Magnetic Domain Wall Motion Research Articles

Relation between the alignment dependence of coercive force decrease ratio and the angular dependence of coercive force of ferrite magnets

The relation of the coercive force decrease ratio (CFDR) and the angular dependence of the coercive force (ADCF) of ferrite magnets and their temperature properties were investigated.When we compared that against the angle of the magnetization reverse area obtained from these calculation results, which was obtained from the Gaussian distribution of the grain alignment and the postulation that every grain follows the Kondorskii law or the 1/cosθ law, and against the angle of the reverse magnetization area calculated from the experiment CFDR data of these magnets, it was found that this latter expanded at room temperature, to 36° from the calculated angle, for magnet with α=0.96. It was also found that, as temperature increased from room temperature to 413K, the angle of the reverse magnetization area of ferrite magnets obtained from the experiment data expanded from 36° to 41°.When we apply these results to the temperature properties of ADCF, it seems that the calculated ADCF could qualitatively and reasonably explain these temperature properties, even though the difference between the calculated angular dependence and the experimental data still exists in the high angle range.These results strongly suggest that the coercive force of these magnets is determined by the magnetic domain wall motion. The magnetic domain walls are strongly pinned at tilted grains, and when the domain walls are de-pinned from their pinning sites, the coercive force is determined.

Domain wall dynamics of periodic magnetic domain patterns in Co2MnGe-Heusler microstripes

Highly symmetric periodic domain patterns were obtained in Co2MnGe-Heusler microstripes as a result of the competition between growth-induced in-plane magnetic anisotropy and shape anisotropy. Zero field magnetic configurations and magnetic field-induced domain wall (DW) motion were studied by magnetic force microscopy-image technique for two different cases: dominant uniaxial- and dominant cubic in-plane anisotropy. We implemented a magneto-optical Kerr effect susceptometer to investigate the DW dynamics of periodic domain structures by measuring the in-phase and out-of-phase components of the Kerr signal as a function of magnetic field frequency and amplitude. The DW dynamics for fields applied transversally to the long stripe axis was found to be dominated by viscous slide motion. We used the inherent symmetry/periodicity properties of the magnetic domain structure to fit the experimental results with a theoretical model allowing to extract the DW mobility for the case of transverse DWs (μTDW = 1.1 m s−1 Oe−1) as well as for vortex-like DWs (μVDW = 8.7 m s−1 Oe−1). Internal spin structure transformations may cause a reduction of DW mobility in TDWs as observed by OMMFF simulations.

Electric-field-driven dynamics of magnetic domain walls in magnetic nanowires patterned on ferroelectric domains

Strong coupling of magnetic domain walls onto straight ferroelastic boundaries of a ferroelectric layer enables full and reversible electric-field control of magnetic domain wall motion. In this paper, the dynamics of this new driving mechanism is analyzed using micromagnetic simulations. We show that transverse domain walls with a near-180° spin structure are stabilized in magnetic nanowires and that electric fields can move these walls with high velocities. Above a critical velocity, which depends on material parameters, nanowire geometry and the direction of domain wall motion, the magnetic domain walls depin abruptly from the ferroelastic boundaries. Depinning evolves either smoothly or via the emission and annihilation of a vortex or antivortex core (Walker breakdown). In both cases, the magnetic domain wall slows down after depinning in an oscillatory fashion and eventually comes to a halt. The simulations provide design rules for hybrid ferromagnetic–ferroelectric domain-wall-based devices and indicate that material disorder and structural imperfections only influence Walker-breakdown-like depinning at high domain wall velocities.

Spintronics: Chiral damping.

Analysis of the magnetic domain-wall motion in a nanostructured magnetic system with strong spin–orbit coupling shows that the energy dissipation can be chiral when the inversion symmetry is broken.

