Understanding magnetization dynamics in nanosized systems is a key condition not only to realize innovative new applications, but also to further expand our comprehension of the underlying fundamental physics. Only recently has it been possible to image magnetic objects such as domain walls (DWs) with high temporal and spatial resolution and versatile environments or excitations, using, for example time resolved x-ray magnetic circular dichroism with scanning transmission x-ray microscopy (XMCD STXM). Continuous developments of this technique have allowed for a shift of interest from simple systems such as flat nanostrips, that lend themselves more readily to magnetic imaging, to more intricate systems such as three dimensional nanostructures, with added complexity from the volume [1,2]. A textbook case for such an investigation is provided by cylindrical magnetic nanowires (NWs) featuring a novel type of DW, the Bloch-point wall (BPW) [3] which exhibits azimuthal curling of magnetic moments around a Bloch-point on the NW axis. The dynamics of these walls stand out compared to DWs in flat nanostrips due to fascinating theoretical predictions of fast, stable speeds and the controlled emission of spin waves [4]. Recent experiments in NWs indicate that the Œrsted field induced by nanosecond pulses of current plays a key role in stabilising walls exclusively of the BPW type and further switches the azimuthal circulation to be parallel to the field [5]. This allows controlling the wall structure and enables fast DW motion with speeds &gt; 600 m/s and an absence of Walker breakdown. The importance of the Œrsted field in NWs was further studied with simulations to determine a strong radial dependence, scaling as one-over radius cubed, and a complex mechanism of the BPW switching process, involving nucleation and annihilation of pairs of Bloch-points [6]. In the case of longitudinally magnetised domains, the peripheral magnetic moments also tend to align with the Œrsted field with the degree of tilt related to a competition between magnetic exchange and Zeeman energy. It is clear that the Œrsted field has a major influence on magnetization dynamics in NWs, yet few predictions have been confirmed experimentally due to the complexity of such experiments. Further, without time resolved measurements, no quantitative comparisons of eg. tilt angles in magnetization may be made with the simulations. Verifications of these effects are therefore strongly required in order to control the system and employ it in possible future applications. Here, we make use of time resolved XMCD STXM to image the magnetization dynamics in NWs subjected to nanosecond pulses of electrical current. Time resolved images were acquired with a temporal resolution of 200 ps, to image the effect of positive and negative polarity 3 ns duration voltage pulses of chosen amplitude applied to magnetically soft Co30Ni70 NWs with diameters 93, 97 and 101 nm. We first observed the tilting of magnetization towards the applied Œrsted field direction in longitudinally magnetized domains (Fig. 1a) and created a model based on the absorptivity of x-rays and a description of the magnetization in a NW cross section to accurately reproduce the observed magnetic contrast and extract quantitative information. We find that the degree of tilt on the surface of these NW samples is of the order of 18±8° per 1012 A/m2 applied (Fig. 1b), which is in agreement with theoretical predictions from ref. [6]. We then observe the expansion (Fig. 2b,d) and compression (Fig. 2a,c) of the BPW width due to the application of a parallel and antiparallel Œrsted field, respectively. This effect, previously predicted by simulations, occurs when the applied current density is insufficiently strong to induce the BPW circulation switching. The magnetic contrast of the phenomenon is again reproduced with our simple model giving quantitative information about this “breathing” of the BPW. We expect that this work lays the foundation for and provides an incentive to further studying complex magnetisation dynamics in NWs. With increased control of the NW materials, the predicted ultrafast DW motion and associated spin wave emissions [4] may be visualized using this technique. Further, the quantitative analysis provided herein shows the depth of information obtainable with time resolved XMCD STXM and that a direct comparison of the observed dynamics to ie. simulations and theory is possible. This type of direct collaboration will significantly grow the understanding of three dimensional magnetic nanosized systems and enable better control over them.

