sn has a high domain wall velocity without a Walker breakdown and a stable uniform precession mode with a tunable frequency.

Observation of the domain wall propagation in CoFe and CoFeB nanowires driven by sub-nanosecond magnetic pulse using micromagnetic simulation

In this study, we have observed the domain wall (DW) propagation in CoFe and CoFeB nanowires driven by sub-nanosecond magnetic pulse using micromagnetic simulation approach. The length of the nanowire is 2000 nm, the widths are varied of 50, 100, and 150 nm, and the thicknesses are 2.5 and 5.0 nm. The simulation was performed using a rectangular cell size of 5×5×t nm3 with t is the thickness of the nanowire and the damping factor is 0.05. The sub-nanosecond magnetic pulse length of 0.5 ns was used to move DW through the nanowire. We found that the DW velocity increased as the magnitude of magnetic pulse increased then abruptly decreased which known as the Walker Breakdown (H WB). The transverse type DW structure is observed below the H WB field while vortex/anti-vortex wall structure was formed above H WB. We found that the H WB value of CoFe and CoFeB decreased as the width and thickness of the nanowire increased. The increasing of nanowire thickness also caused the velocity reduction of DW. The energy competition between exchange and demagnetization energy contributed to the DW structure during propagation. The exchange energy is higher than the demagnetization energy as the formation of vortex/anti-vortex wall.

Ultrafast domain wall motion in ferrimagnets induced by magnetic anisotropy gradient

The ultrafast magnetic dynamics in compensated ferrimagnets not only provides information similar to antiferromagnetic dynamics, but more importantly opens new opportunities for future spintronic devices [Kim et al., Nat. Mater. 16, 1187 (2017)]. One of the most essential issues for device design is searching for low-power-consuming and high-efficient methods of controlling domain wall. In this work, we propose to use the voltage-controlled magnetic anisotropy gradient as an excitation source to drive the domain wall motion in ferrimagnets. The ultrafast wall motion under the anisotropy gradient is predicted theoretically based on the collective coordinate theory, which is confirmed by the atomistic micromagnetic simulations. The antiferromagnetic spin dynamics is realized at the angular momentum compensation point, and the wall shifting has a constant speed under small gradient and can be slightly accelerated under large gradient due to the broadened wall width during the motion. For nonzero net angular momentum, the Walker breakdown occurs at a critical anisotropy gradient significantly depending on the second anisotropy and interfacial Dzyaloshinkii-Moriya interaction, which is highly appreciated for further experiments including the materials selection and device geometry design. More importantly, this work unveils a low-power-consuming method of controlling the domain wall in ferrimagnets, benefiting to future spintronic applications.

Ultrafast domain wall propagation due to the interfacial Dzyaloshinskii–Moriya interaction

It is shown that the interplay between curvature and interfacial Dzyalonshinsky–Moriya interaction (DMI) is a pathway to ultrafast domain wall (DW) dynamics in ferromagnetic nanotubes. In this work, we theoretically study the effect that interfacial DMI has on the average velocity of a vortex DW in thin ferromagnetic nanotubes grown around a core composed of heavy atoms. Our main result shows that by delaying the Walker breakdown instability, the DW average velocity is of the order of 103 m s−1, which is greater than usual values for these systems. The remarkable velocities achieved through this configuration could greatly benefit the development of spintronic devices.

Study of Domain Wall Propagation in FePt and FePd Nanowires Driven by Sub-nanosecond Pulse of Magnetic Field by Micromagnetic Simulation

In this study, we investigated the domain wall propagation behavior in FePt and FePd nanowires by micromagnetic simulation based on LLG equation. A rectangular shape nanowire model was generated with a fixed length of 2000 nm and varied thicknesses of 2.5 nm and 5 nm. The wire widths were varied of 50 nm, 100 nm, and 150 nm. The 500 ps length of magnetic-pulse was applied in-plane to a transverse type domain wall. We observed the Walker Breakdown field (HWB), which means the maximum domain wall velocity before it was abruptly decreased. The transverse DW structure was maintained below HWB while vortex/antivortex wall structure was formed in the higher magnetic field. Interestingly, the HWB value of both FePt and FePd were decreased as the width and thickness of the nanowires increased. We have also analyzed the changing of the demagnetization and exchange energy for the domain wall structure transition from transverse wall to vortex/anti-vortex wall.