Direct Observation of Reverse Magnetic Domain and Magnetic Domain Wall Motion in Nd-Fe-B Magnet at High Temperature by Lorentz Microscop

ABSTRACTWe conducted the in-situ observations of the magnetic domain structure change in Nd-Fe-B magnets at high temperature by transmission electron microscopy (TEM) / Lorentz microscopy with applying an external magnetic field. Prior to observation, a thin foil was magnetized by an external magnetic field of 2.0 T to almost saturation, then the magnetic domain structures were observed by the Fresnel mode with in-situ heating. At 225°C, reverse magnetic domains were found to generate in the thin foil sample without applying an external magnetic field. When we applied a magnetic field on the same direction to the pre-magnetization direction at 225°C, one magnetic domain wall was pinned by a grain boundary and the other magnetic domain wall moved. As the results, the reverse magnetic domain shrank then annihilated. When we cut the applied magnetic field, the reverse magnetic domain generated at almost the same location. On the other hand, when we applied a magnetic field to the foils in the opposite direction, the reverse domain started to grow, i.e., magnetic domain walls started to move. The observation results of the shrink or growth of the reverse domain showed that the pinning effect of grain boundary against domain wall motion would be different depending on the applied magnetic field direction. Moreover, domain walls was observed to be pinned by grain boundaries at elevated temperature, so that the coercivity of Nd-Fe-B magnet would occur by pinning mechanism.

The stability of steady motion of magnetic domain wall: Role of higher-order spin-orbit torques

The steady motion of magnetic domain wall driven by spin-orbit torques is investigated analytically in the heavy/ferromagnetic metal nanowires for three cases with a current transverse to the in-plane and perpendicular easy axis, and along the in-plane easy axis. By the stability analysis of Walker wall profile, we find that if including the higher-order spin-orbit torques, the Walker breakdown can be avoided in some parameter regions of spin-orbit torques with a current transverse to or along the in-plane easy axis. However, in the case of perpendicular anisotropy, even considering the higher-order spin-orbit torques, the velocity of domain wall cannot be efficiently enhanced by the current. Furthermore, the direction of wall motion is dependent on the configuration and chirality of domain wall with a current along the in-plane easy axis or transverse to the perpendicular one. Especially, the direction of motion can be controlled by the initial chirality of domain wall. So, if only involving the spin-orbit mechanism, it is preferable to adopt the scheme of a current along the in-plane easy axis for enhancing the velocity and controlling the direction of domain wall.

Micromagnetic modeling of domain wall motion in sub-100-nm-wide wires with individual and periodic edge defects

Reducing the switching energy of devices that rely on magnetic domain wall motion requires scaling the devices to widths well below 100 nm, where the nanowire line edge roughness (LER) is an inherent source of domain wall pinning. We investigate the effects of periodic and isolated rectangular notches, triangular notches, changes in anisotropy, and roughness measured from images of fabricated wires, in sub-100-nm-wide nanowires with in-plane and perpendicular magnetic anisotropy using micromagnetic modeling. Pinning fields calculated for a model based on discretized images of physical wires are compared to experimental measurements. When the width of the domain wall is smaller than the notch period, the domain wall velocity is modulated as the domain wall propagates along the wire. We find that in sub-30-nm-wide wires, edge defects determine the operating threshold and domain wall dynamics.

The magnetization behavior and open recoil loops of hot-deformed Nd-Fe-B magnets infiltrated by low melting point PrNd-Cu alloys

Ultrahigh coercivity of hot-deformed Nd-Fe-B magnets was obtained by low melting point PrNd-Cu alloys diffusion process. The coercivity was largely increased from 15.35 to 27.30 kOe. Magnetic isolation by nonmagnetic phases should be the primary explanation for the enhancement of coercivity. High susceptibility of the recoil loops at low field indicated that magnetic domain wall motion within grains was easy, while a near-zero reversible susceptibility of recoil loops implied that domain wall strong pinning at grain boundaries was dominant at higher field in initial magnetization process. Open recoil loops were also obtained in the infiltrated magnets and disappeared when the external field exceeded about 16 kOe lightly higher than the coercivity of the magnet without diffusion process. The inhomogeneous distribution of infiltrated phases that led to the grains aggregation and single grains with softer and harder magnetic characteristics, respectively, may be the primary reason for the phenomenon. The stray field produced by isolated single grains plays a critical role in the magnetization behavior. A phenomenological model for the magnetization reversal was built to interpret the open recoil loops in a recoil loop process.

