Circular Nanopillars Research Articles

Dynamics of magnetic system formed by two semi-skyrmions in circular nano-pillars with a perpendicular anisotropy

Magnetic skyrmion has the advantages of stable topology and small volume. Many researchers choose different materials or build double free layers for using skyrmions in spin torque nano-oscillators capable of producing GHz frequencies. In this paper, the dynamics of the two semi-skyrmions in a circular nano-pillar with perpendicular magnetic anisotropy free layer and a spin polarizer are studied using micromagnetic simulation. The oscillation frequency of two semi-skyrmions is more than two times higher that of the single semi-skyrmion. In addition, we also explore the influences of different parameters (current density, damping coefficient, anisotropy constant, and temperature) on the motion of two semi-skyrmions. The results show that damping coefficient and exchange interaction constant have the most pronounced influence on the oscillation frequency of the system.

Cubic-Phase Metasurface for Three-Dimensional Optical Manipulation.

The optical tweezer is one of the important techniques for contactless manipulation in biological research to control the motion of tiny objects. For three-dimensional (3D) optical manipulation, shaped light beams have been widely used. Typically, spatial light modulators are used for shaping light fields. However, they suffer from bulky size, narrow operational bandwidth, and limitations of incident polarization states. Here, a cubic-phase dielectric metasurface, composed of GaN circular nanopillars, is designed and fabricated to generate a polarization-independent vertically accelerated two-dimensional (2D) Airy beam in the visible region. The distinctive propagation characteristics of a vertically accelerated 2D Airy beam, including non-diffraction, self-acceleration, and self-healing, are experimentally demonstrated. An optical manipulation system equipped with a cubic-phase metasurface is designed to perform 3D manipulation of microscale particles. Due to the high-intensity gradients and the reciprocal propagation trajectory of Airy beams, particles can be laterally shifted and guided along the axial direction. In addition, the performance of optical trapping is quantitatively evaluated by experimentally measured trapping stiffness. Our metasurface has great potential to shape light for compact systems in the field of physics and biological applications.

Spin torque nano-oscillators based on isolated edge skyrmions in nano-pillars with perpendicular anisotropy

The magnetic skyrmions have received a lot of attention because they have potential applications in spin torque nano-oscillators. In this paper, we numerically and analytically study the dynamics of edge skyrmions in circular nano-pillar oscillators with perpendicular magnetic anisotropy (PMA) free layer and spin polarizer. Numerical simulations demonstrate that a steady edge skyrmion oscillation mode with GHz frequency can be driven by spin currents and magnetic fields. The oscillation frequencies in circular nano-pillars with different radius are analytically derived, which agrees well with the numerical results. In addition, the steady oscillations of edge skyrmions are also observed in elliptical nano-pillars, in which the oscillation frequencies strongly depend on the eccentricity and perimeter of the elliptical nanopillar. It is found that the oscillation frequency of this edge skyrmion can range from 1 GHz to 6.7 GHz. The line width is about 55 MHz.

Double-layer metalens with a reduced meta-atom aspect ratio.

A dielectric metalens usually has a rather high meta-atom aspect ratio, causing difficulty in fabrication. In this Letter, we develop a kind of metalens constituting two different materials, which can lead to a much lower meta-atom aspect ratio for a full 0-2π phase modulation. The designed metalens is composed of double-layer circular nanopillars, and the pillars are constructed by a polycrystalline silicon layer and a titanium dioxide (TiO2) layer. The experimental results demonstrate that the required aspect ratio can be much smaller than that of a single material, and the metalens can realize a focusing spot close to the diffraction limit. Numerical simulations show that the double-layer metalens is also achromatic due to the different dispersion characteristics of the two materials as compared with its TiO2 only counterpart. Furthermore, it is polarization-independent with a focusing efficiency exceeding 22%.

Magnetic Skyrmion Spin‐Torque Nano‐Oscillators

The skyrmion oscillation frequency and steady orbit radius in ultrathin ferromagnetic layer of circular nanopillar are calculated in response to a spin‐polarized current. The analytical model of the rigid skyrmion motion is used. It is shown that the steady skyrmion oscillations with a frequency of about 1 GHz exist within finite range of the current. The case of the current perpendicular to the free layer plane and two types of the reference layer polarizations, uniform and vortex‐like, are considered. The first critical current can be very low in the case of zero difference between the skyrmion and vortex helicities. The second critical current is considered as a current of the skyrmion expelling from the free layer (dot). The oscillation frequency increases essentially with the current increasing. It is a function of the skyrmion equilibrium radius, dot radius, and the dot magnetic parameters.

