Recent studies in three dimensional spintronics propose that the Œrsted 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 Œrsted field pulses. We observe the tilting of longitudinally magnetized domains towards the azimuthal Œrsted 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.
Magnetic cylindrical nanowires are very fascinating objects where the curved geometry allows many novel magnetic effects and a variety of non-trivial magnetic structures. Micromagnetic modelling plays an important role in revealing the magnetization distribution in magnetic nanowires, often not accessible by imaging methods with sufficient details. Here we review the magnetic properties of the shape anisotropy-dominated nanowires and the nanowires with competing shape and magnetocrystalline anisotropies, as revealed by micromagnetic modelling. We discuss the variety of magnetic walls and magne…
Understanding the domain wall dynamics is an important issue in modern magnetism. Here we present results of domain wall displacement in curved cylindrical nanowires at a constant magnetic field. We show that the average velocity of a transverse domain wall increases with curvature. Contrary to what it is observed in stripes, in a curved wire the transverse domain wall oscillates along and rotates around the nanowire with the same frequency. These results open the possibility of new oscillation-based applications.
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 l…
We discuss the robustness of Majorana edge modes in a finite quantum nanowire of cylindrical shape. The nanowire is modeled as a bidimensional cylindrical shell of semiconductor material with proximity-induced superconductivity and an intrinsic Rashba spin-orbit interaction. The latter is characterized by effective electric and magnetic fields in transverse direction of the nanowire. An applied external magnetic field pointing in an arbitrary orientation is also assumed. The numerical diagonalization of the Hamiltonian allows us to study the spectrum of the nanowire for different experimental …
The recent advances in nanowire (NW) growth technology have made possible the growth of more complex structures such as core-multi-shell (CMS) NWs. We propose the approach for calculation of electron subbands in cylindrical CMS NWs within the simple effective mass approximation. Numerical results are presented for ${\rm GaAs/Al_{0.3}Ga_{0.7}As}$ radial heterostructure with AlGaAs-core and 4 alternate GaAs and AlGaAs shells. The influence of an effective mass difference in heterolayers is discussed.
We model the exchange bias effect in thin cylindrical nanowires composed of a ferromagnetic core and an antiferromagnetic shell implementing a classical spin Hamiltonian and Monte Carlo simulations. We address systematically the effect of shell polycrystallinity on the characteristic fields of the isothermal hysteresis loop (coercivity, exchange-bias) and their angular dependence upon the direction of the applied / cooling field. We relate the observed trends to modifications of the underlying magnetization reversal mechanism. We fit our simulation results to an extended Stoner-Wohlfarth model…
Cylindrical magnetic nanowires are promising systems for the development of three-dimensional spintronic devices. Here, we simulate the evolution of magnetic states during fabrication of strongly-coupled cylindrical nanowires with varying degrees of overlap. By varying the separation between wires, the relative strength of exchange and magnetostatic coupling can be tuned. Hence leading to the formation of six fundamental states as a function of both inter-wire separation and wire height. In particular, two complex three-dimensional magnetic states, a 3D Landau Pattern and a Helical Domain wall…
Achieving high velocities of magnetic domain walls is a crucial factor for their use as information carriers in modern nanoelectronic applications. In nanomagnetism and spintronics, these velocities are often limited either by internal domain wall instabilities, known as the Walker breakdown phenomenon, or by spin wave emission, known as the magnonic regime. In the rigid domain wall model, the maximum magnon velocity acts as an effective "speed of light", providing a relativistic analogy for the domain wall speed limitation. Cylindrical magnetic nanowires are an example of systems with the abs…
We study the current-driven domain wall (DW) motion in cylindrical nanowires using micromagnetic simulations by implementing the Landau-Lifshitz-Gilbert equation with nonlocal spin-transfer torque in a finite difference micromagnetic package. We find that in the presence of DW Gaussian wave packets (spin waves) will be generated when the charge current is applied to the system suddenly. And this effect is excluded when using the local spin-transfer torque. The existence of spin waves emission indicates that transverse domain walls can not move arbitrarily fast in cylindrical nanowires although…
This brief proposes an analytical approach to model the dc electrical behavior of extremely narrow cylindrical junctionless nanowire field-effect transistor (JLNW-FET). The model includes explicit expressions, taking into account the first-order perturbation theory for calculating eigenstates and corresponding wave functions obtained by the Schrodinger equation in the cylindrical coordinate. Assessment of the proposed model with technology computer-aided design (TCAD) simulations and measurement results confirms its validity for all regions of operation. This represents an essential step towar…
Magnetic nanowires (NW) are promising candidates for heat generation under AC-field application due to their large shape anisotropy. They may be used for catalysis, hyperthermia or water purification treatments. In the present work we theoretically evaluate the heat dissipated by a single magnetic nanowire, originated from the domain wall dynamics under the action of an AC-field. We compare the Permalloy NWs (which demagnetize via the transverse wall propagation) with the Co fcc NWs whose reversal mode is via a vortex domain wall. The average hysteresis loop areas -which are proportional to th…
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~$Δ_\mathrm{mod}$, larg…
We report that the irreversible magnetization switching process in ferromagnetic nanoparticles is governed by the formation and dynamics of topological point-defects in the form of hedgehog-antihedgehog pairs. After nucleation, these pairs rapidly separate with speeds exceeding domain wall velocities, and they generate an emergent electric field of solenoidal character and substantial magnitude.
