Search

Cylindrical magnetic nanowires have been proposed as a means of storing and processing information in a 3D medium, based on the motion of domain walls~(DWs). Introducing short chemical modulations in such wires would allow for reliable digital control of DWs. Here, we outline the intricate physics of the interaction of domain walls with modulations to control their motion, combining micromagnetic simulations and experimental evidence. This interaction combines a long-range moderate magnetostatic repulsion with a local energy well. The latter depends on the respective circulation sense of magnetization in the domain wall and modulation. We also show that a modulation has the ability to switch the internal circulation of a DW upon its propagation, thereby acting as a polarizing component and opening the possibility to exploit not only the position of walls, but also their internal structure.

Topology is a powerful tool for categorizing magnetization textures, highlighting specific features in both 2D systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D nanomagnetism within confined geometries, the contributions from both volume and surface must be considered, requiring appropriate topological analysis to obtain a complete view of the system. Here, we consider domain walls in cylindrical magnetic nanowires to illustrate the use of topological invariants. We begin with micromagnetic simulations of domain wall transformation under the stimulus of an \OErsted field, tracking bulk and surface topological signatures, and analyzing the interplay between multiple micromagnetic objects. For instance, the extensive analysis allowed us to highlight mechanisms of domain wall type conversion from topologically non-trivial to trivial states, a phenomenon disregarded in previous studies. Additionally, we provide experimental evidence of the transient states predicted to occur during the dynamical process.

The concept of Perpendicular Shape-Anisotropy Spin-Transfer-Torque Magnetic Random-Access Memory tackles the downsize scalability limit of conventional ultrathin magnetic tunnel junctions (MTJ) below sub-20 nm technological nodes. This concept uses a thicker storage layer with a vertical aspect ratio, enhancing the thermal stability factor thanks to the favorable contribution of the shape anisotropy. However, the increased aspect ratio comes with an increase in switching time under applied voltage and the cross-over to non-uniform reversal mechanism at higher aspect ratio, limiting the gain in scalability. Additionally, the larger volume of the magnetic cell significantly increases the stray field acting on the neighboring devices compared to thin MTJs. In this work, we propose the use of a dipolar-coupled core-shell system as a storage layer. This improves both bottlenecks, as predicted by micromagnetic simulations for magnetisation reversal, and a macrospin model to estimate the stray field in a dense array., Comment: 11 pages, 11 figures

We analyze the micromagnetics of short longitudinal modulations of a high-magnetization material in cylindrical nanowires made of a soft-magnetic material of lower magnetization such as permalloy, combining magnetic microscopy, analytical modeling, and micromagnetic simulations. The mismatch of magnetization induces curling of magnetization around the axis in the modulations, in an attempt to screen the interfacial magnetic charges. The curling angle increases with modulation length, until a plateau is reached with nearly full charge screening for a specific length scale~$\Delta_\mathrm{mod}$, larger than the dipolar exchange length of any of the two materials. The curling circulation can be switched by the Oersted field arising from a charge current with typical magnitude $10^{12} A/m^{2}$ for a diameter of $\sim$100 nm, and reaching a maximum for $\Delta_\mathrm{mod}$.

Speed and reliability of magnetic domain wall (DW) motion are key parameters that must be controlled to realize the full potential of DW-based magnetic devices for logic and memory applications. A major hindrance to this is extrinsic DW pinning at specific sites related to shape and material defects, which may be present even if the sample synthesis is well controlled. Understanding the origin of DW pinning and reducing it is especially desirable in electrochemically-deposited cylindrical magnetic nanowires (NWs), for which measurements of the fascinating physics predicted by theoretical computation have been inhibited by significant pinning. We experimentally investigate DW pinning in Co$_x$Ni$_{100-x}$ NWs, by applying quasistatic magnetic fields. Wire compositions were varied with $x=20,30,40$, while the microstructure was changed by annealing or varying the pH of the electrolyte for deposition. We conclude that pinning due to grain boundaries is the dominant mechanism, decreasing inversely with both the spontaneous magnetization and grain size. Second-order effects include inhomogeneities in lattice strain and the residual magnetocrystalline anisotropy. Surface roughness, dislocations and impurities are not expected to play a significant role in DW pinning in these wire samples., Comment: 10 pages, 4 figures, regular manuscript

Recent studies in three dimensional spintronics propose that the \OE rsted field plays a significant role in cylindrical nanowires. However, there is no direct report of its impact on magnetic textures. Here, we use time-resolved scanning transmission X-ray microscopy to image the dynamic response of magnetization in cylindrical Co$_{30}$Ni$_{70}$ nanowires subjected to nanosecond \OE rsted field pulses. We observe the tilting of longitudinally magnetized domains towards the azimuthal \OE rsted field direction and create a robust model to reproduce the differential magnetic contrasts and extract the angle of tilt. Further, we report the compression and expansion, or breathing, of a Bloch-point domain wall that occurs when weak pulses with opposite sign are applied. We expect that this work lays the foundation for and provides an incentive to further studying complex and fascinating magnetization dynamics in nanowires, especially the predicted ultra-fast domain wall motion and associated spin wave emissions., Comment: 6 pages, 3 figures in main text and supplementary materials

