Pinning-dependent field-driven domain wall dynamics and thermal scaling in an ultrathin Pt/Co/Pt magnetic film

Nonsteady dynamics at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model

With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the transition fields as well as static and dynamic exponents are accurately determined based on the short-time dynamic scaling form. Different from the usual assumption, two distinguished growth processes of spatial correlation lengths for the velocity and height of the domain wall are found. Thus, the universality class of the depinning transition is established, which significantly differs from that of the quenched disorder equation but agrees with that of the recent experiment as well as other simulations works. Under the influence of the mesoscopic time regime, the crossover from the second-order phase transition to the first-order one is confirmed in the weak-disorder regime, yielding an abnormal disorder-dependent nature of the criticality.

Optically Triggered Néel Vector Manipulation of a Metallic Antiferromagnet Mn2Au under Strain

The absence of stray fields, their insensitivity to external magnetic fields, and ultrafast dynamics make antiferromagnets promising candidates for active elements in spintronic devices. Here, we demonstrate manipulation of the Néel vector in the metallic collinear antiferromagnet Mn₂Au by combining strain and femtosecond laser excitation. Applying tensile strain along either of the two in-plane easy axes and locally exciting the sample by a train of femtosecond pulses, we align the Néel vector along the direction controlled by the applied strain. The dependence on the laser fluence and strain suggests the alignment is a result of optically triggered depinning of 90° domain walls and their motion in the direction of the free energy gradient, governed by the magneto-elastic coupling. The resulting, switchable state is stable at room temperature and insensitive to magnetic fields. Such an approach may provide ways to realize robust high-density memory device with switching time scales in the picosecond range.

Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles

Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modeled as an elastic system subject to quenched disorder. The ensuing field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group (RG) flow involves a function, the disorder correlator Δ(w), and is therefore termed the functional RG. Δ(w) is a physical observable, the auto-correlation function of the center of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of the mappings between these systems requires specific techniques, which we develop, including modeling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and non-linear surface growth with additional Kardar-Parisi-Zhang (KPZ) terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random-field magnets. Emphasis is given to numerical and experimental tests of the theory.

Depinning Exponents of Thin Film Domain Walls Depend on Disorder Strength

Domain wall dynamics in ferromagnets is complicated by internal degrees of freedom of the domain walls. We develop a model of domain walls in disordered thin films with perpendicular magnetic anisotropy capturing such features, and use it to study the depinning transition. For weak disorder, excitations of the internal magnetization are rare, and the depinning transition takes on exponent values of the quenched Edwards-Wilkinson equation. Stronger disorder results in disorder-dependent exponents concurrently with nucleation of an increasing density of Bloch lines within the domain wall.

Skyrmion Formation in Nanodisks Using Magnetic Force Microscopy Tip

We demonstrated numerically the skyrmion formation in ultrathin nanodisks using a magnetic force microscopy tip. We found that the local magnetic field generated by the magnetic tip significantly affects the magnetization state of the nanodisks and leads to the formation of skyrmions. Experimentally, we confirmed the influence of the local field on the magnetization states of the disks. Micromagnetic simulations explain the evolution of the magnetic state during magnetic force microscopy scanning and confirm the possibility of skyrmion formation. The formation of the horseshoe magnetic domain is a key transition from random labyrinth domain states into the skyrmion state. We showed that the formation of skyrmions by the magnetic probe is a reliable and repetitive procedure. Our findings provide a simple solution for skyrmion formation in nanodisks.

Universality classes of the domain-wall creep motion driven by spin-transfer torques

With the stochastic Landau-Lifshitz-Gilbert equation, we numerically simulate the creep motion of a magnetic domain wall driven by the adiabatic and nonadiabatic spin-transfer torques induced by the electric current. The creep exponent μ and the roughness exponent ζ are accurately determined from the scaling behaviors. The creep motions driven by the adiabatic and nonadiabatic spin-transfer torques belong to different universality classes. The scaling relation between μ and ζ based on certain simplified assumptions is valid for the nonadiabatic spin-transfer torque, while invalid for the adiabatic one. Our results are compatible with the experimental ones, but go beyond the existing theoretical prediction. Our investigation reveals that the disorder-induced pinning effect on the domain-wall rotation alters the universality class of the creep motion.

