Ferromagnetic Nanostripes Research Articles

Remarkably enhanced current-driven 360\xb0 domain wall motion in nanostripe by tuning in-plane biaxial anisotropy

By micromagnetic simulations, we study the current-driven 360° domain wall (360DW) motion in ferromagnetic nanostripe with an in-plane biaxial anisotropy. We observe the critical annihilation current of 360° domain wall can be enhanced through such a type of anisotropy, the reason of which is the suppression of out-of-plane magnetic moments generated simultaneously with domain-wall motion. In details, We have found that the domain-wall width is only related to Ky − Kx, with Kx(y) the anisotropy constant in x(y) direction. Taking domain-wall width into consideration, a prior choice is to keep Ky ≈ Kx with large enough K. The mode of domain-wall motion has been investigated as well. The traveling-wave-motion region increases with K, while the average DW velocity is almost unchanged. Another noteworthy feature is that a Walker-breakdown-like motion exists before annihilation. In this region, though domain wall moves with an oscillating behavior, the average velocity does not reduce dramatically, but even rise again for a large K.

Theory of the Dzyaloshinskii domain-wall tilt in ferromagnetic nanostrips

We present an analytical theory of domain wall tilt due to a transverse in-plane magnetic field in a ferromagnetic nanostrip with out-of-plane anisotropy and Dzyaloshinskii-Moriya interaction (DMI). The theory treats the domain walls as one-dimensional objects with orientation-dependent energy, which interact with the sample edges. We show that under an applied field the domain wall remains straight, but tilts at an angle to the direction of the magnetic field that is proportional to the field strength for moderate fields and sufficiently strong DMI. Furthermore, we obtain a nonlinear dependence of the tilt angle on the applied field at weaker DMI. Our analytical results are corroborated by micromagnetic simulations.

Influence of the thermal contact resistance in current-induced domain wall depinning

In this work we study the influence of the thermal contact resistance on the temperature of a typical nanostripe used in current induced magnetic domain wall movement or depinning. The thermal contact resistance arises from an imperfect heat transport across the interface between the metallic ferromagnetic nanostripe and the substrate. We show that this parameter, which is likely non-zero in any experimental device, increases the temperature in the nanostripe considerably. When the current is injected in the nanostripe in nanosecond long pulses, the larger temperature also implies a reduction of the effective current density delivered by the pulse generator. Both the thermal contact resistance and the dynamic response of the pulse generator are usually neglected in theoretical estimations of the influence of spin transfer torque on domain wall displacement and depinning. Here we show that only if the thermal contact resistance and the electric resistivity of the ferromagnetic nanostripe are optimized to the best values reported in the bibliography, the Joule heating may not be so crucial for current densities of the order of 108 A cm−2. Also, the use of physical constrictions (notch) to pin the magnetic domain wall may complicate the interpretation of the results as they always come together with relevant thermal gradients.

Nuclear Resonant Surface Diffraction of Synchrotron Radiation.

Nuclear resonant x-ray diffraction in grazing incidence geometry is used to determine the lateral magnetic configuration in a one-dimensional lattice of ferromagnetic nanostripes. During magnetic reversal, strong nuclear superstructure diffraction peaks appear in addition to the electronic ones due to an antiferromagnetic order in the nanostripe lattice. We show that the analysis of the angular distribution together with the time dependence of the resonantly diffracted x rays reveals surface spin structures with very high sensitivity. This scattering technique provides unique access to laterally correlated spin configurations in magnetically ordered nanostructures and, in perspective, also to their dynamics.

Suhl instabilities for spin waves in ferromagnetic nanostripes and ultrathin films

A microscopic (or Hamiltonian-based) theory is employed for the spin-wave instability thresholds of nonlinear processes in ultrathin ferromagnetic stripes and films under perpendicular pumping with an intense microwave field. The spatially-quantized linear spin waves in these nanostructures may participate in parametric processes through the three-magnon interactions (the first-order Suhl process) and the four-magnon interactions (the second-order Suhl process) when pumped. By contrast with most previous studies of spin-wave instabilities made for larger samples, where macroscopic (or continuum) theories involving Maxwell's equations for magnetic dipolar effects are used, a discrete lattice of effective spins is employed. Then a dipole-exchange spin Hamiltonian is employed to investigate the behavior of the quantized spin waves under perpendicular pumping, when modifications due to the more extensive spatial confinement and edges effects in these nanostructures become pronounced. The instability thresholds versus applied magnetic field are calculated, with emphasis on the size effects and geometries of the nanostructures and on the different relative strengths of the magnetic dipole-dipole and exchange interactions in materials. Numerical results are presented using parameters for Permalloy, YIG, and EuS.

