Vortex Chirality Research Articles

A comparison of numerical simulations and analytical theory of the dynamics of interacting magnetic vortices

Magnetostatic interactions between vortices in closely spaced planar structures are important for applications including vortex-based magnonic crystals and spin torque oscillator networks. Analytical theories that include magnetostatic interaction effects have been proposed but have not yet been rigorously tested. Here, we compare micromagnetic simulations of the dynamics of magnetic vortices confined in three disks in an equilateral triangle configuration to analytical theories that include coupling. Micromagnetic simulations show that the magnetostatic coupling between the disks leads to splitting of the gyrotropic resonance into three modes and that the frequency splitting increases with decreasing separation. The temporal profiles of the magnetization depend on the vortex polarities and chiralities; however, the frequencies depend only on the polarity combinations and will fall into one of two categories: all polarities equal or one polarity opposite to the others, where the latter leads to a larger frequency splitting. Although the magnitude of the splitting observed in the simulations is larger than what is expected based on purely dipolar interactions, a simple analytical model that assumes dipole-dipole coupling captures the functional form of the frequency splitting and the motion patterns just as well as more complex models.

Vortex manipulation and chirality control in asymmetric bilayer nanomagnets

This paper presents a method of controlling the chirality of magnetic vortex in a permalloy nanodisk having a cobalt nanostripe at the top. Features of magnetization reversal of the disk + stripe nanostructure are investigated using the magneto-optical Kerr effect magnetometer and magnetic force microscope. Micromagnetic simulations reveal peculiarities in the vortex nucleation process and in trajectory of the vortex core under the impact of external magnetic fields.

Manipulation of magnetic vortex parameters in disk-on-disk nanostructures with various geometry.

Magnetic nanostructures in the form of a sandwich consisting of two permalloy (Py) disks with diameters of 600 and 200 nm separated by a nonmagnetic interlayer are studied. Magnetization reversal of the disk-on-disk nanostructures depends on the distance between centers of the small and big disks and on orientation of an external magnetic field applied during measurements. It is found that manipulation of the magnetic vortex chirality and the trajectory of the vortex core in the big disk is only possible in asymmetric nanostructures. Experimentally studied peculiarities of a motion path of the vortex core and vortex parameters by the magneto-optical Kerr effect (MOKE) magnetometer are supported by the magnetic force microscopy imaging and micromagnetic simulations.

Controllable vortex chirality switching on spherical shells

A simple mechanism of controllable switching of magnetic vortex chirality is proposed. We consider curvilinear magnetic nanoshells of spherical geometry whose ground state is a vortex magnetization distribution. Chirality of this magnetic vortex can be switched in controllable way by applying a Gaussian pulse of spatially uniform magnetic field along the symmetry axis of the shell. The chirality switching process is explored in detail numerically for various parameters of magnetic pulse: the corresponding switching diagram is build. The role of the curvature is ascertained by studying the switching diagram evolution under the continuous transition from hemispherical shell to the disk shaped sample with the volume and thickness kept constant.