We present a theoretical study of a nanowire made of a three-dimensional topological insulator. The bulk topological insulator is described by a continuum-model Hamiltonian, and the cylindrical-nanowire geometry is modelled by a hard-wall boundary condition. We provide the secular equation for the eigenergies of the systems (both for bulk and surface states) and the analytical form of the energy eigenfunctions. We describe how the surface states of the cylinder are modified by finite-size effects. In particular, we provide a $1/R$ expansion for the energy of the surface states up to second ord…
Nanoscale magnetic systems have been studied extensively in various geometries, such as wires of different cross-sections, arrays of wires, dots, rings, etc. Such systems have interesting physical properties and promising applications in advanced magnetic devices. Uniform magnetic nanowires are the basic structures which were broadly investigated. However, some of their dynamical properties, like: (anti)crossing between the spin wave modes and impact of the magnetic field on spin wave spectrum, still need to be exploited. We continue this research by investigation of the spin wave dynamics in …
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 …
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.
Ordered ferromagnetic nanowire arrays are widely studied due to the diversity of possible applications. However, there is still no complete understanding of the relation between the array's parameters and its magnetic behavior. The effect of vortex states on the magnetization reversal of large-diameter nanowires is of particular interest. Here, we compare analytical and micromagnetic models with experimental results for three arrays of iron nanowires with diameters of 33, 52 and 70 nm in order to find the balance between the number of approximations and resources used for the calculations. The…
Interactions between pairs of magnetic domain walls (DW) and pinning by radial constrictions were studied in cylindrical nanowires with surface roughness. It was found that a radial constriction creates a symmetric pinning potential well, with a change of slope when the DW is situated outside the notch. Surface deformation induces an asymmetry in the pinning potential as well as dynamical pinning. The depinning fields of the domain walls were found generally to decrease with increasing surface roughness. A DW pinned at a radial constriction creates a pinning potential well for a free DW in a p…
A next-generation memory device utilizing a three-dimensional nanowire system requires the reliable control of domain wall motion. In this letter, domain walls are studied in cylindrical nanowires consisting of alternating segments of cobalt and nickel. The material interfaces acting as domain wall pinning sites, are utilized in combination with current pulses, to control the position of the domain wall, which is monitored using magnetoresistance measurements. Magnetic force microscopy results further confirm the occurrence of current assisted domain wall depinning. Data bits are therefore shi…
We investigate the effect of curvature on the energy and stability of domain wall configurations in curved cylindrical nanotubes and nanowires. We use micromagnetic simulations to calculate the phase diagram for the transverse wall (TW) and vortex wall (VW) states in tubes, finding the ground state configuration and the metastability region where both types of walls can exist. The introduction of curvature shifts the range for which the TW is the ground state domain wall to higher diameters, and increases the range of metastability. We interpret this behavior to be primarily due to the curvatu…
Spin torque from spin current applied to a nanoscale region of a ferromagnet can act as negative magnetic damping and thereby excite self-oscillations of its magnetization. In contrast, spin torque uniformly applied to the magnetization of an extended ferromagnetic film does not generate self-oscillatory magnetic dynamics but leads to reduction of the saturation magnetization. Here we report studies of the effect of spin torque on a system of intermediate dimensionality - a ferromagnetic nanowire. We observe coherent self-oscillations of magnetization in a ferromagnetic nanowire serving as the…
The period of magnetization oscillations that occur near the surface of a nanotube or nanowire under the influence of surface magnetic anisotropy is determined by means of numerical simulation as a function of nanowire geometry and material parameters. The hopping mode is observed for stationary movement of a head-to-head domain wall along nanowire axis in applied magnetic field. The average speed of the domain wall in the hopping mode is found to be several times less than the stationary velocity of the wall in the absence of surface anisotropy.