Thermally rounded depinning of an elastic interface on a washboard potential

The thermal rounding of the depinning transition of an elastic interface sliding on a washboard potential is studied through analytic arguments and very accurate numerical simulations. We confirm the standard view that well below the depinning threshold the average velocity can be calculated considering thermally activated nucleation of defects. However, we find that the straightforward extension of this analysis to near or above the depinning threshold does not fully describe the physics of the thermally assisted motion. In particular, we find that exactly at the depinning point the average velocity does not follow a pure power law of the temperature as naively expected by the analogy with standard phase transitions but presents subtle logarithmic corrections. We explain the physical mechanisms behind these corrections and argue that they are nonpeculiar collective effects which may also apply to the case of interfaces sliding on uncorrelated disordered landscapes.

Highly Anisotropic Magnetic Domain Wall Behavior in In-Plane Magnetic Films

We have studied the nucleation of magnetic domains and propagation of magnetic domain walls (DWs) induced by pulsed magnetic field in a ferromagnetic film with in-plane uniaxial anisotropy. In contrast to observed behavior in films with out-of-plane anisotropy, the nucleated domains have a rectangular shape in which a pair of the opposite sides are perfectly linear DWs, while the other pair present zigzags. The field induced propagation of these two DW types are found to be different. The linear ones follow a creep law identical to what is usually observed in out-of-plane films, while the velocity of zigzag DWs depends linearly on the applied field amplitude down to very low field. This unexpected feature can be explained by the shape of the DW, and these results provide first experimental evidence of the applicability of the 1D model in two-dimensional ferromagnetic thin films.

Numerical simulations of critical dynamics in anisotropic magnetic films with the stochastic Landau-Lifshitz-Gilbert equation

With the stochastic Landau-Lifshitz-Gilbert (sLLG) equation, critical dynamic behaviors far from equilibrium or stationary around the order-disorder and pinning-depinning phase transitions in anisotropic magnetic films are investigated. From the dynamic relaxation with and without an external field, the Curie temperature and critical exponents of the order-disorder phase transition are accurately determined. For the pinning-depinning phase transition induced by quenched disorder, the nonstationary creep motion of domain wall activated by finite temperatures is simulated, and the thermal rounding exponent is extracted. The results show that the dynamic universality class of the sLLG equation is different from those of the Monte Carlo dynamics and quenched Edwards-Wilkinson equation, and it may lead to alternative understanding of experiments. The dynamic approach shows its great efficiency for the sLLG equation.

Magnetic domain wall creep and depinning: A scalar field model approach

Magnetic domain wall motion is at the heart of new magnetoelectronic technologies and hence the need for a deeper understanding of domain wall dynamics in magnetic systems. In this context, numerical simulations using simple models can capture the main ingredients responsible for the complex observed domain wall behavior. We present a scalar field model for the magnetization dynamics of quasi-two-dimensional systems with a perpendicular easy axis of magnetization which allows a direct comparison with typical experimental protocols, used in polar magneto-optical Kerr effect microscopy experiments. We show that the thermally activated creep and depinning regimes of domain wall motion can be reached and the effect of different quenched disorder implementations can be assessed with the model. In particular, we show that the depinning field increases with the mean grain size of a Voronoi tessellation model for the disorder.