Two types of domain walls exist in magnetically soft cylindrical nanowires: the transverse-vortex wall (TVW) and the Bloch-point wall (BPW). The latter is expected to prevent the usual Walker breakdown, and thus enable high domain wall speed. We showed recently [M. Sch\"obitz \etal, Phys. Rev. Lett. 123, 217201 (2019)] that the previously overlooked OErsted field associated with an electric current is a key in experiments to stabilize the BPW and reach speed above 600 m/s with spin-transfer. Here, we investigate in detail this situation with micromagnetic simulations and modeling. The switching of the azimuthal circulation of the BPW to match that of the OErsted field occurs above a threshold current scaling with $1/R^3$ ($R$ is the wire radius), through mechanisms that may involve the nucleation and/or annihilation of Bloch points. The domain wall dynamics then remains of a below-Walker type, with speed largely determined by spin-transfer torque alone.

The concept of perpendicular shape anisotropy spin-transfer torque magnetic random-access memory (PSA-STT-MRAM) consists in increasing the storage layer thickness to values comparable to the cell diameter, to induce a perpendicular shape anisotropy in the magnetic storage layer. Making use of that contribution, the downsize scalability of the STT-MRAM may be extended towards sub-20 nm technological nodes, thanks to a reinforcement of the thermal stability factor $\Delta$. Although the larger storage layer thickness improves $\Delta$, it is expected to negatively impact the writing current and switching time. Hence, optimization of the cell dimensions (diameter, thickness) is of utmost importance for attaining a sufficiently high $\Delta$ while keeping a moderate writing current. Micromagnetic simulations were carried out for different pillar thicknesses of fixed lateral size 20 nm. The switching time and the reversal mechanism were analysed as a function of the applied voltage and aspect-ratio (AR) of the storage layer. For AR $<$ 1, the magnetization reversal resembles a macrospin-like mechanism, while for AR $>$ 1 a non-coherent reversal is observed, characterized by the nucleation of a transverse domain wall at the ferromagnet/insulator interface which then propagates along the vertical axis of the pillar. It was further observed that the inverse of the switching time is linearly dependent on the applied voltage. This study was extended to sub-20 nm width with a value of $\Delta$ around 80. It was observed that the voltage necessary to reverse the magnetic layer increases as the lateral size is reduced, accompanied with a transition from macrospin-reversal to a buckling-like reversal at high aspect-ratios., Comment: 7 pages with a total of 8 figures

We demonstrate that magnetic skyrmions with a mean diameter around 60 nm can be stabilized at room temperature and zero external magnetic field in an exchange-biased Pt/Co/NiFe/IrMn multilayer stack. This is achieved through an advanced optimization of the multilayer stack composition in order to balance the different magnetic energies controlling the skyrmion size and stability. Magnetic imaging is performed both with magnetic force microscopy and scanning Nitrogen-Vacancy magnetometry, the latter providing unambiguous measurements at zero external magnetic field. In such samples, we show that exchange bias provides an immunity of the skyrmion spin texture to moderate external magnetic field, in the tens of mT range, which is an important feature for applications as memory devices. These results establish exchange-biased multilayer stacks as a promising platform towards the effective realization of memory and logic devices based on magnetic skyrmions., Comment: 5 pages, 3 figures

Domain wall propagation in cylindrical nanowires with modulations of diameter is a key phenomenon to design physics-oriented devices, or a disruptive three-dimensional magnetic memory. This chapter presents a combination of analytical modelling and micromagnetic simulations, with the aim to present a comprehensive panorama of the physics of pinning of domain walls at modulations, when moved under the stimulus of a magnetic field or a spin-polarized current. For the sake of considering simple physics, we consider diameters of a few tens of nanometers at most, and accordingly domain walls of transverse type. Modeling with suitable approximations provides simple scaling laws, while simulations are more accurate, refining the results and defining the range of validity of the models. While pinning increases with the relative change of diameter, a key feature is the much larger efficiency of pinning at an increase of diameter upon considering current rather than field, due to the drastic decrease of current density related to the increase of diameter., Comment: 37 pages, 14 figures, overview chapter

Since its proposal, the idea to vastly increase data storage density with a magnetic non-volatile 3D shift-register has sustained interest in current-induced domain wall (DW) motion. So far, experimental efforts have focused on flat nanostrips, which exhibit a wide range of noteworthy effects, yet suffer from intrinsic DW instabilities limiting their mobility. In contrast, ferromagnetic cylindrical nanowires (NWs) can host a novel type of magnetic DW, namely the Bloch-point wall (BPW), which due to its specific 3D topology should not experience the same fundamental issue. This could give rise to DW velocities over ~1000 m/s and fascinating new physics including coupling to magnetic spin waves, however, experimental evidence of DW dynamics in NWs is lacking until now. Here we report experimental results on current-induced DW motion in NWs with velocities >600 m/s, quantitatively consistent with predictions. Furthermore, our results indicate that although previously disregarded, the OErsted field induced by the current plays instead a crucial and valuable role in stabilising exclusively BPWs., Comment: 6 pages, 4 figures