Soliton-like magnetic domain wall motion induced by the interfacial Dzyaloshinskii–Moriya interaction

Topological defects such as magnetic solitons, vortices, Bloch lines, and skyrmions have started to play an important role in modern magnetism because of their extraordinary stability, which can be exploited in the production of memory devices. Recently, a novel type of antisymmetric exchange interaction, namely the Dzyaloshinskii-Moriya interaction (DMI), has been uncovered and found to influence the formation of topological defects. Exploring how the DMI affects the dynamics of topological defects is therefore an important task. Here we investigate the dynamic domain wall (DW) under a strong DMI and find that the DMI induces an annihilation of topological vertical Bloch lines (VBLs) by lifting the four-fold degeneracy of the VBL. As a result, velocity reduction originating from the Walker breakdown is completely suppressed, leading to a soliton-like constant velocity of the DW. Furthermore, the strength of the DMI, which is the key factor for soliton-like DW motion, can be quantified without any side effects possibly arising from current-induced torques or extrinsic pinnings in magnetic films. Our results therefore shed light on the physics of dynamic topological defects, which paves the way for future work in topology-based memory applications.

Scaling properties of a ferromagnetic thin film model at the depinning transition

.In this paper, we perform a detailed study of the scaling properties of a ferromagnetic thin film model. Recently, interest has increased in the scaling properties of the magnetic domain wall (MDW) motion in disordered media when an external driving field is present. We consider a (1 + 1)-dimensional model, based on evolution rules, able to describe the MDW avalanches. The global interface width of this model shows Family–Vicsek scaling with roughness exponent and growth exponent . In contrast, this model shows scaling anomalies in the interface local properties characteristic of other systems with depinning transition of the MDW, e.g. the quenched Edwards–Wilkinson (QEW) equation and random-field Ising model (RFIM) with driving. We show that, at the depinning transition, the saturated average velocity vanishes very slowly (with ) when the reduced force . The simulation results show that this model verifies all accepted scaling relations which relate the global exponents and the correlation length (or time) exponents, valid in systems with a depinning transition. Using the interface tilting method, we show that the model, close to the depinning transition, exhibits a nonlinearity similar to the one included in the Kardar–Parisi–Zhang (KPZ) equation. The nonlinear coefficient with , which implies that as the depinning transition is approached, a similar qualitative behaviour to the driven RFIM. We conclude this work by discussing the main features of the model and the prospects opened by it.

Current-Driven Motion of Magnetic Domain Wall with Many Bloch Lines

The current-driven motion of a domain wall (DW) in a ferromagnet with many Bloch lines (BLs) via the spin transfer torque is studied theoretically. It is found that the motion of BLs changes the current-velocity ($j$-$v$) characteristic dramatically. Especially, the critical current density to overcome the pinning force is reduced by the factor of the Gilbert damping coefficient $\alpha$ even compared with that of a skyrmion. This is in sharp contrast to the case of magnetic field driven motion, where the existence of BLs reduces the mobility of the DW.

Accurate calculation of the transverse anisotropy of a magnetic domain wall in perpendicularly magnetized multilayers