Mechanically driven domain wall movement in magnetoelastic nanomagnets

Magnetic domain walls are fundamental objects arising in ferromagnetic materials, largely investigated both through micromagnetic simulations and experiments. While current- and field-based techniques for inducing domain wall propagation have been widely studied for fundamental understanding and application-oriented purposes, the possibility to manipulate domain walls using mechanical stress in magnetoelastic materials has only recently drawn interest. Here, a complete analytical model describing stress-induced transverse domain wall movement in ferromagnetic nanostripe with variable cross-section is presented. This approach yields a nonlinear integro-differential equation describing the magnetization field. Its numerical implementation, based on the nonlinear relaxation method, demonstrates the possibility to precisely control the position of a domain wall through mechanical action.

A Methodology to Design Spin-Wave-Based Logic Gates in a Single Ferromagnetic Nanostripe Using Spin-Transfer Torque Effects

We present a methodology design of spin-wave-based multi-input logic gates by applying a local spin-polarized current on a single ferromagnetic stripe. Micromagnetic simulation shows that the phase of propagating spin waves in a single ferromagnetic nanostripe can be shifted by $\pi $ /5 without decreasing its amplitude when they pass through an area with nonlinear internal field. The methodology adopting spin-transfer torque effects to fulfill spin-wave-based multi-input logic gates is demonstrated in a single ferromagnetic waveguide. The structure of designed logic gates can be simplified significantly compared with the prototype Mach–Zehnder-type interferometer type gates.

Stress-mediated magnetoelectric control of ferromagnetic domain wall position in multiferroic heterostructures

The motion of a ferromagnetic domain wall in nanodevices is usually induced by means of external magnetic fields or polarized currents. Here, we demonstrate the possibility to reversibly control the position of a Néel domain wall in a ferromagnetic nanostripe through a uniform mechanical stress. The latter is generated by an electro-active substrate combined with the nanostripe in a multiferroic heterostructure. We develop a model describing the magnetization distribution in the ferromagnetic material, properly taking into account the magnetoelectric coupling. Through its numerical implementation, we obtain the relationship between the electric field applied to the piezoelectric substrate and the position of the magnetic domain wall in the nanostripe. As an example, we analyze a structure composed of a PMN-PT substrate and a TbCo2/FeCo composite nanostripe.

Impact of current on static and kinetic depinning fields of domain wall in ferromagnetic nanostrip

The impact of current on static and kinetic depinning fields of a domain wall in a one- dimensional ferromagnetic nanostrip is investigated analytically and numerically by solving the Landau–Lifshitz–Gilbert equation with adiabatic and non-adiabatic spin-transfer torques. The results show that in the absence of current, the static depinning field is greater than the kinetic depinning field. Both the depinning fields decrease by increasing the current applied in a direction opposite to the direction of the applied field. Both the depinning fields can also be tuned by the current to make them equal.

Joule heating in ferromagnetic nanostripes with a notch

The temperature in a ferromagnetic nanostripe with a notch subject to Joule heating has been studied in detail. We first performed an experimental real-time calibration of the temperature versus time as a 100 ns current pulse was injected into a Permalloy nanostripe. This calibration was repeated for different pulse amplitudes and stripe dimensions and the set of experimental curves were fitted with a computer simulation using the Fourier thermal conduction equation. The best fit of these experimental curves was obtained by including the temperature-dependent behavior of the electrical resistivity of the Permalloy and of the thermal conductivity of the substrate $(\mathrm{Si}{\mathrm{O}}_{2})$. Notably, a nonzero interface thermal resistance between the metallic nanostripe and the substrate was also necessary to fit the experimental curves. We found this parameter pivotal to understand our results and the results from previous works. The higher current density in the notch, together with the interface thermal resistance, allows a considerable increase of the temperature in the notch, creating a large horizontal thermal gradient. This gradient, together with the high temperature in the notch and the larger current density close to the edges of the notch, can be very influential in experiments studying the current assisted domain wall motion.

