Domain Wall Depinning Research Articles

Time-resolved resistive switching on manganite surfaces: Creep and1/fαnoise signatures indicate pinning of nanoscale domains

We performed time-resolved nanoscale studies on the resistive switching of perovskite manganite thin films by means of conductive atomic force microscopy. Creep and recovery features have been observed in the evolution of metallic domains via pulse-train experiments and current map sequences. Local $I(t)$ curves show $1/{f}^{\ensuremath{\alpha}}$ noise signatures during the switching process, a phenomenon which occurs in various physical processes consisting of discrete jumps of different sizes, such as the Barkhausen effect. Our results imply that the resistive switching falls into this universal class of effects with dynamics determined by the pinning and depinning of structural domain walls.

Controlling depinning and propagation of single domain-walls in magnetic microwires

The magnetization reversal in magnetostrictive amorphous microwires takes place by depinning and propagation of a single domain wall. This is a consequence of the particular domain structure determined by the strong uniaxial anisotropy from the reinforcement of magnetoelastic and shape contributions. In the present study, after an overview on the current state-of-the art on the topic, we introduce the general behaviour of single walls in 30 to 40 cm long Fe-base microwires propagating under homogeneous field. Depending on the way the walls are generated, we distinguish among three different walls namely, standard wall, DWst, depinned and propagating from the wire’s end under homogeneous field which motion is the first one to switch on; reverse wall, DWrev, propagating from the opposite end under non-homogeneous field, and defect wall, DWdef, nucleated around local defect. Both, DWrev and DWdef are observed only under large enough applied field. In the subsequent section, we study the propagation of a wall under applied field smaller than the switching field. There, we conclude that a minimum field, Hdep,0, is needed to depin the DWst, as well as that a minimum field, Hprop,0, is required for the wall to propagate long distances. In the last section, we analyse the shape of induced signals in the pickup coils upon the crossing of the walls and its correlation to the domain walls shape. We conclude that length and shape of the wall are significantly distorted by the fact that the wall is typically as long as the measuring coils.

Domain Wall Depinning Process in Bistable Glass-Coated Microwire

A simple analytically solvable model for description of dynamics of the domain wall depinning process from the closure domain structure in bistable microwires was proposed. In this model closure domain structure is modelled by a single domain wall located in quadratic potential well. Critical parameters of rectangular magnetic field pulse needed to release this wall from the potential well were calculated. Theoretical dependence obtained in this way was fitted to experimental data measured on glass-coated Fe77.5B15Si7.5 microwire. Information about the order of closure domain structure dimension and about the mass of the domain wall, which is depinned from the wire end were obtained in this way.

Domain wall motion in nanopillar spin-valves with perpendicular anisotropy driven by spin-transfer torques

Using transport measurements and micromagnetic simulations we have investigated the domain wall motion driven by spin-transfer torques in all-perpendicular hexagonal nanopillar spin-valves. In particular, we probe domain walls nucleated in the free layer of the spin-valves, which are then pinned in the devices. We have determined both the field-current state diagrams for the domain-wall state and the thermally activated dynamics of the nucleation and depinning processes. We show that the nucleation process is well-described by a modified N\'eel-Brown model taking into account the spin-transfer torque, whereas the depinning process is independent of the current. This is confirmed by an analytical calculation which shows that spin-torques have no effect on the Arrhenius escape rate associated with thermally activated domain wall depinning in this geometry. Furthermore, micromagnetic simulations indicate that spin-transfer only weakly affects the domain wall motion, but instead modifies the inner domain wall structure.

Strain controlled ferroelectric switching time of BiFeO3 capacitors

The ferroelectric switching kinetics of BiFeO3 capacitors grown on a piezoelectric substrate has been investigated in different strain states and at various temperatures. The switching behavior is in good agreement with the Kolmogorov-Avrami-Ishibashi model. The effect of reversible biaxial in-plane compression on the switching time is an enhancement at low electric field and a reduction at high field. The two field regimes are found to correspond to the creep and the depinning of domain walls. The strain effect on the switching time depends strongly on temperature and reaches a tenfold slowing down upon ∼0.1% of biaxial compression at 50 K. This work provides a route to realize strain control of ferroelectric switching kinetics in BiFeO3 and is significant for potential applications.