Bloch domain walls are the most common type of transition between two out-of-plane magnetized domains (one magnetized upwards, one downwards) in films with perpendicular magnetic anisotropy. The rotation of the spins of such domain walls in the plane of the film requires energy, which is described by an effective anisotropy, the so-called transverse or hard axis anisotropy ${K}_{\ensuremath{\perp}}$. This anisotropy and the related D\"oring mass density of the domain wall are key parameters of the one-dimensional model to describe the motion of magnetic domain walls. In particular, the critical field strength or current density where oscillatory domain wall motion sets in (Walker breakdown) is directly proportional to ${K}_{\ensuremath{\perp}}$. So far, no general framework is available to determine ${K}_{\ensuremath{\perp}}$ from static characterizations such as magnetometry measurements. Here, we derive a universal analytical expression to calculate the transverse anisotropy constant for the important class of perpendicular magnetic multilayers. All the required input parameters of the model, such as the number of repeats, the thickness of a single magnetic layer, and the layer periodicity, as well as the effective perpendicular anisotropy, the saturation magnetization, and the static domain wall width are accessible by static sample characterizations. We apply our model to a widely used multilayer system and find that the effective transverse anisotropy constant is a factor of seven different from that when using the conventional approximations, showing the importance of using our analysis scheme. Our model is also applicable to domain walls in materials with Dzyaloshinskii-Moriya interaction (DMI). The accurate knowledge of ${K}_{\ensuremath{\perp}}$ is needed to determine other unknown parameters from measurements, such as the DMI strength or the spin polarization of the spin current in current-induced domain wall motion experiments.

RC-Circuit-Like Dynamic Characteristic of the Magnetic Domain Wall in Flat Ferromagnetic Nanowires**Supported by the National Natural Science Foundation of China under Grant Nos 11474183, 51371105 and 51177088, the Korea Research Foundation (NRF) under Grant No 2010-0021735, the Leading Foreign Research Institute Recruitment Program of Korea under Grant No 2010-00471, and the Science and Technology Department of Hubei Province under Grant

We investigate the dynamic behavior of the magnetic domain wall under perpendicular magnetic field pulses in flat ferromagnetic nanowires using micromagnetic simulations. It is found that the perpendicular magnetic field pulse can trigger the magnetic domain wall motion, where all the field torques are kept on the plane of nanowire strip. The speed of magnetic domain walls faster than several hundreds of meters per second is predicted without the Walker breakdown for the perpendicular magnetic driving field stronger than 200 mT. Interestingly, the dynamic behavior of the moving magnetic domain wall driven by perpendicular magnetic field pulses is explained by charging- and discharging-like behaviors of an electrical RC-circuit model, where the charging and the discharging of magnetic charges on the nanowire planes are considered. The concept of the RC-model-like dynamic characteristic of the magnetic domain wall might be promising for the applications in spintronic functional devices based on the magnetic domain wall motion.

Controlling magnetic domain wall motion in the creep regime in He+-irradiated CoFeB/MgO films with perpendicular anisotropy

This study presents the effective tuning of perpendicular magnetic anisotropy in CoFeB/MgO thin films by He+ ion irradiation and its effect on domain wall motion in a low field regime. Magnetic anisotropy and saturation magnetisation are found to decrease as a function of the irradiation dose which can be related to the observed irradiation-induced changes in stoichiometry at the CoFeB/MgO interface. These changes in the magnetic intrinsic properties of the film are reflected in the domain wall dynamics at low magnetic fields (H) where irradiation is found to induce a significant decrease in domain wall velocity (v). For all irradiation doses, domain wall velocities at low fields are well described by a creep law, where Ln(v) vs. H−1∕4 behaves linearly, up to a maximum field H*, which has been considered as an approximation to the value of the depinning field Hdep. In turn, H* ≈ Hdep is seen to increase as a function of the irradiation dose, indicating an irradiation-induced extension of the creep regime of domain wall motion.

Controlled manipulation of domain walls in ultra-thin CoFeB nanodevices

We report on studies of magnetic domain wall (DW) movement within nanodevices containing magnetic components formed from perpendicularly magnetised CoFeB (0.6nm) thin films. Methods for low energy and smooth DW propagation as well as controlled and reproducible pinning of DWs at geometrically defined sites along nanowires are presented. Conventional anomalous Hall effect measurements as well as an indirect method using overlying electrodes are presented and compared. The results obtained from the individual studies of DW injection, propagation, pinning and measurement are assimilated into a prototype device suitable for the controlled pinning and annihilation of a single domain wall within the structure.

