Field-driven Domain Wall Motion Research Articles

Modulation of switching current density in T-type magnetic structure through magnetic anisotropy

We investigate magnetic field driven domain wall motion and spin-orbit torque (SOT) induced perpendicular magnetization switching of the ferrimagnetic layer in a T-type magnetic heterojunction with the structure of Pt/Co/Ta/Co81Tb19/Ta, where the bottom Co layer has in-plane magnetic anisotropy and the top Co81Tb19 layer has perpendicular magnetic anisotropy. It is found that the magnetic field driven domain wall motion and the depinning field of the Co81Tb19 layer can be effectively tuned by the thickness of the Co layer (tCo). Meanwhile, SOT-induced perpendicular magnetization switching of the Co81Tb19 layer is observed, and the critical switching current density first decreases and then increases with increasing the thickness of the Co layer. A lower critical switching current density was obtained at the optimized thickness (tCo = 1.2 nm), resulting in a 37% reduction in critical switching current density. Meanwhile, the research reveals a strong correlation between critical switching current density and magnetic anisotropy field, indicating that tuning the magnetic anisotropy is an efficient way to modulate the switching current density in a T-type magnetic structure. These results provide a new perspective on SOT manipulation and will be useful for the design of SOT-based devices.

Field-driven domain wall motion in ferrimagnetic nanowires

The fascinating high-speed field-driven domain wall (DW) motion along ferrimagnetic nanowires near the angular momentum compensation point (AMCP) is solved based on the generic ferrimagnetic dynamics. The physics of the absences of precessional torque and infinite high Walker breakdown field at the AMCP is proved under general conditions. Based on the energy conservation principle, an almost exact DW velocity formula, valid beyond the Walker breakdown field, is obtained. Our results agree with all existing experiments and simulations. This theory provides useful guidances to DW manipulation.

Novel interpretation of recent experiments on the dynamics of domain walls along ferrimagnetic strips

Domain wall motion along ferrimagnets is evaluated using micromagnetic simulations and a collective-coordinates model, both considering two sublattices with independent parameters. Analytical expressions are derived for strips on top of either a heavy metal or a substrate with negligible interfacial Dzyaloshinskii–Moriya interaction. The work focuses its findings in this latter case, with a field-driven domain wall motion depicting precessional dynamics which become rigid at the angular momentum compensation temperature, and a current-driven dynamics presenting more complex behavior, depending on the polarization factors for each sublattice. Importantly, our analyses provide also novel interpretation of recent evidence on current-driven domain wall motion, where walls move either along or against the current depending on temperature. Besides, our approach is able to substantiate the large non-adiabatic effective parameters found for these systems.

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.

Depinning phase transitions of current- and field-driven domain wall motion

With the Landau–Lifshitz–Gilbert (LLG) equation, we investigate critical dynamic behaviors of the domain wall driven by the electric current and the magnetic field in disordered magnetic films. Based on the dynamic scaling form far from stationary, the critical points, and both the static and dynamic exponents of the depinning phase transition are accurately determined. The phase diagram is comprehensively depicted, which agrees with and goes beyond that of the experiments. The adiabatic and non-adiabatic spin-transfer torques induced by the electric current play distinct roles in the depinning phase transition. The novel dynamic approach to the numerical simulations of the LLG equation shows its great efficiency.

Field and Current Controlled Domain Wall Propagation in Twisted Glass-Coated Magnetic Microwires

The torsion effect on the field and current driven magnetization reversal and the associated domain wall velocity in cylindrical amorphous and nanocrystalline glass-coated microwires is reported. Samples from three representative compositions have been investigated: (1) amorphous Fe77.5Si7.5B15 with positive magnetostriction, λ ≅ 25 × 10−6, (2) amorphous Co68.18Fe4.32Si12.5B15 with nearly zero negative magnetostriction, λ ≅ −1 × 10−7, and (3) nanocrystalline Fe73.5Si13.5B9Cu1Nb3 (FINEMET) with small positive magnetostriction, λ ≅ 2.1 × 10−6, all having the diameter of the metallic nucleus, d, of 20 µm and the glass coating thickness, tg, of 11 µm. The results are explained through a phenomenological interpretation of the effects of applied torque on the anisotropy axes within the microwires with different characteristics. Among all the complex mechanical deformations caused by the application of torque on magnetic microwire samples, the most important are the axial compression – for axial field-driven domain wall motion, and the circumferential tension – for electrical current/circumferential field-driven domain wall motion. The Co68.18Fe4.32Si12.5B15 microwire, annealed at 300 °C for 1 hour and twisted at 168 Rad/m exhibits the optimum characteristics, e.g. the lowest switching current (down to 9 mA~2.9 × 10−3 A/cm2) and the largest domain wall velocity (up to 2300 m/s).