Simultaneous control of the Dzyaloshinskii-Moriya interaction and magnetic anisotropy in nanomagnetic trilayers

Magneto-optical Kerr effect (MOKE) microscopy measurements of magnetic bubble domains demonstrate that Ar^{+} irradiation around 100 eV can tune the Dzyaloshinskii-Moriya interaction (DMI) in Pt/Co/Pt trilayers. Varying the irradiation energy and dose changes the DMI sign and magnitude separately from the magnetic anisotropy, allowing tuning of the DMI while holding the coercive field constant. This simultaneous control emphasizes the different physical origins of these effects. To accurately measure the DMI, we propose and apply a physical model for a poorly understood peak in domain wall velocity at zero in-plane field. The ability to tune the DMI with the spatial resolution of the Ar^{+} irradiation enables new fundamental investigations and technological applications of chiral nanomagnetics.

Spatiotemporal Patterns in Ultraslow Domain Wall Creep Dynamics

In the presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps called avalanches, while, at much smaller fields, these interfaces creep by thermal activation. In this Letter, we develop a novel numerical technique that captures the ultraslow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatiotemporal patterns that resemble the complex sequence of aftershocks observed after a large earthquake. Remarkably, we show that events assemble in independent clusters that display at large scales the same statistics as critical depinning avalanches. We foresee these correlated dynamics being experimentally accessible by magnetooptical imaging of ferromagnetic films.

Universal domain wall dynamics under electric field in Ta/CoFeB/MgO devices with perpendicular anisotropy

Electric field effects in ferromagnetic metal/dielectric structures provide a new route to control domain wall dynamics with low-power dissipation. However, electric field effects on domain wall velocities have only been observed so far in the creep regime where domain wall velocities are low due to strong interactions with pinning sites. Here we show gate voltage modulation of domain wall velocities ranging from the creep to the flow regime in Ta/Co₄₀Fe₄₀B₂₀/MgO/TiO₂ structures with perpendicular magnetic anisotropy. We demonstrate a universal description of the role of applied electric fields in the various pinning-dependent regimes by taking into account an effective magnetic field being linear with the electric field. In addition, the electric field effect is found to change sign in the Walker regime. Our results are consistent with voltage-induced modification of magnetic anisotropy. Our work opens new opportunities for the study and optimization of electric field effect at ferromagnetic metal/insulator interfaces.

Domain walls in ferromagnetic–oxide structures can be moved using an electric field, which could be useful for low-power electronic devices. Here, the authors demonstrate the modulation of the velocity of these domain walls between a creep and a flow regime.

Spin orbit torques and Dzyaloshinskii-Moriya interaction in dual-interfaced Co-Ni multilayers

We study the spin orbit torque (SOT) and Dzyaloshinskii-Moriya interaction (DMI) in the dual-interfaced Co-Ni perpendicular multilayers. Through the combination of top and bottom layer materials (Pt, Ta, MgO and Cu), SOT and DMI are efficiently manipulated due to an enhancement or cancellation of the top and bottom contributions. However, SOT is found to originate mostly from the bulk of a heavy metal (HM), while DMI is more of interfacial origin. In addition, we find that the direction of the domain wall (DW) motion can be either along or against the electron flow depending on the DW tilting angle when there is a large DMI. Such an abnormal DW motion induces a large assist field required for hysteretic magnetization reversal. Our results provide insight into the role of DMI in SOT driven magnetization switching, and demonstrate the feasibility of achieving desirable SOT and DMI for spintronic devices.

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.

Chiral damping of magnetic domain walls

Structural symmetry breaking in magnetic materials is responsible for the existence of multiferroics, current-induced spin-orbit torques and some topological magnetic structures. In this Letter we report that the structural inversion asymmetry (SIA) gives rise to a chiral damping mechanism, which is evidenced by measuring the field-driven domain-wall (DW) motion in perpendicularly magnetized asymmetric Pt/Co/Pt trilayers. The DW dynamics associated with the chiral damping and those with Dzyaloshinskii-Moriya interaction (DMI) exhibit identical spatial symmetry. However, both scenarios are differentiated by their time reversal properties: whereas DMI is a conservative effect that can be modelled by an effective field, the chiral damping is purely dissipative and has no influence on the equilibrium magnetic texture. When the DW motion is modulated by an in-plane magnetic field, it reveals the structure of the internal fields experienced by the DWs, allowing one to distinguish the physical mechanism. The chiral damping enriches the spectrum of physical phenomena engendered by the SIA, and is essential for conceiving DW and skyrmion devices owing to its coexistence with DMI (ref. ).