Electrical Probing of Magnetic Phase Transition and Domain Wall Motion in Single-Crystalline Mn5Ge3 Nanowire

In this Letter, the magnetic phase transition and domain wall motion in a single-crystalline Mn(5)Ge(3) nanowire were investigated by temperature-dependent magneto-transport measurements. The ferromagnetic Mn(5)Ge(3) nanowire was fabricated by fully germaniding a single-crystalline Ge nanowire through the solid-state reaction with Mn contacts upon thermal annealing at 450 °C. Temperature-dependent four-probe resistance measurements on the Mn(5)Ge(3) nanowire showed a clear slope change near 300 K accompanied by a magnetic phase transition from ferromagnetism to paramagnetism. The transition temperature was able to be controlled by both axial and radial magnetic fields as the external magnetic field helped maintain the magnetization aligned in the Mn(5)Ge(3) nanowire. Near the magnetic phase transition, the critical behavior in the 1D system was characterized by a power-law relation with a critical exponent of α = 0.07 ± 0.01. Besides, another interesting feature was revealed as a cusp at about 67 K in the first-order derivative of the nanowire resistance, which was attributed to a possible magnetic transition between two noncollinear and collinear ferromagnetic states in the Mn(5)Ge(3) lattice. Furthermore, temperature-dependent magneto-transport measurements demonstrated a hysteretic, symmetric, and stepwise axial magnetoresistance of the Mn(5)Ge(3) nanowire. The interesting features of abrupt jumps indicated the presence of multiple domain walls in the Mn(5)Ge(3) nanowire and the annihilation of domain walls driven by the magnetic field. The Kurkijärvi model was used to describe the domain wall depinning as thermally assisted escape from a single energy barrier, and the fitting on the temperature-dependent depinning magnetic fields yielded an energy barrier of 0.166 eV.

Thermal effects in spin-torque assisted domain wall depinning

We have investigated the magnetization reversal in V-shaped permalloy (Py) nanowires under high dc currents via anisotropic magnetoresistance (AMR) measurements. Utilizing a diamond substrate as heat sink, current densities up to $2\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\text{A}/\text{m}}^{2}$ can be applied. These high current densities enabled us to observe spin-torque assisted switching in thermal equilibrium, without the influence of transient effects. At high currents, the field driven magnetization reversal process is influenced by Joule heating, Oersted fields, and spin-torque effects. These contributions can be identified in our experiment due to their different symmetry properties under magnetization and current reversal. We obtain two important results when evaluating the spin-torque efficiency $\ensuremath{\epsilon}$, which is proportional to the nonadiabaticity parameter $\ensuremath{\beta}$. First, we find different values for $\ensuremath{\epsilon}$ within the same sample, obtained with just a slight variation of the experimental parameters. Second, within the temperature range of 77 to 327 K, $\ensuremath{\epsilon}$ is found to be constant.

Piezoelectric nonlinearity and frequency dispersion of the direct piezoelectric response of BiFeO3 ceramics

We report on the frequency and stress dependence of the direct piezoelectric d33 coefficient in BiFeO3 ceramics. The measurements reveal considerable piezoelectric nonlinearity, i.e., dependence of d33 on the amplitude of the dynamic stress. The nonlinear response suggests a large irreversible contribution of non-180° domain walls to the piezoelectric response of the ferrite, which, at present measurement conditions, reached a maximum of 38% of the total measured d33. In agreement with this interpretation, both types of non-180° domain walls, characteristic for the rhombohedral BiFeO3, i.e., 71° and 109°, were identified in the poled ceramics using transmission electron microscopy. In support to the link between nonlinearity and non-180° domain-wall contribution, we found a correlation between nonlinearity and processes leading to depinning of domain walls from defects, such as quenching from above the Curie temperature and high-temperature sintering. In addition, the nonlinear piezoelectric response of BiFeO3 showed a frequency dependence that is qualitatively different from that measured in other nonlinear ferroelectric ceramics, such as “soft” (donor-doped) Pb(Zr,Ti)O3 (PZT), i.e., in the case of the BiFeO3 large nonlinearities were observed only at low field frequencies (<0.1 Hz); possible origins of this dispersion are discussed. Finally, we show that, once released from pinning centers, the domain walls can contribute extensively to the electromechanical response of BiFeO3; in fact, the extrinsic domain-wall contribution is relatively as large as in Pb-based ferroelectric ceramics with morphotropic phase boundary (MPB) composition, such as PZT. This finding might be important in the search of new lead-free MPB compositions based on BiFeO3 as it suggests that such compositions might also exhibit large extrinsic domain-wall contribution to the piezoelectric response.

Soft magnetic property and magnetization reversal mechanism of Sm doped FeCo thin film for high-frequency application

A series of (Fe0.67Co0.33)1−xSmx (0≤x<0.25) thin films with thickness around 110nm have been fabricated on silicon(111) substrates by magnetron co-sputtering at ambient condition with a 2.4kA/m magnetic field applied in the film plane during deposition. With the Sm concentration increasing, FeCo grain size gradually decreases and FeCoSm film eventually becomes amorphous, while the isotropic magnetic property changes to in-plane uniaxial anisotropy as long as Sm is doped. The investigation of the angular dependence of coercivity and switching field indicates that the magnetization reversal mechanism of FeCoSm film is domain-wall depinning and coherent rotation when the applied field is close to the easy axis and hard axis, respectively. The anisotropy field and the resonance frequency of FeCoSm films can be tuned in the range of 15.0–109.5kA/m and 5.2–11.8GHz, respectively, by controlling the content of Sm, indicating that FeCoSm films have much potential in high-frequency applications.