Walker solution for Dzyaloshinskii domain wall in ultrathin ferromagnetic films

We analyze the electric current and magnetic field driven domain wall motion in perpendicularly magnetized ultrathin ferromagnetic films in the presence of interfacial Dzyaloshinskii-Moriya interaction and both out-of-plane and in-plane uniaxial anisotropies. We obtain exact analytical Walker-type solutions in the form of one-dimensional domain walls moving with constant velocity due to both spin-transfer torques and out-of-plane magnetic field. These solutions are embedded into a larger family of propagating solutions found numerically. Within the considered model, we find the dependencies of the domain wall velocity on the material parameters and demonstrate that adding in-plane anisotropy may produce domain walls moving with velocities in excess of 500 m/s in realistic materials under moderate fields and currents.

Magnetic properties and field-driven dynamics of chiral domain walls in epitaxial Pt/Co/AuxPt1−x trilayers

Chiral domain walls in ultrathin perpendicularly magnetised layers have a N\'{e}el structure stabilised by a Dzyaloshinskii-Moriya interaction (DMI) that is generated at the interface between the ferromagnet and a heavy metal. Different heavy metals are required above and below a ferromagnetic film in order to generate the structural inversion asymmetry needed to ensure that the DMI arising at the two interfaces does not cancel. Here we report on the magnetic properties of epitaxial Pt/Co/Au$_x$Pt$_{1-x}$ trilayers grown by sputtering onto sapphire substrates with 0.6 nm thick Co. As $x$ rises from 0 to 1 a structural inversion asymmetry is generated. We characterise the epilayer structure with x-ray diffraction and cross-sectional transmission electron microscopy, revealing (111) stacking. The saturation magnetization falls as the proximity magnetisation in Pt is reduced, whilst the perpendicular magnetic anisotropy $K_\mathrm{u}$ rises. The micromagnetic DMI strength $D$ was determined using the bubble expansion technique and also rises from a negligible value when $x=0$ to $\sim 1$ mJ/m$^2$ for $x = 1$. The depinning field at which field-driven domain wall motion crosses from the creep to the depinning regime rises from $\sim 40$ to $\sim 70$ mT, attributed to greater spatial fluctuations of the domain wall energy with increasing Au concentration. Meanwhile, the increase in DMI causes the Walker field to rise from $\sim 10$ to $\sim 280$ mT, meaning that only in the $x = 1$ sample is the steady flow regime accessible. The full dependence of domain wall velocity on driving field bears little resemblance to the prediction of a simple one-dimensional model, but can be described very well using micromagnetic simulations with a realistic model of disorder. These reveal a rise in Gilbert damping as $x$ increases.

Field-driven single domain wall motion in ferromagnetic nanowires.

