Domain wall (DW) motion is a crucial process involved in magnetization reversal, be it under magnetic field or spin-polarized current stimulus. In most cases DW speed does not exceed ≈100m/s and collapses above a given threshold of the stimulus, an effect known as Walker breakdown. A few specific material properties have been identified to delay the breakdown of speed by increasing the energy barrier preventing internal precession. We show that in a 3D nanomagnetic system, here with vortex-state domains, the topology of the magnetization distribution may intrinsically and robustly delay the Walker breakdown due to an exchange-spring effect. In addition, curvature induces a major non-reciprocal effect, delaying or not the Walker breakdown depending on the chirality of the azimuthal domain versus the direction of motion of the DW.

The Perpendicular Shape Anisotropy Spin Transfer Torque Magnetic Random Access Memory (PSA-STT-MRAM) is a recent concept proposed to maintain the thermal stability of standard MRAM at small diameters, considering thick vertical pillars as the free layer. In order to explore the specific physics of PSA-STT-MRAMs expected in relation with their three-dimensional nature, we have performed simulations combining a micromagnetic model coupled self-consistently with spin-dependent transport equations. The 3D shape induces flower states at the upper and lower surfaces. Besides, the field-like component of STT is found to be larger than in standard MRAMs, suggesting that it needs to be considered. The combination of both effects leads to the excitation of high-order 3D ferromagnetic resonance modes, playing a key role in magnetisation reversal. These results highlight features of 3D nanomagnetic systems, largely disregarded so far, which need to be considered to optimise PSA-STT-MRAM to be a competitive solution for technological implementation.

Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D nanomagnetism, both volume and surface topological numbers must be considered, requiring the identification of a proper global topological invariant to support categorization. Here we consider domain walls in cylindrical nanowires as an excellent playground for 3D nanomagnetic systems, excited by a charge current, that generates an OErsted field. We first provide experimental evidence of previously unreported domain-wall transformations of topology occurring at the nanosecond timescale. We investigate these transformations with micromagnetic simulations, tracking both bulk and surface topological signatures.We demonstrate a topological invariant combining both signatures, while the topological charge varies from bulk to surface during the dynamics. The experimental change of topology is reproduced when the pulse duration matches the timescale of the internal transformations of the wall, and the current is switched off before the transformation is complete. We expect that the topological categorization and dynamical exploitation apply to any 3D nanomagnetic system.

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.

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 $\Delta_\mathrm{mod}$.

Recent studies in three-dimensional spintronics propose that the Œrsted field plays a significant role in cylindrical nanowires. However, there is no direct report on its impact on magnetic textures. Here, we use time-resolved scanning transmission x-ray microscopy to image the dynamic response of magnetization in cylindrical Co30Ni70 nanowires subjected to nanosecond Œrsted field pulses. We observe the tilting of longitudinally magnetized domains toward the azimuthal Œrsted field direction and create a robust model to reproduce the differential magnetic contrasts and extract the angle of tilt. Furthermore, we report the compression and expansion, or breathing, of a Bloch-point domain wall that occurs when weak pulses with opposite signs 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.

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 et al., 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 $600\phantom{\rule{0.28em}{0ex}}\mathrm{m}/\mathrm{s}$ 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.

F. Cheynis, 2 A. Massebœuf, O. Fruchart, ∗ N. Rougemaille, J. C. Toussaint, 2 R. Belkhou, 5 P. Bayle-Guillemaud, and A. Marty Institut NÉEL, CNRS & Université Joseph Fourier – BP166 – F-38042 Grenoble Cedex 9 – France Institut National Polytechnique de Grenoble – France CEA-Grenoble, INAC/SP2M/LEMMA, 17 rue des Martyrs, Grenoble, France Synchrotron SOLEIL, L’Orme des Merisiers Saint-Aubin BP 48, F-91192 Gif-sur-Yvette Cedex, France ELETTRA, Sincrotrone Trieste, I-34012 Basovizza, Trieste, Italy CEA-Grenoble, INAC/SP2M/NM, 17 rue des Martyrs, Grenoble, France (Dated: January 26, 2021)

We report a theoretical overview of the magnetic domain wall behavior under an electric current in infinitely long nanotubes with azimuthal magnetization, combining the one-dimensional analytic model and micromagnetic simulations. We highlight effects that, besides spin-transfer torques already largely understood in flat strips, arise specifically in the tubular geometry: the \OE{}rsted field and curvature-induced magnetic anisotropy resulting both from the exchange interaction and material growth. Depending on both the geometry of the tube and the strength of the azimuthal anisotropy, Bloch or N\'eel walls arise at rest, resulting in two regimes of motion largely dominated by either spin-transfer torques or the \OE{}rsted field. We determine the Walker breakdown current in all cases, and highlight the most suitable parameters to achieve high domain wall speed.