Spin wave free spectrum and magnetic field gradient of nanopatterned planes of ferromagnetic cobalt nanoparticles: key properties for magnetic resonance based quantum computing

We present a study by ferromagnetic resonance at microwave Q band of two sheets of cobalt nanoparticles obtained by annealing SiO2 layers implanted with cobalt ions. This ex- perimental study is performed as a function of the applied magnetic field orientation, tempera- ture, and dose of implanted cobalt ions. We demonstrate that each of those magnetic sheet of cobalt nanoparticles can be well modelled by a nearly two dimensional ferromagnetic sheet hav- ing a reduced effective saturation magnetization, compared to a regular thin film of cobalt. The nanoparticles are found superparamagnetic above around 210 K and ferromagnetic below this blocking temperature. Magnetostatic calculations show that a strong magnetic field gradient of around 0.1 G/nm could be produced by a ferromagnetic nanostripe patterned in such magnetic sheet of cobalt nanoparticles. Such a strong magnetic field gradient combined with electron para- magnetic resonance may be relevant for implementing an intermediate scale quantum computer based on arrays of coupled electron spins, as previously reported (Eur. Phys. J. B (2014) 87, 183). However, this new approach only works if no additional spin decoherence is introduced by the spin waves exitations of the ferromagnetic nanostructure. We thus suggest theoretically some possible magnetic anisotropy engineering of cobalt nanoparticles that could allow to suppress the spin qubit decoherence induced by the unwanted collective excitation of their spins.

All-optical investigation of tunable picosecond magnetization dynamics in ferromagnetic nanostripes with a width down to 50 nm.

Ferromagnetic nanostripes are important elements for a number of interesting technologies including magnetic racetrack memory, spin logic and magnonics. Understanding and controlling magnetization dynamics in such nanostripes are hence important problems in nanoscience and technology. Here we present an all-optical excitation and detection of ultrafast magnetization dynamics, including spin waves, in 5 μm long Ni80Fe20 nanostripes with varying stripe widths from 200 nm down to 50 nm. We observed a strong width dependent variation in the frequency, anisotropy and the spatial nature of spin waves in these systems. The effect of inter-stripe interaction is also studied and the 50 nm wide stripe is found to be nearly magnetostatically isolated, allowing us to detect the dynamics of a 50 nm wide individual stripe using an all-optical measurement technique. The tunability in magnetization dynamics with stripe widths is important for their applications in various spin based technologies.

Domain Walls in Nanostripes of Cubic-Anisotropy Ferromagnetic Materials

We discuss the structure of the domain walls (DWs) in ferromagnetic nanostripes formed of cubic-anisotropy materials. Within certain approximations, such stationary textures are described by soliton solutions to the sine-Gordon equation in 2-D that is obtained with a constraint on the Landau-Lifshitz equation. Preferable stable and metastable types of the DWs (transverse DWs, vortex DWs, and others) are established with dependence on the stripe width and thickness using the micromagnetic simulations for a set of the so-called spintronic materials, which are of the current interest with regard to controlling the DW state. The simulated DW textures are classified on the basis of the stationary multisoliton states of the sine-Gordon model in 2-D.

Hybrid paramagnetic-ferromagnetic quantum computer design based on electron spin arrays and a ferromagnetic nanostripe

Electron spins placed in a magnetic field gradient, interacting by dipolar magnetic couplings and manipulated by microwave pulses represent a possible architecture for a quantum computer. Here, a general design for the practical implementation of such nanodevice is presented on the example of electron spins in silicon carbide placed nearby a permalloy ferromagnetic nanostripe. Firstly, the confined spin wave resonance spectrum of the nanostripe and the properties of its magnetic field gradient are calculated. Then, I show how to avoid microwave driven electron spin decoherence. Then, I show that at temperatures requiring only nitrogen gaz cooling, the silicon vacancy decoherence process due to ferromagnetic fluctuations is negligible compared to the one due to a two phonons Raman process, as long as the silicon vacancies spins are placed far enough from the ferromagnetic nanostripe. I then show that a nitrogen cooled hybrid quantum processor with 32 silicon vacancies spins qubits in SiC is theoretically possible. NV centers in diamond, N@C60 molecules, and radical molecules are three other good spin qubits candidates for implementing this hybrid quantum processor.

Microwave magnetic dynamics in highly conducting magnetic nanostructures

We performed low-noise broadband microstrip ferromagnetic resonance (FMR) measurements of the resonant modes of an array of metallic ferromagnetic nanostripes. In addition to a strong signal of the fundamental mode, we observed up to five weak-amplitude peaks in the field-resolved FMR traces, depending on the frequency. These higher-order absorption peaks have been theoretically identified as due to resonant excitation of odd and even standing spin waves across the direction of confinement in array plane (i.e., across the stripe width). The theory we developed suggests that the odd modes become excited in the spatially uniform microwave field of the FMR setup due to the large conductivity of metals. This promotes excitation of large-amplitude eddy currents in the sample by the incident microwave magnetic field and ultimately results in excitation of these modes. Following this theory, we found that the eddy current contribution is present only for patterned materials and when the microwave magnetic field is incident on one surface of sample surface, as it is in the case of a microstrip FMR.