Controlling of magnetic vortex chirality and polarity by spin-polarized current

For a nanodisk, magnetic vortex characterized by a curling magnetization is an energetically stable state. The magnetization in the center of the magnetic vortex is directed upward or downward, namely, the vortex core polarity p=+1 or p=-1 refers to up or down, respectively. The curling direction of magnetization, namely, the vortex chirality, is either counter-clockwise or clockwise. Thus, different combinations of chirality and polarity in a vortex structure demonstrate four stable magnetic states, which can be used to design a multibit memory cell. Such a multibit memory application requires the independent controlling of both the vortex chirality and vortex polarity, which has received considerable attention recently. Switching the vortex polarity has been achieved by using either a magnetic field or a current. The vortex chirality can be controlled by introducing asymmetric geometry of nanodisks. In this article, by using micromagnetic simulations, we present an effective method to simultaneously control the vortex chirality and polarity in a spin valve structure, in which the fixed spin polarizer layer is magnetized in the film plane when the free layer has a magnetic vortex configuration. The free layer is designed into a ladder shape with the right part being thicker than the left part. Our simulations indicate that a combination of desirable vortex chirality and polarity can be easily controlled by a Gaussian current pulse with proper strength and pulse duration through the spin-transfer torque effect. The insight into physical mechanism of the controllable vortex is demonstrated by a series of snapshots. If the magnetic moment of the free layer is saturated in the direction of 0θ θ is the angle between the magnetization and+x axis, the vortex with the counter-clockwise chirality will be generated after the pulse. In contrast, if the free layer magnetization is saturated along the direction πθ <2π, after the pulse, the vortex will have the clockwise chirality. The core polarity of the remanent vortex state is determined by the sign of the magnetic charges which are formed in the step-side of nanodisk during the current pulse.

STXM observation and quantitative study of magnetic vortex structure

Magnetic recording has now played an important role in the development of non-volatile information storage technologies, so it becomes essential to quantitatively understand the magnetization distribution in magnetic microstructures. In ferromagnetic disks, squares and triangles with submicron sizes, it is energetically favorable for the magnetization to form a closed in-plane vortex and a perpendicular vortex core at the center. This vortex magnetic structure is a new candidate for future magnetic memory device because both the vortex chirality and the core polarity can be manipulated by applying an external magnetic field or a spin-polarized current. Further development of vortex-based memory devices requires quantitative measurement of vortex domain structures, which is still lacking.In this paper, magnetization configuration in a vortex structure has been quantitatively studied by scanning transmission X-ray microscope (STXM) utilizing X-ray magnetic circular dichroism (XMCD) effect in Shanghai Synchrotron Radiation Facility. Samples have been fabricated on the 100 nm silicon-nitride membranes. The patterns are first transferred to PMMA photoresist using e-beam lithography, then a 50 nm thick Ni80Fe20 film is deposited by e-beam evaporation. Magnetic vortex configurations are characterized with the X-ray energy at Fe L3 absorption edge and Ni L3 absorption edge, respectively. The image taken at Fe edge shows greater contrast than that at Ni edge. Experimental results indicate that the magnetic vortex state remains stable in permalloy circle, square and triangle structures with diameters from 2 to 5 m. The STXM images indicate that the magnetization in circular geometry changes continuously along the concentric circles without clear domain boundaries. In contrast, magnetization in square geometry consists of four distinct domains with clear diagonal domain boundaries. Similarly, three domains can be observed in triangle geometry. In order to quantify the in-plane magnetization configuration in magnetic vortices, we also use micromagnetic simulation to calculate the magnetization distributions of these three geometries. By extracting Mx along the circular profiles in both experimental and simulated vortex images, we find that the experimental magnetic profiles in the STXM images are consistent with the simulation data quantitatively. These magnetic structures are also studied by magnetic force microscopy (MFM). Since MFM is only sensitive to the dipolar magnetic field around the domain boundary, the MFM images show different configurations from the STXM images.

Control of the magnetic vortex chirality in Permalloy nanowires with asymmetric notches

We have investigated the motion of vortex domain walls passing across non symmetric triangular notches in single Permalloy nanowires. We have measured hysteresis cycles using the focused magneto-optical Kerr effect before and beyond the notch, which allowed to probe beyond the notch the occurrence probability of clockwise (CW) and counter-CW (CCW) walls in tail-to-tail (TT) and head-to-head (HH) configurations. We present experimental evidence of chirality flipping provided by the vortex–notch interaction. With a low exit angle, the probability of chirality flipping increases and here with the lowest angle of 15°, the probability of propagation of the energetically favored domain wall configuration (CCW for TT or CW for HH walls) is ≈75%. Micromagnetic simulations reveal details of the chirality reversal dynamics.