**References:**

[1] C. Donnelly et al., Time-resolved imaging of three-dimensional nanoscale magnetization dynamics. Nat. Nanotech. 15 p.356-360 (2020) [2] A. Fernández-Pacheco et al., Three-dimensional nanomagnetism. Nat. Comm. 8 p.15756 (2017) [3] S. Da Col et al., Observation of Bloch-point domain walls in cylindrical magnetic nanowires. Phys. Rev. B. 89 p.180405 (2014) [4] R. Wieser et al., Current-driven domain wall motion in cylindrical nanowires. Phys. Rev. B. 82, p.1-7 (2010) [5] M. Schöbitz et al. Fast Domain Wall Motion Governed by Topology and Œrsted Fields in Cylindrical Magnetic Nanowires. Phys. Rev. Lett. 123 p.217201 (2019) [6] A. De Riz et al. Mechanism of current-assisted Bloch-point wall stabilization for ultra fast dynamics. arxiv: 2011.14869v1

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dad38862b68e88e07ac7345f1feba12e.jpg)
Figure 1: (a) Time resolved imaging of the tilting of magnetization in cylindrical NWs due to an applied Oersted field with white arrows indicating the direction of the Œrsted field. (b) Tilt angle calculated from the magnetic images for three different NW diameters and compared with theoretical predictions.

![](https://assets.underline.io/uploads/markdown_image/1/image/266b1bac51bb6fd30599e47d72aee2f6.jpg)
Figure 2: (a) Time resolved images of the compression (a) and expansion (b) of a Bloch-point DW in cylindrical NWs due to an applied Oersted field. Illustrations of the compressed (c) and expanded (d) DW from (a,b) with the Oersted field direction indicated.

 Time resolved imaging of Œrsted field induced magnetization dynamics in cylindrical magnetic nanowires

Current-driven domain wall dynamics in circular cross-section nanowires is a key phenomenon to be studied with a view to designing three-dimensional magnetic memory devices. The information stored in this type of device would be encoded by magnetic domains separated by magnetic domain walls. Two types of domain walls exist in magnetically soft cylindrical nanowires: the transverse-vortex wall (TVW) and the Bloch-point wall (BPW). The latter has a distinct topology and exhibits azimuthal curling of magnetic moments (also called circulation) around a Bloch point – a micromagnetic singularity. This micromagnetic object is expected to prevent the usual Walker breakdown, and thus enable high domain wall speed. The Walker breakdown is expected to not occur in the case of the Bloch-point wall, as it would require a too large energy of dipolar origin with a head-on magnetization configuration along all three directions. We showed recently [1] that the previously overlooked Oersted field associated with an electric current is a key in experiments to stabilize the BPW and reach speed above 600m/s with spin-transfer. Here we use micromagnetic simulations, analytical modeling and topological arguments to understand in detail and quantitatively the underlying phenomena, in particular the switching from negative to positive circulation of the BPW, with respect to the applied current [2]. The switching of the azimuthal circulation of the BPW to match that of the OEersted field occurs above a threshold current which we quantify as a function of geometry and material parameters. The key result is a 1/R3 dependence of the switching threshold, with R the wire radius, with the effect of the OErsted field becoming predominant for wire radius above typically 30nm. To the contrary, the speed of walls remains largely determined by spin-transfer alone, in a below-Walker regime. Thanks to a generalized micromagnetic scaling of lengths and densities of current, the present result can be applied to wires made of any magnetically soft material. We also highlight the complexity of BPW transformation involving the nucleation and/or annihilation of the topological objects at the surface (vortex/antivortex pairs) and in the volume (Bloch points) [Fig.1].

**References:**

[1] M. Schöbitz, A. de Riz, S. Martin et al., Phys. Rev. Lett. 123, 217201 (2019) [2] A. De Riz, J. Hurst, M. Schöbitz, C. Thirion, J. Bachmann, J. C. Toussaint, O. Fruchart, D. Gusakova, arXiv:2011.14869 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/639b0dd3d6b4627fa77ee50fcccf7ce4.jpg)
Figure 1: Snapshots illustrating the switching mechanism of BPW circulation in a permalloy wire under applied current. Top row: unrolled maps of radial magnetization, wire axis along z, periphery along φ. Bottom row: same surface maps of radial magnetization seen from inside of the wire as a 3D view. A, V and B labels highlight surface vortex and antivortex as well as Bloch point.