Walker Breakdown with a Twist: Dynamics of Multilayer Domain Walls and Skyrmions Driven by Spin-Orbit Torque

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 in mobility. This phenomenon originates from complex stray field interactions and occurs for a wide range of multilayer materials and structures that include at least three ferromagnetic layers and finite Dzyaloshinskii-Moriya interaction. An analytical model is developed to describe the precessional dynamics in multilayers with surface-volume stray field interactions, yielding qualitative agreement with micromagnetic simulations.

Analytical computation of the demagnetizing energy of thin-film domain walls

Due to its non-local nature, calculating the demagnetizing field remains the biggest challenge in understanding domain structures in ferromagnetic materials. Analytical descriptions of demagnetizing effects typically approximate domain walls as uniformly magnetized ellipsoids, neglecting both the smooth rotation of magnetization from one domain to the other and the interaction between the two domains. Here, instead of the demagnetizing field, we compute analytically the demagnetizing energy of a straight domain wall described by the classical $\tanh$ magnetization profile in a thin film with perpendicular magnetic anisotropy. We then use our expression for the demagnetizing energy to derive an improved version of the 1D model of field-driven domain wall motion, resulting in accurate expressions for important properties of the domain wall such as the domain wall width and the Walker breakdown field. We verify the accuracy of our analytical results by micromagnetic simulations.

Voltage-induced high-speed DW motion in a synthetic antiferromagnet

Voltage-induced motion of a magnetic domain wall (DW) has potential in developing novel devices with ultralow dissipation. However, the speed for the voltage-induced DW motion (VIDWM) in a single ferromagnetic layer is usually very low. In this work, we proposed VIDWM with high speed in a synthetic antiferromaget (SAF). In the medium with a small damping coefficient, the velocity for the coupled DWs in the SAF is significantly higher than its counterpart in a single ferromagnetic layer. Strong interlayer antiferromagnetic exchange coupling plays a critical role for the high DW velocity since it inhibits the tilting of DW plane with Dzyaloshinskii–Moriya interaction. On the other hand, in the material with a large damping coefficient, the Walker breakdown of DW motion is also inhibited due to the stabilization of moment orientation under a strong interlayer antiferromagnetic coupling. In theory, the voltage-induced gradient of magnetic anisotropy is proved to be equal to an effective magnetic field that drives DW.

Multistep Bloch-line-mediated Walker breakdown in ferromagnetic strips

A well-known feature of magnetic field driven dynamics of domain walls in ferromagnets is the existence of a threshold driving force at which the internal magnetization of the domain wall starts to precess -- a phenomenon known as the Walker breakdown -- resulting in an abrupt drop of the domain wall propagation velocity. Here, we report on micromagnetic simulations of magnetic field driven domain wall dynamics in thin ferromagnetic strips with perpendicular magnetic anisotropy which demonstrate that in wide enough strips Walker breakdown is a multistep process: It consists of several distinct velocity drops separated by short linear parts of the velocity vs field curve. These features originate from the repeated nucleation, propagation and annihilation of an increasing number of Bloch lines within the domain wall as the driving field magnitude is increased. This mechanism arises due to magnetostatic effects breaking the symmetry between the two ends of the domain wall.

Understanding current-driven dynamics of magnetic Néel walls in heavy metal/ferromagnetic metal/oxide trilayers