Investigation of magnetic anisotropy and magnetization process of tetragonal distorted FeCo multilayer films

Tetragonal distorted [Rh/FeCo(1.5nm)]n (n=1–4) multilayer films with strong perpendicular magnetic anisotropy(PMA) were successfully deposited on MgO (100) substrates. Magnetic properties and dynamic magnetization reversal process of the multilayer films have been investigated. With the repeat number of Rh/FeCo bilayer(n) increases from 1 to 4, effective uniaxial anisotropy(Keff) increases from 2.86×106erg/cm3 to 7.37×106erg/cm3. For Rh/FeCo(1.5nm) film, the reversal is governed by the magnetic moments reverse and domain wall movement. For [Rh\\FeCo(1.5nm)]n (n=2–4) films, the top FeCo layer reverses firstly, then other layers reverse gradually. These different reversal behaviors arise from the demagnetization energy and exchange coupling between FeCo layers and multilayer films.

Magnetic study of M-type Ru–Ti doped strontium hexaferrite nanocrystalline particles

We carried out a systematic study on the effect of the substitution of Ti2+ and Ru4+ ions for Fe3+ ions on the structural and magnetic properties of the strontium ferrite SrFe12−2xRuxTixO19 nanoparticles with (0≤x≤0.3), using x-ray diffraction, Quantum Design PPMS-9 magnetometry, and electrical resistivity. A clear irreversibility between the zero-field-cooled and field-cooled curves was observed below room temperature and the zero-field-cooled magnetization curves displayed a broad peak at a temperature TM. These results were discussed within the framework of random particle assembly model and associated with the magnetic domain wall motion. The resistivity data showed some kind of a transition from insulator to perfect insulator around TM. The high-temperature magnetization measurements exhibited sharp peaks just below Tc indicating a superparamagnetic behavior. With Ru–Ti substitution, the saturation magnetization at 5 K showed small variations were it slightly increased with increasing x up to 0.2, and then decrease for x = 0.3, while the coercivity decreased monotonically, recording a reduction of about 78% at x = 0.3. These results were discussed in light of the cationic distributions based on the results of the structural refinements.

Precise control of magnetic domain wall displacement by a nanosecond current pulse in Co/Ni nanowires

Magnetic domain wall (DW) motion induced by nanosecond current pulses is investigated in Co/Ni nanowires where the DW motion is driven by either adiabatic spin transfer torque (STT) or spin Hall torque (SHT). The DW displacement, including transient displacement and steady-state displacement, is found to be linearly related to the current pulse duration for both current-induced torques. The transient displacement is found to be less than 10% of the DW displacement. This result implies that the DW position can be controlled by tuning the duration of the current pulse, which enables a robust operation of racetrack memory.

Dynamics of magnetic field penetration into soft ferromagnets

We propose an approach to solve the coupled problem of the magnetic field penetration into soft ferromagnets and a frequency dependent magnetic hysteresis. The magnetic field diffusion is related to the macroscopic eddy currents. The hysteresis model is related to the microscopic eddy currents derived from the magnetic domain wall movements, and is responsible for the frequency dependence of hysteresis loops. In this paper, based on a lumped model and fractional derivative operators, we demonstrate that it is possible to replace the coupled diffusion/dynamic hysteresis in a simplest formulation using fractional operators. Such a formulation can be solved easily. Instead of solving a 1D problem of diffusion, we show here that a lumped model with appropriate fractional time derivative operator can be an exact formulation of the problem. In addition, we confirm that the model is using experimental available information, obtained by standard single sheet tester measuring bench (the tangential surface excitation field, and the cross section average induction).

Chiral magnetic domain wall in ferrimagnetic GdFeCo wires

Field-driven magnetic domain wall (DW) motion was investigated in ferrimagnetic GdFeCo wires with perpendicular magnetic anisotropy. The DW velocity as a function of the out-of-plane magnetic field exhibited the Walker breakdown phenomenon. The DW velocity was found to be significantly affected by the in-plane bias field: a minimum DW velocity was observed at a finite in-plane magnetic field (Hm), and the sign of Hm was found to reverse when the DW structure was changed from up-down- to down-up. These results imply that chiral DWs are formed in ferrimagnetic GdFeCo wires, despite their bulk and amorphous phase.