Field and current induced asymmetric domain wall motion in a giant magnetoresistance spin-valve stripe with a circular ring

Giant magnetoresistance (GMR) signals and the magneto-optic Kerr effect (MOKE) are combined to investigate the asymmetric domain wall (DW) motion in a GMR spin-valve stripe consisting of a wire and a circular ring. In the propagation of a tail-to-tail DW, the left-hand side, top-half ring, bottom-half ring, and the right-hand side are reversed in sequence. However, in the propagation of a head-to-head DW, the left-hand side, bottom half-ring, right-hand side, and top-half ring are switched in sequence. In addition, the critical current density for DW depinning shows asymmetric behavior. For tail-to-tail DW depinning, the critical current density of negative current pulses are lower than that of current pulses in the positive direction, and vice versa for head-to-head DW depinning.

Anisotropic bimodal distribution of blocking temperature with multiferroic BiFeO3 epitaxial thin films

Controlling BiFeO3 (BFO)/ferromagnet (FM) interfacial coupling appears crucial for electrical control of spintronic devices using this multiferroic. Here, we analyse the magnetic behaviour of exchange-biased epitaxial-BiFeO3/FM bilayers with in-plane or out-of-plane magnetic anisotropies. We report bimodal distributions of blocking temperatures similar to those of polycrystalline-antiferromagnet (AF)/FM bilayers. The high-temperature contribution depends on the FM anisotropy direction and is likely related to thermally activated depinning of domain walls in the BiFeO3 single crystal film as opposed to thermally activated reversal of spins in AF grains for polycrystalline AF. In contrast, the low-temperature contribution weakly depends on the anisotropy direction, consistent with a spin-glass origin.

Effect of Current on Domain Wall Depinning Field in Co/Ni Nanowire

We have investigated the effect of dc current on magnetic domain wall (DW) depinning fields in a perpendicularly magnetized Co/Ni nanowire by utilizing the giant magnetoresistance (GMR) effect. It was found that the current assisted (prevented) the domain wall depinning when the electron flow was parallel (antiparallel) to the DW depinning direction. The depinning field was found to exhibit a linear dependence on the dc current density, from which the efficiency of the effective field was estimated to be -1.5×10-14 T m2/A.

Effect of Current on Domain Wall Depinning Field in Co/Ni Nanowire

We have investigated the effect of dc current on magnetic domain wall (DW) depinning fields in a perpendicularly magnetized Co/Ni nanowire by utilizing the giant magnetoresistance (GMR) effect. It was found that the current assisted (prevented) the domain wall depinning when the electron flow was parallel (antiparallel) to the DW depinning direction. The depinning field was found to exhibit a linear dependence on the dc current density, from which the efficiency of the effective field was estimated to be -1.5×10-14 T m2/A.

Controlled pinning and depinning of domain walls in nanowires with perpendicular magnetic anisotropy

We investigate switching and field-driven domain wall motion in nanowires with perpendicular magnetic anisotropy comprising local modifications of the material parameters. Intentional nucleation and pinning sites with various geometries inside the nanowires are realized via a local reduction of the anisotropy constant. Micromagnetic simulations and analytical calculations are employed to determine the switching fields and to characterize the pinning potentials and the depinning fields. Nucleation sites in the simulations cause a significant reduction of the switching field and are in excellent agreement with analytical calculations. Pinning potentials and depinning fields caused by the pinning sites strongly depend on their shapes and are well explained by analytical calculations.

Magnetic soft x-ray microscopy of the domain wall depinning process in permalloy magnetic nanowires

Full-field magnetic transmission x-ray microscopy at high spatial resolution down to 20 nm is used to directly observe field-driven domain wall motion in notch-patterned permalloy nanowires. The depinning process of a domain wall around a notch exhibits a stochastic nature in most nanowires. The stochasticity of the domain wall depinning sensitively depends on the geometry of the nanowire such as the wire thickness, the wire width, and the notch depth. We propose an optimized design of the nanowire for deterministic domain wall depinning field at a notch.

Current-induced domain wall motion and magnetization dynamics in CoFeB/Cu/Co nanostripes

Current-induced domain wall motion and magnetization dynamics in the CoFeB layer of CoFeB/Cu/Co nanostripes were studied using photoemission electron microscopy combined with x-ray magnetic circular dichroism (XMCD-PEEM). Quasi-static measurements show that current-induced domain wall motion in the CoFeB layer is similar to the one observed in the NiFe layer of NiFe/Cu/Co trilayers, although the threshold current densities for domain wall depinning are lower. Time-resolved XMCD-PEEM measurements are used as an efficient probe of domain wall depinning statistics. They also reveal that, during the application of current pulses, the CoFeB magnetization rotates in the direction transverse to the nanostripe. The corresponding tilt angles have been quantified and compared to analytical and micromagnetic calculations, highlighting the influence of magnetostatic interactions between the two magnetic layers on the magnetization rotation.