We consider analytically current-driven dynamics of magnetic Néel walls in heavy metal/ferromagnetic metal/oxide trilayers where strong spin–orbit coupling and interfacial Dzyaloshinskii–Moriya interaction (i-DMI) coexist. We show that field-like spin–orbit torque (FL-SOT) with effective field along (n being the interface normal and being the charge current direction) and i-DMI induced torque can both lead to Walker breakdown suppression meanwhile leaving the wall mobility (velocity versus current density) unchanged. However, i-DMI itself can not induce the ‘universal absence of Walker breakdown’ (UAWB) while FL-SOT exceeding a certain threshold can. Finitely-enlarged Walker limits before UAWB are theoretically calculated and well explain existing data. In addition, change in wall mobility and even its sign-inversion can be understood only if the anti-damping-like SOT is appended. For Néel walls in ferromagnetic-metal layer with both perpendicular and in-plane anisotropies, we have calculated the respective modifications of wall mobility under the coexistence of spin-transfer torque, SOTs and i-DMI. Analytics shows that in trilayers with perpendicular anisotropy strong enough spin Hall angle and appropriate sign of i-DMI parameter can lead to sign-inversion in wall mobility even under small enough current density, while in those with in-plane anisotropy this only occurs for current density in a specific range.

Dragging of Magnetic Domain Walls by Interlayer Exchange

Magnetic domain walls can be moved by spin‐polarized currents due to spin‐transfer torques. This opens the possibility to use them in spintronic memory devices as, e.g., in racetrack storage. Naturally, in miniaturized devices domain walls can get very close to each other and affect each other's dynamics. In this work, two separated domain walls in different layers which interact via an interlayer exchange coupling have been considered. One of these walls is moved by a spin‐polarized current. Depending on several parameters as the current density, the interlayer coupling or the pinning potential, the combined dynamics of the two domain walls can change very strongly, allowing for, e.g., a correlated motion of the walls. In addition, a more subtle effect appears as a suppression of the Walker breakdown accompanied by an increase of the domain wall velocity.

Experimental method for surface domain wall shape studies in thin magnetic cylinders

Abstract Thin magnetic cylinders are in focus of interest due to peculiar features of domain wall motion like absence of the Walker breakdown. Here, we propose an experimental technique based on magneto-optical Kerr effect that allows surface studies of a domain wall shape in thin microwires. Our setup is optimized for characteristic optical and magneto-optical features of thin magnetic cylinders. Time-resolved measurements of a magnetic contrast along the circumference of wire are used to reconstruct a three-dimensional image of a surface domain wall shape. Our measurements confirmed a tilted shape of domain wall, in agreement with previous observations of microwires with positive magnetostriction alloy. The experimental technique represents a new way for direct visualizations of a surface magnetism of thin cylinders in optical range.

Spin-motive force due to domain-wall motion in the presence of Dzyaloshinskii-Moriya interaction

We theoretically demonstrate that the presence of Dzyaloshinskii-Moriya Interaction (DMI) can lead to enhancement of the spin-motive force (SMF) arising due to field-induced ferromagnetic domain wall motion. A SMF refers to an electric voltage induced by dynamical magnetic textures, which reflects the temporal and spatial variations of the magnetization. A DMI can introduce extra spatial rotation of the magnetization in the domain wall region, which turns out to cause the enhancement of the SMF. We derive an expression for the SMF, and examine the field- and DMI-dependences of the SMF. We find that the SMF can be amplified by up to an order of magnitude in the low field regime, where the external field is lower than the so-called Walker breakdown field.

Domain-wall dynamics for an in-plane magnetized thin film with a large perpendicular hard-axis anisotropy including the Dzyaloshinskii-Moriya interaction

We consider a thin ferromagnetic layer to which an external field or a current are applied along an in plane easy axis. The perpendicular hard axis anisotropy constant is large so that the out of plane magnetization component is smaller than the in plane components. A perturbation approach is used to obtain the profile and velocity of the moving domain wall. The dynamics of the in plane components of the magnetization is governed by a reaction diffusion equation which determines the speed of the profile. We find a simple analytic expression for the out of plane magnetization showing a symmetric distortion due to the motion in addition to the asymmetric component due to the Dzyaloshinskii--Moriya interaction. The results obtained complement previous studies in which either the Dzyalozhinskii vector or the out of plane hard axis anisotropy were assumed small. In the regime studied the Walker breakdown is not observed but the reaction diffusion dynamics predicts a slowing down of the domain wall for sufficiently large magnetic field. The transition point depends on the applied field, saturation magnetization and easy axis anisotropy.