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.

Proposal for a Domain Wall Nano-Oscillator driven by Non-uniform Spin Currents

We propose a new mechanism and a related device concept for a robust, magnetic field tunable radio-frequency (rf) oscillator using the self oscillation of a magnetic domain wall subject to a uniform static magnetic field and a spatially non-uniform vertical dc spin current. The self oscillation of the domain wall is created as it translates periodically between two unstable positions, one being in the region where both the dc spin current and the magnetic field are present, and the other, being where only the magnetic field is present. The vertical dc spin current pushes it away from one unstable position while the magnetic field pushes it away from the other. We show that such oscillations are stable under noise and can exhibit a quality factor of over 1000. A domain wall under dynamic translation, not only being a source for rich physics, is also a promising candidate for advancements in nanoelectronics with the actively researched racetrack memory architecture, digital and analog switching paradigms as candidate examples. Devising a stable rf oscillator using a domain wall is hence another step towards the realization of an all domain wall logic scheme.

Suppression of creep-regime dynamics in epitaxial ferroelectric BiFeO3 films

Switching dynamics of ferroelectric materials are governed by the response of domain walls to applied electric field. In epitaxial ferroelectric films, thermally-activated ‘creep’ motion plays a significant role in domain wall dynamics, and accordingly, detailed understanding of the system’s switching properties requires that this creep motion be taken into account. Despite this importance, few studies have investigated creep motion in ferroelectric films under ac-driven force. Here, we explore ac hysteretic dynamics in epitaxial BiFeO₃ thin films, through ferroelectric hysteresis measurements, and stroboscopic piezoresponse force microscopy. We reveal that identically-fabricated BiFeO₃ films on SrRuO₃ or La_0.67Sr_0.33MnO₃ bottom electrodes exhibit markedly different switching behaviour, with BiFeO₃/SrRuO₃ presenting essentially creep-free dynamics. This unprecedented result arises from the distinctive spatial inhomogeneities of the internal fields, these being influenced by the bottom electrode’s surface morphology. Our findings further highlight the importance of controlling interface and defect characteristics, to engineer ferroelectric devices with optimised performance.

Finite-temperature crossovers in periodic disordered systems

We consider the static properties of periodic structures in weak random disorder. We apply a functional renormalization group approach (FRG) and a Gaussian variational method (GVM) to study their displacement correlations. We focus in particular on the effects of temperature and we compute explicitly the crossover length scales separating different regimes in the displacement correlation function. We compare the FRG and GVM results and find excellent agreement. We show that the FRG predicts, in addition, the existence of a third length scale associated with the screening of the disorder by thermal fluctuations and discuss a protocol to observe it.

Modification of perpendicular magnetic anisotropy and domain wall velocity in Pt/Co/Pt by voltage-induced strain

The perpendicular magnetic anisotropy K_eff, magnetization reversal, and field-driven domain wall velocity in the creep regime are modified in Pt/Co(0.85–1.0 nm)/Pt thin films by strain applied via piezoelectric transducers. K_eff, measured by the extraordinary Hall effect, is reduced by 10 kJ/m³ by tensile strain out-of-plane ε_z = 9 × 10⁻⁴, independently of the film thickness, indicating a dominant volume contribution to the magnetostriction. The same strain reduces the coercive field by 2–4 Oe, and increases the domain wall velocity measured by wide-field Kerr microscopy by 30-100%, with larger changes observed for thicker Co layers. We consider how strain-induced changes in the perpendicular magnetic anisotropy can modify the coercive field and domain wall velocity.