We present a Lorentz microscopy study of polycrystalline permalloy 2D nanostructures with a thickness of 20 nm. Each structure was designed as a single domain wall trap. The trap comprises two horizontal nanowires with an in-plane dimension of 200 × 1000 nm2, and three tilted pads with different shapes. These structures allow us to create head-to-head domain walls, and these created walls can propagate in the structures by an external magnetic field. These designed traps were simulated using the micro-magnetic OOMMF simulation software. Those nanostructures were also patterned using electron beam lithography and focussed-ion beam techniques. This aims to determine the geometric parameters required to propagate a single magnetic domain wall in these structures reproducibly. Among the studied structures with one and two field directions, we found that the motion of a domain wall can be reproducibly driven by two alternative field directions in a trap which consists of the two horizontal nanowires and three 90°-tilted ones. We investigated systematically the viability of both single field and sequential switching of two field directions. Lorentz microscopy and micro-magnetic simulation results indicate that the propagation of a domain wall is strongly affected by the precise shape of the corner sections linking the trap elements, and the angles of the horizontal nanowires and tilted pads. Domain wall pinning and transformation of wall chirality are strongly correlated to the trap geometries. Our results are vital to design an optimal trap which supports a reproducible domain wall motion. This might also support a greater understanding of domain wall creation and propagation in magnetic nanowires which are of interest for concepts of high-density and ultrafast nonvolatile data storage devices, including racetrack memory and magnetic logic gates.

Effect of Magnetostatic Interactions on Stochastic Domain Wall Motion in Sub-100 nm Wide Nanowires

Magnetic field-driven domain wall motion is investigated in closely spaced sub-100 nm wide Co nanowires. Anticorrelations appear in the spatial distribution of pinning sites within weakly interacting nanowires, with a reduced probability of pinning adjacent to another pinning site over a mean correlation length similar to the line width roughness. In contrast, strong magnetostatic interactions between domain walls in adjacent nanowires eliminate the correlations, reducing the domain wall propagation distance for a given applied magnetic field.

Nonrecessive and Sustained Precessional Domain Wall Motion Driven by Perpendicular Field Pulses in Thin Magnetic Nanocylinders

In a conventional field-driven domain wall (DM) motion, the external field is applied along the magnetization of the magnetic domain which is expanded during the process. Recently, a novel approach is proposed to utilize a perpendicular field pulse rather than an in-plane one to drive DWs in magnetic nanostripes. In this paper, we apply this idea to transverse DWs in thin cylindrical nanowires. In the case of driving a single DW, this approach displays apparent advantages. Owing to the zero DW mass and inertia, a net DW displacement can be attained by applying a field pulse which is initially vertical to the DW magnetization. Therefore, no artificial pinning sites are required as in flat strips. Furthermore, we propose to rotate the external field with a particular frequency to maintain a right angle between the field and the DW magnetization. In this way, a continuous DW motion with maximum speed can be realized. The feasibility of this proposed approach is demonstrated by micromagnetic simulations and an analytical calculation.

Probing the Dzyaloshinskii-Moriya interaction in CoFeB ultrathin films using domain wall creep and Brillouin light spectroscopy

We have characterized the strength of the interfacial Dyzaloshinskii-Moriya interaction (DMI) in ultrathin perpendicularly magnetized CoFeB/MgO films, grown on different underlayers of W, TaN, and Hf, using two experimental methods. First, we determined the effective DMI field from measurements of field-driven domain wall motion in the creep regime, where applied in-plane magnetic fields induce an anisotropy in the wall propagation that is correlated with the DMI strength. Second, Brillouin light spectroscopy was employed to quantify the frequency non-reciprocity of spin waves in the CoFeB layers, which yielded an independent measurement of the DMI. By combining these results, we show that DMI estimates from the different techniques only yield qualitative agreement, which suggests that open questions remain on the underlying models used to interpret these results.

Influence of nonlocal damping on the field-driven domain wall motion

We derive the complete expression of nonlocal damping in noncollinear magnetization due to the nonuniform spin current pumped by precessional magnetization and incorporate it into a generalized Thiele equation to study its effects on the dynamics of the transverse and vortex domain walls (DWs) in ferromagnetic nanowires. We demonstrate that the transverse component of nonlocal damping slows down the field-driven DW propagation and increases the Walker breakdown field whereas it is neglected in many previous works in literature. The experimentally measured DW mobility variation with the damping tuned by doping with heavy rare-earth elements that had discrepancy from micromagnetic simulation are now well understood with the nonlocal damping. Our results suggest that the nonlocal damping should be properly included as a prerequisite for quantitative studies of current-induced torques in noncollinear magnetization.

Universal Pinning Energy Barrier for Driven Domain Walls in Thin Ferromagnetic Films.

