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

Room-Temperature Intrinsic Ferromagnetic Chromium Tellurium Compounds with Thickness-Tunable Magnetic Texture

2D ferromagnetic chromium tellurides exhibit intriguing spin configurations and high-temperature intrinsic ferromagnetism, providing unprecedented opportunities to explore the fundamental spin physics and build spintronic devices. Here, a generic van der Waals epitaxial approach is developed to synthesize the 2D ternary chromium tellurium compounds with thicknesses down to mono-, bi-, tri-, and few-unit cells (UC). The Mn_0.14 Cr_0.86 Te evolves from intrinsic ferromagnetic behavior in bi-UC, tri-UC, and few-UC to temperature-induced ferrimagnetic behavior as the thickness increases, resulting in a sign reversal of the anomalous Hall resistance. Temperature- and thickness-tunable labyrinthine-domain ferromagnetic behaviors are derived from the dipolar interactions in Fe_0.26 Cr_0.74 Te and Co_0.40 Cr_0.60 Te. Furthermore, the dipolar-interaction-induced stripe domain and field-induced domain wall (DW) motion velocity are studied, and multibit data storage is realized through an abundant DW state. The magnetic storage can function in neuromorphic computing tasks, and the pattern recognition accuracy can reach up to 97.93%, which is similar to the recognition accuracy of ideal software-based training (98.28%). Room-temperature ferromagnetic chromium tellurium compounds with intriguing spin configurations can significantly promote the exploration of the processing, sensing, and storage based on 2D magnetic systems.

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.

Dynamic Symmetry Breaking in Chiral Magnetic Systems

The Dzyaloshinskii-Moriya interaction (DMI) in magnetic systems stabilizes spin textures with preferred chirality, applicable to next-generation memory and computing architectures. In perpendicularly magnetized heavy-metal/ferromagnet films, the interfacial DMI originating from structural inversion asymmetry and strong spin-orbit coupling favors chiral Néel-type domain walls (DWs) whose energetics and mobility remain at issue. Here, a new effect is characterized in which domains expand unidirectionally in response to a combination of out-of-plane and in-plane magnetic fields, with the growth direction controlled by the in-plane field strength. These growth directionalities and symmetries with applied fields cannot be understood from static treatments alone. The authors theoretically demonstrate that perpendicular field torques stabilize steady-state magnetization profiles highly asymmetric in elastic energy, resulting in a dynamic symmetry breaking consistent with the experimental findings. This phenomenon sheds light on the mechanisms governing the dynamics of Néel-type DWs and expands the utility of field-driven DW motion to probe and control chiral DWs.

Model of magnetic friction obeying the Dieterich-Ruina law in the steady state

We propose a model of magnetic friction and investigate the relation between the frictional force and the relative velocity of surfaces in the steady state. The model comprises two square lattices adjacent to each other, the upper of which is subjected to an external force, and the magnetic interaction acts as a kind of potential barrier that prevents the upper lattice from moving. We consider two surface types for the upper lattice: smooth and rough. The behavior of this model is classified into two domains, which we refer to as domains I and II. In domain II, the external force is dominant compared with other forces, whereas in domain I, the velocity of the lattice is suppressed by the magnetic interaction and obeys the Dieterich-Ruina law. This characteristic property can be observed regardless of whether the surface is smooth or rough.

Domain-wall motion and interfacial Dzyaloshinskii-Moriya interactions in Pt/Co/Ir(t Ir)/Ta multilayers

The interfacial Dzyaloshinskii-Moriya interaction (DMI) is important for chiral domain walls (DWs) and for stabilizing magnetic skyrmions. We study the effects of introducing increasing thicknesses of Ir, from zero to 2 nm, into a Pt/Co/Ta multilayer between the Co and Ta layers. There is a marked increase in magnetic moment, due to the suppression of the dead layer at the interface with Ta, but the perpendicular anisotropy is hardly affected. All samples show a universal scaling of the field-driven DW velocity across the creep and depinning regimes. Asymmetric bubble expansion shows that DWs in all of the samples have the left-handed Néel form. The value of in-plane magnetic field at which the creep velocity shows a minimum drops markedly on the introduction of Ir, as does the frequency shift of the Stokes and anti-Stokes peaks in Brillouin light scattering (BLS) measurements. Despite this qualitative similarity, there are quantitative differences in the DMI strength given by the two measurements, with BLS often returning higher values. Many features in bubble expansion velocity curves do not fit simple models commonly used, namely a lack of symmetry about the velocity minimum and no difference in velocities at high in-plane fields. These features are explained by the use of a new model in which the depinning field is allowed to vary with in-plane field in a way determined from micromagnetic simulations. This theory shows that the velocity minimum underestimates the DMI field, consistent with BLS giving higher values. Our results suggest that the DMI at an Ir/Co interface has the same sign as the DMI at a Pt/Co interface.

Domain wall energy and strain in Pt/Co/Ir thin films on piezoelectric transducers

We study the energy and creep velocity of magnetic domain walls in perpendicularly magnetised Pt/Co/Ir thin films under strain. We find that the enhancement of domain wall creep velocity under strain from piezoelectric transducers is largest in films with the thinnest Co layers (0.56 nm), in which the strain causes the smallest relative change in perpendicular magnetic anisotropy and the largest relative change in domain wall creep velocity. We show how domain wall energy is predictive of the sensitivity of domain wall creep velocity to changes in strain, and thus provide a route to designing magnetic thin film systems for optimum strain control.

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.

Magnetization switching through domain wall motion in Pt/Co/Cr racetracks with the assistance of the accompanying Joule heating effect

Heavy metal/ferromagnetic layers with perpendicular magnetic anisotropy (PMA) have potential applications for high-density information storage in racetrack memories and nonvolatile magnetic random access memories.

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.