Temperature-dependent dynamics of stochastic domain-wall depinning in nanowires

The temperature dependence of domain-wall depinning in permalloy nanowires is investigated by measuring depinning fields and corresponding depinning times as a function of the external magnetic bias field. Domain walls are pinned at triangular notches in the nanowires and detected noninvasively by Hall micromagnetometry. This technique allows one to acquire depinning-field and depinning-time distributions in the temperature range between 5 and 50 K and thus to determine the stochastics of the depinning process. The results are discussed in terms of the Néel–Brown model for thermally activated magnetization reversal, assuming a single energy barrier to overcome. In general, the cases presented deviate from this description and give a clear indication that a more complex term for the energy landscape of domain-wall depinning at constrictions in nanowires is obligatory.

Electric Current Effect on the Energy Barrier of Magnetic Domain Wall Depinning: Origin of the Quadratic Contribution

The energy barrier of a magnetic domain wall trapped at a defect is measured experimentally. When the domain wall is pushed by an electric current and/or a magnetic field, the depinning time from the barrier exhibits perfect exponential distribution, indicating that a single energy barrier governs the depinning. The electric current is found to generate linear and quadratic contributions to the energy barrier, which are attributed to the nonadiabatic and adiabatic spin-transfer torques, respectively. The adiabatic spin-transfer torque reduces the energy barrier and, consequently, causes depinning at lower current densities, promising a way toward low-power current-controlled magnetic applications.

Composition-controlled exchange bias training effect in FeCr/IrMn bilayers

For FeCr/IrMn bilayers, the exchange bias training effect and the magnetization reversal mechanism are correlated to each other and depend on the composition of the ferromagnetic layer. For high Fe contents, the asymmetric magnetization reversal is observed. During the training effect, both exchange field and coercivity decrease monotonically, suggesting a type I training effect. For low Fe contents, the domain wall depinning takes place for the two hysteresis loop branches. Only exchange field diminution happens in the training effect. The coercivity almost does not change in the process, corresponding to a type II training effect. It is suggested that the motion of antiferromagnetic spins is modified by the magnetization reversal mechanism in the ferromagnetic layer.

Enhanced spin transfer torque effect for transverse domain walls in cylindrical nanowires

Recent studies have predicted extraordinary properties for transverse domain walls in cylindrical nanowires: zero depinning current, the absence of the Walker breakdown, and applications as domain wall oscillators. In order to reliably control the domain wall motion, it is important to understand how they interact with pinning centers, which may be engineered, for example, through modulations in the nanowire geometry (such as notches or extrusions) or in the magnetic properties of the material. In this paper we study the motion and depinning of transverse domain walls through pinning centers in ferromagnetic cylindrical nanowires. We use (i) magnetic fields and (ii) spin-polarized currents to drive the domain walls along the wire. The pinning centers are modelled as a section of the nanowire which exhibits a uniaxial crystal anisotropy where the anisotropy easy axis and the wire axis enclose a variable angle ${\ensuremath{\theta}}_{\mathrm{P}}$. Using (i) magnetic fields, we find that the minimum and the maximum fields required to push the domain wall through the pinning center differ by $30%$. On the contrary, using (ii) spin-polarized currents, we find variations of a factor 130 between the minimum value of the depinning current density (observed for ${\ensuremath{\theta}}_{\mathrm{P}}={0}^{\ensuremath{\circ}}$, i.e., anisotropy axis pointing parallel to the wire axis) and the maximum value (for ${\ensuremath{\theta}}_{\mathrm{P}}={90}^{\ensuremath{\circ}}$, i.e., anisotropy axis perpendicular to the wire axis). We study the depinning current density as a function of the height of the energy barrier of the pinning center using numerical and analytical methods. We find that for an industry standard energy barrier of $40\phantom{\rule{0.28em}{0ex}}{k}_{\mathrm{B}}T$, a depinning current of about $5\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{A}$ (corresponding to a current density of $6\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.28em}{0ex}}\mathrm{A}/{\mathrm{m}}^{2}$ in a nanowire of $10\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ diameter) is sufficient to depin the domain wall. We reveal and explain the mechanism that leads to these unusually low depinning currents. One requirement for this depinning mechanism is for the domain wall to be able to rotate around its own axis. With the right barrier design, the spin torque transfer term is acting exactly against the damping in the micromagnetic system, and thus the low current density is sufficient to accumulate enough energy quickly. These key insights may be crucial in furthering the development of novel memory technologies, such as the racetrack memory, that can be controlled through low current densities.