Exchange stiffness in ultrathin perpendicularly magnetized CoFeB layers determined using the spectroscopy of electrically excited spin waves

We measure the frequencies of spin waves in nm-thick perpendicularly magnetized FeCoB systems, and model the frequencies to deduce the exchange stiffness of this material in the ultrathin limit. For this, we embody the layers in magnetic tunnel junctions patterned into circular nanopillars of diameters ranging from 100 to 300 nm, and we use magneto-resistance to determine which rf-current frequencies are efficient in populating the spin wave modes. Micromagnetic calculations indicate that the ultrathin nature of the layer and the large wave vectors used ensure that the spin wave frequencies are predominantly determined by the exchange stiffness, such that the number of modes in a given frequency window can be used to estimate the exchange stiffness. For 1 nm layers, the experimental data are consistent with an exchange stiffness A=20±2 pJ/m, which is slightly lower than its bulk counterpart. The thickness dependence of the exchange stiffness has strong implications for the numerous situations that involve ultrathin films hosting strong magnetization gradients, and the micromagnetic description thereof.

Impact of MgO Thickness on the Performance of Spin-Transfer Torque Nano-Oscillators

A magnetic tunnel junction (MTJ) stack incorporating an MgO wedge was deposited over a 200 mm wafer and nanofabricated into circular nanopillars with a diameter of 200 nm. Due to the variable MgO thickness, we could obtain MTJ nanopillars with resistance $\times $ area (RA) ranging from less than $1~\Omega \mu \text{m}^{2}$ up to $15~\Omega \mu \text{m}^{2}$ and tunnel magnetoresistance ratios up to $\sim 100$ %. It was observed that the ferromagnetic coupling ( $H_{F})$ displayed by the transfer curves increases for smaller values of RA. This variation is attributed to the orange-peel coupling, which is caused by the MgO roughness, with a larger impact for thinner barriers. The RF output of the nanopillars caused by the spin-transfer torque-induced magnetic precession of the free layer was measured as a function of bias current and external magnetic fields for nanopillars with different RA values. Results concerning typical devices in the thin MgO region ( $1.3~\Omega \mu \text{m}^{2})$ and in a thicker MgO region ( $2.7~\Omega \mu \text{m}^{2})$ are shown to illustrate the dependence found. It was observed that the higher output power ( $\sim 300$ nW) and the smaller linewidth ( $\sim 90$ MHz) could be obtained with the higher RA region. These results suggest that there must be an optimum RA value for the production of nano-oscillator devices, which depends on the tradeoffs between the need for large breakdown voltages and strong spin polarization of the bias current (favored for larger RA values) and between the need of endurance under large current densities (favored for smaller RA values). Provided the breakdown voltage of the MgO barrrier can be made large enough, nanopillars based on MTJ stacks with an intermediate RA can provide a solution for the production of large output power spin-transfer nano-oscillators.

Spin wave eigenmodes excited by spin transfer torque in circular nanopillars: influence of lateral size and Oersted field studied by micromagnetic simulations

Micromagnetic simulations are exploited to analyse the spectrum of low-amplitude dynamical modes excited by spin-transfer torque in the free layer of a cylindrical nanopillar, with either in-plane, out-of-plane or tilted magnetization. It is found that the frequency and the spatial character of the specific subset of excited eigenmodes appreciably depend on the pillar diameter (either 100 or 300 nm), as well as on the direction of the free-layer magnetization and the current polarization. Moreover, the spatial symmetry and the frequency of the excited modes are substantially influenced by the Oersted field generated by the injected current. These results demonstrate that a comprehension of the incipient dynamics of spin-torque oscillators, just above the current threshold for persistent precession, is only possible taking into account the influence of the Oersted field as well as the spatial inhomogeneity of the excited eigenmodes.

