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.

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.

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

Frequency modulation experiments were performed on a spin torque vortex oscillator for a wide range of modulation frequency, up to 10 % of the oscillator frequency. A thorough analysis of the intermodulation products shows that the key parameter that describes these experiments is the deviation sensitivity, which is the dynamical frequency-current dependence. It differs significantly from the oscillator tunability discussed so far in the context of spin-transfer oscillators. The essential difference between these two concepts is related to the response time of the vortex oscillator, driven either in quasi-steady state or in a transient regime., Comment: to be published in Physical Review B (in press)

Radiofrequency vortex spin-transfer oscillators based on magnetic tunnel junctions with very low resistance area product were investigated. A high power of excitations has been obtained characterized by a power spectral density containing a very sharp peak at the fundamental frequency and a series of harmonics. The observed behaviour is ascribed to the combined effect of spin transfer torque and Oersted-Amp\`ere field generated by the large applied dc-current. We furthermore show that the synchronization of a vortex oscillation by applying a ac bias current is mostly efficient when the external frequency is twice the oscillator fundamental frequency. This result is interpreted in terms of a parametric oscillator., Comment: 4 pages, 4 figures

Magnetization reversal in magnetic particles is one of the fundamental issues in magnetic data storage. Technological improvements require the understanding of dynamical magnetization reversal processes at nanosecond time scales. New strategies are needed to overcome current limitations. For example, the problem of thermal stability of the magnetization state (superparamagnetic limit) can be pushed down to smaller particle sizes by increasing the magnetic anisotropy. High fields are then needed to reverse the magnetization that are difficult to achieve in current devices. Here we propose a new method to overcome this limitation. A constant applied field, well below the switching field, combined with a radio-frequency (RF) field pulse can reverse the magnetization of a nanoparticle. The efficiency of this method is demonstrated on a 20 nm cobalt particle by using the micro-SQUID technique. Other applications of this method might be nucleation or depinning of domain walls., Comment: 11 pages, 5 figures

The low temperature spin dynamics of a Fe8 Single-Molecule Magnet was studied under circularly polarized electromagnetic radiation allowing us to establish clearly photon-assisted tunneling. This effect, while linear at low power, becomes highly non-linear above a relatively low power threshold. This non-linearity is attributed to the nature of the coupling of the sample to the thermostat.These results are of great importance if such systems are to be used as quantum computers., Comment: 4 pages, 4 figures

We present a fabrication method of superconducting quantum interference devices (SQUIDs) based on direct write lithography with an Atomic Force Microscope (AFM). This technique involves maskless local anodization of Nb or NbN ultrathin films using the voltage biased tip of the AFM. The SQUIDs are of weak-link type, for which two geometries have been tested: Dayem and variable thickness nanobridges. The magnetic field dependence of the maximum supercurrent Ic(flux) in resulting SQUIDs is thoroughly measured for different weak link geometries and for both tested materials. It is found that the modulation shape and depth of Ic(flux) curves are greatly dependent on the weak link size. We analyze the results taking into account the kinetic inductance of nanobridges and using the Likharev-Yakobson model. Finally we show that the present resolution reached by this technique (20nm) enables us to fabricate Nb weak-links which behavior approaches those of ideal Josephson junctions., Comment: 22 pages, 8 figures

We present a method for fabricating Josephson junctions and superconducting quantum interference devices (SQUIDs) which is based on the local anodization of niobium strip lines 3 to 6.5 nm-thick under the voltage-biased tip of an Atomic Force Microscope. Microbridge junctions and SQUID loops are obtained either by partial or total oxidation of the niobium layer. Two types of weak link geometries are fabricated : lateral constriction (Dayem bridges) and variable thickness bridges. SQUIDs based on both geometries show a modulation of the maximum Josephson current with a magnetic flux periodic with respect to the superconducting flux quantum h/2e. They persist up to 4K. The modulation shape and depth for SQUIDs based on variable thickness bridges indicate that the weak link size becomes comparable to the superconducting film coherence length which is of the order of 10nm., Comment: 12 pages

An improved micro-SQUID technique is presented allowing us to measure the temperature dependence of the magnetisation switching fields of single nanoparticles well above the critical superconducting temperature of the SQUID. Our first measurements on 3 nm cobalt nanoparticle embedded in a niobium matrix are compared to the Neel Brown model describing the magnetisation reversal by thermal activation over a single anisotropy barrier., Comment: 3 pages, 4 figures; conference proceeding: 1st Joint European Magnetic Symposia (JEMS'01), Grenoble (France), 28th August - 1st September, 2001

The combination of high sensitive superconducting quantum interference device (SQUID) with high quality nanoparticles allowed to check the simplest classical model describing the magnetisation reversal by uniform rotation which were proposed more than 50 years ago by Neel, Stoner and Wohlfarth. The micrometer sized SQUIDs were elaborated by electron beam lithography and the nanoparticles were synthesised by arc-discharge. The measured angular dependence of switching fields of nearly all f.c.c. Co nanoparticles revealed a dominating uniaxial magnetic anisotropy. This result suggests that twin boundaries and stacking faults strongly alter the cubic magnetocrystalline anisotropy leading to dominating uniaxial anisotropy. However, few particles were sufficiently "perfect" in order to show a more complex switching field surface and a field path dependence of the switching field which is the important signature of the cubic magnetocrystalline anisotropy., Comment: 9 pages, 10 figures; conference proceeding: 1st Joint European Magnetic Symposia (JEMS'01), Grenoble (France), 28th August - 1st September, 2001

Using a new microSQUID set-up, we investigate magnetic anisotropy in a single 1000-atoms cobalt cluster. This system opens new fields in the characterization and the understanding of the origin of magnetic anisotropy in such nanoparticles. For this purpose, we report three-dimensional switching field measurements performed on a 3 nm cobalt cluster embedded in a niobium matrix. We are able to separate the different magnetic anisotropy contributions and evidence the dominating role of the cluster surface., Comment: 4 pages, 8 figures