The low-energy effective Hamiltonian of the strong `spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire in the presence of a strong magnetic field is studied both numerically and analytically. Basing on the Luttinger-Kohn Hamiltonian in the spherical approximation, we show this strong `spin'-orbit coupled one-dimensional hole gas can be accurately described by an effective two-band Hamiltonian $H^{\rm ef}=\hbar^{2}k^{2}_{z}/(2m^{*}_{h})+ασ^{x}k_{z}+g^{*}_{h}μ_{B}Bσ^{z}/2$, as long as the magnetic field is purely longitudinal or purely transverse. The explicit magnetic fie…
Diameter-modulated nanowires offer an important paradigm to design the magnetization response of 3D magnetic nanostructures by engineering the domain wall pinning. With the aim to understand its nature and to control the process, we analyze the magnetization response in FeCo modulated polycrystalline two-segment nanowires varying the minor diameter. Our modelling indicates a very complex behavior with a strong dependence on the disorder distribution and an important role of topologically non-trivial magnetization structures. We demonstrate that modulated nanowires with a small diameter differe…
We propose a method to control surface phonon transport by weak magnetic fields based on the pumping of surface acoustic waves (SAWs) by magnetostriction. We predict that the magnetization dynamics of a nanowire on top of a dielectric films injects SAWs with opposite angular momenta into opposite directions. Two parallel nanowires form a phononic cavity that at magnetic resonances pump a unidirectional SAW current into half of the substrate.
The pinning effect of the periodic diameter modulations on the domain wall propagation in FeCoCu individual nanowires is determined by Magnetic Force Microscopy, MFM. A main bistable magnetic configuration is firstly concluded from MFM images characterized by the spin reversal between two nearly single domain states with opposite axial magnetization. Complementary micromagnetic simulations confirm a vortex mediated magnetization reversal process. A refined MFM imaging procedure under variable applied field allows us to observe metastable magnetic states where the propagating domain wall is pin…
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 compu…
Magnetization reversal mechanism of double-helix nanowires probed by dark-field magneto-optical Kerr effect
TU Wien（维也纳工业大学）；University of Loughborough（拉夫堡大学）；Instituto de Nanociencia y Materiales de Aragón, CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所，西班牙科学理事会-萨拉戈萨大学）；Synchrotron SOLEIL（SOLEIL同步辐射中心）；University of Vienna（维也纳大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Hiroshima University（广岛大学）
Detailed understanding of spin dynamics in magnetic nanomaterials is necessary for developing ultrafast, low-energy and high-density spintronic logic and memory. Here, we develop micromagnetic models and analytical solutions to elucidate the effect of increasing damping and uniaxial anisotropy on magnetic field pulse-assisted switching time, energy and field requirements of nanowires with perpendicular magnetic anisotropy and yttrium iron garnet-like spin transport properties. A nanowire is initially magnetized using an external magnetic field pulse (write) and self-relaxation. Next, magnetic …
We have studied both experimentally and theoretically the reprogrammable spin wave band structure in Permalloy(10nm)/Cu(5nm)/Permalloy(30nm) nanowire arrays of width w=280 nm and inter-wire separation in the range from 80 to 280 nm. We found that, depending on the inter-wire separation, the anti-parallel configuration, where the magnetizations of the two Permalloy layers point in opposite directions, is stabilized over specific magnetic field ranges thus enabling us to directly compare the band structure with that of the parallel alignment. We show that collective spin waves of the Bloch type …