Robust fabrication and evaluation of nanopattern insert molded parts

Nanopatterning techniques have been developed for optical, magnetic, chemical, biological, and micro/nanoelectronic applications, where the verification of the nanopattern geometry is also critical for quality control of nanoengineered products. Nanopattern insert molding is a new method to produce nanopatterns on polymeric surface with high resolution, good productivity, and low cost. In this study, a disposable polymeric film, made of polyvinyl alcohol (PVA), was used as a stamp for replicating nanopatterns. In addition, a specialized image processing platform was proposed to characterize nanopattern structures, especially circular nanopillars with high accuracy and convenience. Such a tool was used for optimization of nanopattern processing conditions. The “shape dispersity index” was introduced to evaluate the replication quality in more systematic and robust manners.

Magnetization configurations of a tri-layer nanopillar ferromagnet/nonmagnetic spacer/ferromagnet

The equilibrium magnetization configurations of tri-layer circular nanopillar are calculated within micromagnetic approach. Nanopillar is assumed to be a vertical stack of ferromagnetic/nonmagnetic/ferromagnetic layers. The regions of geometrical parameters of nanopillar (radius and thickness), where the magnetic vortices and single domain states appear in the ground state, are calculated analytically and checked by micromagnetic simulations. The interlayer magnetostatic coupling affects essentially the formation of vortices or single domain states in both ferromagnetic layers. A considerable influence of the thicknesses of the ferromagnetic layers and spacer on the stability of vortex states is found. The results can be applied to interpret experiments on spin torque induced magnetization dynamics in nanopillars and tunnel junctions and also to estimate the nanopillar ground states.

Autonomous and forced dynamics in a spin-transfer nano-oscillator: Quantitative magnetic-resonance force microscopy

Using a magnetic-resonance force microscope (MRFM), the power emitted by a spin-transfer nano-oscillator consisting of a normally magnetized Py$|$Cu$|$Py circular nanopillar is measured both in the autonomous and forced regimes. From the power behavior in the subcritical region of the autonomous dynamics, one obtains a quantitative measurement of the threshold current and of the noise level. Their field dependence directly yields both the spin torque efficiency acting on the thin layer and the nature of the mode which first auto-oscillates: the lowest energy, spatially most uniform spin-wave mode. From the MRFM behavior in the forced dynamics, it is then demonstrated that in order to phase lock this auto-oscillating mode, the external source must have the same spatial symmetry as the mode profile, i.e., a uniform microwave field must be used rather than a microwave current flowing through the nanopillar.

Thermal activation in spin‐polarized current driven magnetization reversal process

Magnetization reversal by spin polarized current flowing perpendicular to a 10 nm Co/6 nm Cu/2.5 nm Co circular nanopillar of 130 nm diameter is studied using a micromagnetic model. In addition to the spin transfer torque term, the magnetostatic coupling with the pinned layer and the classical Ampere field created by the current are taken into account. Furthermore, thermal activation is also considered by means of a stochastic white-noise thermal field. The experimental parameters are J0 = 4.5 × 108 A/cm2, Bext = 0.14 T, T = 300 K, whereas the damping parameter is α = 0.005. Firstly computations without thermal activation were performed. Transitions from the parallel state (PS) to the antiparallel one (APS) and backwards were computed. In both cases, magnetization reversal occurs via highly inhomogeneous states revealing that these processes are not accurately described by single-domain models. Considering the non-equilibrium character of the switching process, the thermal activation simulations have to be carried out as many times as possible in order to average for obtaining quantitative results. Thermal activation favors the transition from PS to APS, a decrease in the switching time is observed and the intermediate state which appears in the computations without thermal field is suppressed. On the contrary the transition from APS to PS is not so influenced and an intermediate magnetization state remains stable even after averaging over 100 realizations. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Micromagnetic computations of spin polarized current-driven magnetization processes

Magnetization reversal by spin polarized current flowing perpendicular to a 10nm Co/6nm Cu/2.5nm Co circular nanopillar of 130nm diameter is studied by means of a micromagnetic model. The spin transfer torque is included as an additional term in the Gilbert equation following the theoretical calculations of Slonczewski. The Ampere field due to the current and the dipolar antiferromagnetic coupling between the Co layers are also taken into account. The simulations reveal a complex switching behavior that involves highly inhomogeneous magnetization configurations with multiple domains. It is also found that the Ampere field plays a crucial role in promoting the switching. In fact, switching would not occur unless this contribution is taken into account.