Periodic magnetic structures generated by spin–polarized currents in nanostripes

The influence of a spin-polarized current on long ferromagnetic nanostripes is studied numerically. The current flows perpendicularly to the stripe. The study is based on the Landau-Lifshitz phenomenological equation with the Slonczewski-Berger spin-torque term. The magnetization behavior is analyzed for all range of the applied currents, up to the saturation. It is shown that the saturation current is a nonmonotonic function of the stripe width. For a stripe width increasing it approaches the saturation value for an infinite film. A number of stable periodic magnetization structures are observed below the saturation. Type of the periodical structure depends on the stripe width. Besides the one-dimensional domain structure, typical for narrow wires, and the two-dimensional vortex-antivortex lattice, typical for wide films, a number of intermediate structures are observed, e.g. cross-tie and diamond state. For narrow stripes an analytical analysis is provided.

High domain wall velocities via spin transfer torque using vertical current injection.

Domain walls, nanoscale transition regions separating oppositely oriented ferromagnetic domains, have significant promise for use in spintronic devices for data storage and memristive applications. The state of these devices is related to the wall position and thus rapid operation will require a controllable onset of domain wall motion and high speed wall displacement. These processes are traditionally driven by spin transfer torque due to lateral injection of spin polarized current through a ferromagnetic nanostrip. However, this geometry is often hampered by low maximum wall velocities and/or a need for prohibitively high current densities. Here, using time-resolved magnetotransport measurements, we show that vertical injection of spin currents through a magnetic tunnel junction can drive domain walls over hundreds of nanometers at ~500 m/s using current densities on the order of 6 MA/cm2. Moreover, these measurements provide information about the stochastic and deterministic aspects of current driven domain wall mediated switching.

Approach to writing-induced different types of spin vortex structure into ferromagnetic nanostripes

The control of different types of spin vortex structure in ferromagnetic nanostripes is studied by means of spin dynamics simulation. As for magnetocrystalline anisotropic nanostripe, the transformation between transverse wall and spin vortex can be realized by adjusting the strength of the uniaxial anisotropy. When nanostripe is isotropic or week anisotropic, the static magnetic structure favors spin vortex structure. Our results show that different types of spin vortex structure can be successfully induced by pinning the spins in the boundary of nanostripe. Interestingly, when the pinning is removed, the induced spin vortex structure can keep its stabilization. This approach may help to write digital information with determined spin vortex structure into ferromagnetic nanostripes. Moreover, the stability of spin vortex structure under external field is also investigated. It shows that spin vortex structure with pinned boundary spins is more stable than spin vortex in open boundary condition.

Influence of transverse fields on domain wall pinning in ferromagnetic nanostripes

We report an experimental study dealing with the influence of in-plane transverse fields on the domain wall (DW) pinning in ferromagnetic nanostripes. We analyzed the pinning probability and depinning fields for several fabrication induced pinning sites. For all measurements reported here, the depinning field decreases with increasing transverse field independently from the actual domain wall type and the shape of the pinning site. The pinning probability decreases with increasing transverse fields for weak pinning sites. Stronger pinning sites can be active for large field ranges and show a complex dependence of the pinning probability on the applied transverse field. The occurrence of different domain wall types as well as the influence of a transverse field on the domain wall dynamics can explain this behavior.

On the Travelling Wave Solution for the Current-Driven Steady Domain Wall Motion in Magnetic Nanostrips under the Influence of Rashba Field

Spin-orbit Rashba effect applies a torque on the magnetization of a ferromagnetic nanostrip in the case of structural inversion asymmetry, also affecting the steady domain wall motion induced by a spin-polarized current. This influence is here analytically studied in the framework of the extended Landau-Lifshitz-Gilbert equation, including the Rashba effect as an additive term of the effective field. Results of previous micromagnetic simulations and experiments have shown that this field yields an increased value of the Walker breakdown current together with an enlargement of the domain wall width. In order to analytically describe these results, the standard travelling wave ansatz for the steady domain wall motion is here adopted. Results of our investigations reveal the impossibility to reproduce, at the same time, the previous features and suggest the need of a more sophisticated model whose development requires, in turn, additional information to be extracted from ad hoc micromagnetic simulations.