Domain wall propagation in modulated-diameter cylindrical nanowires is a key phenomenon to be studied with a view to designing three-dimensional magnetic memory devices. This paper presents a theoretical study of transverse domain wall behavior under the influence of a magnetic field within a cylindrical nanowire with diameter modulations. In particular, domain wall pinning close to the diameter modulation was quantified, both numerically, using finite element micromagnetic simulations, and analytically. Qualitative analytical model for gently sloping modulations resulted in a simple scaling law which may be useful to guide nanowire design when analyzing experiments. It shows that the domain wall depinning field value is proportional to the modulation slope., Comment: 9 figures. Regular manuscript

Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The associated phase diagram is now well established and often used to predict the low-energy magnetic configuration in a given magnetic nanostructure. However, besides the transverse and vortex walls, we find numerically that another type of wall exists in permalloy nanostrips. This third type of DW is characterised by a three-dimensional, flux closure micromagnetic structure with an unusual length and three internal degrees of freedom. Magnetic imaging on lithographically-patterned permalloy nanostrips confirms these predictions and shows that these DWs can be moved with an external magnetic field of about 1mT. An extended phase diagram describing the regions of stability of all known types of DWs in permalloy nanostrips is provided., Comment: 19 pages, 7 figures

Shadow X-ray Magnetic Circular Dichroism Photo-Emission Electron Microscopy (XMCD-PEEM) is a recent technique, in which the photon intensity in the shadow of an object lying on a surface, may be used to gather information about the three-dimensional magnetization texture inside the object. Our purpose here is to lay the basis of a quantitative analysis of this technique. We first discuss the principle and implementation of a method to simulate the contrast expected from an arbitrary micromagnetic state. Text book examples and successful comparison with experiments are then given. Instrumental settings are finally discussed, having an impact on the contrast and spatial resolution : photon energy, microscope extraction voltage and plane of focus, microscope background level, electric-field related distortion of three-dimensional objects, Fresnel diffraction or photon scattering.

Magnetic frustration effects in artificial kagome arrays of nanomagnets with out-of-plane magnetization are investigated using Magnetic Force Microscopy and Monte Carlo simulations. Experimental and theoretical results are compared to those found for the artificial kagome spin ice, in which the nanomagnets have in-plane magnetization. In contrast with what has been recently reported, we demonstrate that long range (i.e. beyond nearest-neighbors) dipolar interactions between the nanomagnets cannot be neglected when describing the magnetic configurations observed after demagnetizing the arrays using a field protocol. As a consequence, there are clear limits to any universality in the behavior of these two artificial frustrated spin systems. We provide arguments to explain why these two systems show striking similarities at first sight in the development of pairwise spin correlations., Comment: 7 pages, 6 figures

Magnetic properties of nanometer thick Co films intercalated at the graphene/Ir(111) interface are investigated using spin-polarized low-energy electron microscopy (SPLEEM) and Auger electron spectroscopy. We show that the graphene top layer promotes perpendicular magnetic anisotropy in the Co film underneath, even for relatively thick intercalated deposits. The magnetic anisotropy energy is significantly larger for the graphene/Co interface than for the free Co surface. Hybridization of the graphene and Co electron orbitals is believed to be at the origin of the observed perpendicular magnetic anisotropy.

Magnetic frustration effects in artificial kagome arrays of nanomagnets are investigated using x-ray photoemission electron microscopy and Monte Carlo simulations. Spin configurations of demagnetized networks reveal unambiguous signatures of long range, dipolar interaction between the nanomagnets. As soon as the system enters the spin ice manifold, the kagome dipolar spin ice model captures the observed physics, while the short range kagome spin ice model fails., Comment: 4 pages, 4 figures, 1 table

We have investigated three-dimensional magnetization structures in numerous mesoscopic Fe/Mo(110) islands by means of x-ray magnetic circular dichroism combined with photoemission electron microscopy (XMCD-PEEM). The particles are epitaxial islands with an elongated hexagonal shape with length of up to 2.5 micrometer and thickness of up to 250 nm. The XMCD-PEEM studies reveal asymmetric magnetization distributions at the surface of these particles. Micromagnetic simulations are in excellent agreement with the observed magnetic structures and provide information on the internal structure of the magnetization which is not accessible in the experiment. It is shown that the magnetization is influenced mostly by the particle size and thickness rather than by the details of its shape. Hence, these hexagonal samples can be regarded as model systems for the study of the magnetization in thick, mesoscopic ferromagnets., Comment: 12 pages, 11 figures

We have measured the in-plane angular variation of nucleation and annihilation fields of a multi-domain magnetic single dot with a microsquid. The dots are Fe/Mo(110) self-assembled in UHV, with sub-micron size and a hexagonal shape. The angular variations were quantitatively reproduced by micromagnetic simulations. Discontinuities in the variations are observed, and shown to result from bifurcations related to the interplay of the non-uniform magnetization state with the shape of the dot., Comment: 4 pages, 4 figures, for submission as a regular article