We report a comparative study of magnetic field driven domain wall motion in thin films made of different magnetic materials for a wide range of field and temperature. The full thermally activated creep motion, observed below the depinning threshold, is shown to be described by a unique universal energy barrier function. Our findings should be relevant for other systems whose dynamics can be modeled by elastic interfaces moving on disordered energy landscapes.

Effects of grain size and disorder on domain wall propagation in CoFeB thin films

Micromagnetic simulations are used to investigate the effect of disorder on field-driven domain wall motion in perpendicularly magnetized CoFeB thin films. It is found that some degree of inhomogeneity in the form of an irregular grain structure needs to be introduced in the model in order to account for the domain wall velocities measured experimentally, even for applied fields much larger than the finite propagation field induced by weak disorder in the film. Moreover, the details of this grain structure have a large impact on domain wall motion in this flow regime. In particular, it is found that, for a fixed applied field, domain wall velocity rapidly increases with grain size up to a diameter of 40 nm, above which it slowly decreases. This is explained showing that the grain structure of the material introduces a new form of dissipation of energy via spin wave emission during domain wall propagation. We focus on the relation between grain size and domain wall velocity, finding that the frequency of emission of spin waves packets during domain wall motion depends on the grain size and affects directly the domain wall velocity of propagation.

Field-driven domain wall motion under a bias current in the creep and flow regimes in Pt/[CoSiB/Pt]N nanowires.

The dynamics of magnetic domain wall (DW) in perpendicular magnetic anisotropy Pt/[CoSiB/Pt]N nanowires was studied by measuring the DW velocity under a magnetic field (H) and an electric current (J) in two extreme regimes of DW creep and flow. Two important findings are addressed. One is that the field-driven DW velocity increases with increasing N in the flow regime, whereas the trend is inverted in the creep regime. The other is that the sign of spin current-induced effective field is gradually reversed with increasing N in both DW creep and flow regimes. To reveal the underlying mechanism of new findings, we performed further experiment and micromagnetic simulation, from which we found that the observed phenomena can be explained by the combined effect of the DW anisotropy, Dzyaloshinskii-Moriya interaction, spin-Hall effect, and spin-transfer torques. Our results shed light on the mechanism of DW dynamics in novel amorphous PMA nanowires, so that this work may open a path to utilize the amorphous PMA in emerging DW-based spintronic devices.

Creep turns linear in narrow ferromagnetic nanostrips.

The motion of domain walls in magnetic materials is a typical example of a creep process, usually characterised by a stretched exponential velocity-force relation. By performing large-scale micromagnetic simulations, and analyzing an extended 1D model which takes the effects of finite temperatures and material defects into account, we show that this creep scaling law breaks down in sufficiently narrow ferromagnetic strips. Our analysis of current-driven transverse domain wall motion in disordered Permalloy nanostrips reveals instead a creep regime with a linear dependence of the domain wall velocity on the applied field or current density. This originates from the essentially point-like nature of domain walls moving in narrow, line- like disordered nanostrips. An analogous linear relation is found also by analyzing existing experimental data on field-driven domain wall motion in perpendicularly magnetised media.

Current and field driven domain wall motion under influence of the Dzyaloshinsky–Moriya interaction

AbstractA complete analytical description of the dynamics of current and field driven transverse domain walls under the influence of the Dzyaloshinsky–Moriya interaction using the q– model will be given. Five different scenarios will be observed where the Dzyaloshinsky–Moriya vector is either parallel or perpendicular to the easy axis anisotropy of the system and a direct reversal, respectively, precessional motion will be assumed.

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.

Spin wave emission in field-driven domain wall motion

A domain wall (DW) in a nanowire can propagate under a longitudinal magnetic field by emitting spin waves (SWs). We numerically investigated the properties of SWs emitted by the DW motion, such as frequency and wave number, and their relation with the DW motion. For a wire with a low transverse anisotropy and in a field above a critical value, a DW emits SWs to both sides (bow and stern), while it oscillates and propagates at a low average speed. For a wire with a high transverse anisotropy and in a weak field, the DW emits mostly stern waves, while the DW distorts itself and the DW center propagates forward like a drill at a relative high speed.