We compare two transmission electron microscopy (TEM) based techniques that can provide highly spatially resolved quantitative measurements of magnetic induction fields at high sensitivity. To this end, the magnetic induction of a ferromagnetic NiFe nanowire has been measured and compared to micromagnetic modeling. State-of-the-art off-axis electron holography has been performed using the averaging of large series of holograms to improve the sensitivity of the measurements. These results are then compared to those obtained from pixelated differential phase contrast, a technique that belongs to pixelated (or 4D) scanning transmission electron microscopy (STEM) experiments. This emerging technique uses a pixelated detector to image the local diffraction patterns as the beam is scanned over the sample. For each diffraction pattern, the deflection of the beam is measured and converted into magnetic induction, while scanning the beam allows a map to be generated. Aberration corrected Lorentz (field-free) configurations of the TEM and STEM were used for an improved spatial resolution. We show that the pixelated STEM approach, even when performed using an old generation of charge-coupled device camera, provides better sensitivity at the expense of spatial resolution. A more general comparison of the two quantitative techniques is given.

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. Schöbitz , 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.

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.

This corrects the article DOI: 10.1103/PhysRevLett.123.217201.

We report a theoretical overview of the magnetic domain wall behavior under an electric current in infinitely-long nanotubes with azimuthal magnetization, combining the 1D analytic model and micromagnetic simulations. We highlight effects that, besides spin-transfer torques already largely understood in flat strips, arise specifically in the tubular geometry: the field and curvature-induced magnetic anisotropy resulting both from exchange and material growth. Depending on both the geometry of the tube and the strength of the azimuthal anisotropy, Bloch or Néel walls arise at rest, resulting in two regimes of motion largely dominated by either spin-transfer torques or the field. We determine the Walker breakdown current in all cases, and highlight the most suitable parameters to achieve high domain wall speed.

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.

Cylindrical nanowires made of soft magnetic materials, in contrast to thin strips, may host domain walls of two distinct topologies. Unexpectedly, we evidence experimentally the dynamic transformation of topology upon wall motion above a field threshold. Micromagnetic simulations highlight the underlying precessional dynamics for one way of the transformation, involving the nucleation of a Bloch-point singularity, however, fail to reproduce the reverse process. This rare discrepancy between micromagnetic simulations and experiments raises fascinating questions in material and computer science.

While the usual approach to tailor the behavior of condensed matter and nanosized systems is the choice of material or finite-size or interfacial effects, topology alone may be the key. In the context of the motion of magnetic domain walls (DWs), known to suffer from dynamic instabilities with low mobilities, we report unprecedented velocities >600  m/s for DWs driven by spin-transfer torques in cylindrical nanowires made of a standard ferromagnetic material. The reason is the robust stabilization of a DW type with a specific topology by the Œrsted field associated with the current. This opens the route to the realization of predicted new physics, such as the strong coupling of DWs with spin waves above >600  m/s.

We report the imaging of magnetic domains in ferromagnetic CoNiB nanotubes with very long aspect ratio, fabricated by electroless plating. While axial magnetization is expected for long tubes made of soft magnetic materials, we evidence series of azimuthal domains. We tentatively explain these by the interplay of anisotropic strain and/or grain size, with magneto-elasticity and/or anisotropic interfacial magnetic anisotropy. This material could be interesting for dense data storage, as well as curvature-induced magnetic phenomena such as the non-reciprocity of spin-wave propagation.

We present here a quantitative analysis of the ground state and magnetic properties of Ce3Pt23Si11, based on a crystalline electric field description within the mean-field approximation. In this face-centered cubic compound, the point group symmetry at the Ce site is orthorhombic. One main difficulty in this low symmetry case is that the CEF potential for Ce3+ ions is determined by five independent parameters, while only two magnetic excitations are observed by inelastic neutron scattering. Moreover the anisotropy of the magnetic susceptibility of the Ce ion, that permits an independent determination of the second-order CEF parameters is hidden by the cubic symmetry of the compound. A specific procedure is developed for this purpose that combines genetic algorithms and more conventional optimization methods. A set of CEF parameters is found that best reproduces the different experimental observations in both the paramagnetic and ferromagnetic phases of Ce3Pt23Si11. The analysis accounts for two seemingly contradictory properties: a strong local anisotropy that aligns the moment along a fourfold axis and a rather weak anisotropy of the bulk magnetization with an easy threefold magnetization axis. Ce3Pt23Si11 is shown to be a model system where single site anisotropies compete within a crystal structure of overall high symmetry.