 Mechanism of current-assisted Bloch-point wall stabilization for ultra fast dynamics

Ferromagnetic one-dimensional conduits carry the promises of future high-density and low consumption memories as well as new logic gate paradigms. These systems are indeed ideal for domain walls propagation and spin waves generation, and have also been proposed as field sensor [1]. The emergence of curvilinear magnetism [2] came up with the possibility on dealing with tridimensional consideration of such 1D-conduits (being also of fundamental academic interest as new magnetic textures) : ferromagnetic nanotubes are merging on a single structure the micromagnetism consideration of domain walls and the multi-layered stack needed for spintronic (core-shell structures). Unexpectedly, but technologically ideal, an azimuthal curling of magnetization was initially observed in electroless Co-rich CoNi nanotubes [2], that we attributed to curvature-induced magneto-elastic anisotropy. We report here detailed magnetic and structural information to quantify the effect of anisotropy, and better identify its microscopic origin by analyzing different parameter of tube structure and chemistry as well as using new tools for tube magnetic investigation. CoNiB-based ferromagnetic nanotubes were fabricated by electroless plating in polycarbonate templates with diameters ranging from 160 to 450 nm, wall thicknesses from 20 to 65 nm, and several tens of μm in length. Following template dissolution and dispersion, nanotubes were either contacted using laser lithography for AMR (Anisotropic Magneto-Resistance) measurements, dispersed on suitable TEM (Transmission Electron Microscopy) grids or prepared by means of FIB (Focused Ion Beam) for cross-section analysis. Structural analysis revealed a relative homogeneity in critical parameters such as diameter and tube thickness along the whole object, with expected slight variations towards tubes extremities. We noticed a segregation of Nickel towards the tube surfaces that could be associated to an inhomogeneity of magnetic properties across the tube wall (radial direction) already observed in thin films [4]. This inhomogeneity would imply inverse-magnetostriction (magnetoelastic) related anisotropy, even in the case of an alloy with no expected magnetostriction nor magnetocristaline anisotropy from the nominal composition. Magneto-transport measurements were carried out at varying temperature, applied field magnitude and direction, and showed a material resistivity (at 300K ) below 200 µΩ.cm, still one order of magnitude higher than in the bulk. This has been related to the nanocrystalline nature of the tubes (induced by grain boundaries) and is considered with non curvilinear system (electrodeposited thin films) for magnetostriction investigation. From R(Bext) loops with a magnetic field applied along the tube axis, we confirmed the azimuthal magnetic curling at remanence, inferred the magnetization process and thereby extracted the anisotropy field of the order of Keff = 7.5 kJ.m-3. Such reversal has been then scrutinized through Electron Holography to locally map and quantify the magnetic flux (see Figure) during a magnetic loop. We extended these measurements to various tube parameters to propose a general picture of the curvature-induced anisotropy. These on-going experiments are of fundamental importance to infer for the capacities of such system to experimentally confirm high domain wall velocities (as wall as spin wave propagation) that could offer technological solution for racetrack memories.

**References:**

[1] M. Stano & O. Fruchart. Magnetic nanowires and nanotubes, Handbook of magnetic materials vol.27, Ed. Ekkes Brück,North Holland (2018). [2] Fernández-Pacheco, A. et al. Three-dimensional nanomagnetism. Nature Communications 8,15756 (2017). [3] Michal Stano et al. Flux-closure domains in high aspect ratio electroless-deposited CoNiB nanotubes. SciPost Physics 5, 38 (2018) [4] Hertel, R. Ultrafast domain wall dynamics in magnetic nanotubes and nanowires. Journal of Physics: Condensed Matter 28, 483002 (2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0f4c0e976dc0d77763c639f89b0fd9f3.jpg)
(Top Left) SEM view of a contacted Nanotube for magneto-transport measurements. Inset display an EDX spectra of the tube for Co/Ni composition. (Top right) Single tube hysteresis loop reconstructed from resistance measurement under applied field along the tube axis (two senses) and associated anisotropy field and saturated magnetization. (Bottom) Cosine of phase image obtained by Electron holography on a magnetized tube extremity: the black and withe lines display the magnetic flux. The phase profile (inset) enables to quantify the local saturated magnetization (phase derivative) knowing the sample thickness.

 Exploration of Magnetic Nanotubes as new spintronic building block

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Time resolved imaging of Œrsted field induced magnetization dynamics in cylindrical magnetic nanowires

Mechanism of current-assisted Bloch-point wall stabilization for ultra fast dynamics

Exploration of Magnetic Nanotubes as new spintronic building block

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