Phase locking of vortex cores in two coupled magnetic nanopillars

Abstract

Nonlinear Dynamics in Spin Vortex Pairs With Strong Core–Core Coupling

We investigate the dynamics of spin vortex pairs in magnetic multilayer particles, with the vortices closely spaced vertically and therefore with strong core-core coupling. We focus on the spin-dynamic behavior of the system beyond the linear small-signal regime, and on the state with antiparallel vortex chiralities and parallel cores, in which the vortex cores are strongly dipole coupled. The data show a clear transition from the dominant single rotational resonance at 2-3 GHz for small excitation field amplitudes to a dominant gyrational resonance at high excitation fields. The concomitant changes in the microwave spectra, seen as satellite resonances near the rotational peak as well as a pronounced low-frequency resonance, are interpreted as arising from the nonlinearities of the main rotational mode, which also mediate microwave power transfer from the high- to the low-frequency mode.

Control of magnetic vortex chirality and polarization in indented and notched nanomagnetic disks

Magnetic vortex dynamics in nanoscale structures is currently a topic of intensive research not only from a fundamental physics point of view but also for their potential use in future generation spintronics and magnetic random access memories. We propose a method, where one can independently control the magnetic vortex polarization and chirality states by a combination of fine-tuning the applied magnetic field and breaking the geometrical symmetry of the magnetic nanostructure. Numerical simulations corroborate our proposal of achieving vortex switchability for the two different geometries we investigate: the indented disk and notched disk structures. Our results suggest that the notched disk structure offers more robust vortex dynamics and better switching characteristics, which makes this geometry ideal for use as a vortex-based magnetic memory device.

Controlling the chirality and polarity of vortices in magnetic tunnel junctions

Static and dynamic control of the chirality and polarity of a magnetic vortex confined in a magnetic tunnel junction is demonstrated. The modes associated with the four chirality/polarity vortex configurations are first explored by resonant excitation with a low power rf current. When the rf power is increased, both the chirality and polarity of the vortex can be resonantly switched, which—as shown by micromagnetic simulations—involves vortex expulsion and renucleation. This tunable resonant switching of the vortex parameters are an exciting step forward for the viability of magnetic vortex-based applications.

Simultaneous control of vortex polarity and chirality in thickness-modulated [Co/Pd]n/Ti/Ni80Fe20 disks

Simultaneous vortex chirality and polarity control are observed in thickness-modulated [Co/Pd]n/Ti/Ni80Fe20 disks using magnetic force microscopy by applying a proper sequence of in-plane and out-of-plane reset fields. The thickness modulation in the NiFe layer introduces an additional shape anisotropy, which defines the vortex chirality during the in-plane reset field, while the [Co/Pd]n underlayer produces a large out-of-plane stray field, which stabilizes the vortex polarity in the NiFe layer. Micromagnetic simulations are compared with experiment results.

Determination of magnetic vortex chirality by local field excited gyration

We show the chirality dependent dynamics of the single magnetic vortex in a submicron permalloy rectangle due to the symmetry breaking by a local magnetic field. For the clockwise (counter-clockwise) chirality, the local positive (negative) field leads to the softening of the gyrotropic mode of vortex core relative to the case of the homogeneous field, resulting in an asymmetric dependence of the gyrotropic frequency which depends on the vortex chirality. The gyrotropic frequency has strong correlation with the distance from the vortex core equilibrium position to the edge of the rectangle. We enlighten that the measurement of the gyrotropic frequency of single vortex under the local field can be an alternative way to determine the vortex chirality at room temperature.

Detection of a vortex nucleation position in a circular ferromagnet using asymmetrically configured electrodes

We demonstrated that the anisotropic magneto-resistance of a ferromagnetic micro-disk measured by the asymmetrically configured electrodes provide the information of the vortex chirality. The large difference of the electrical resistivity between the ferromagnetic disk and the nonmagnetic electrodes creates an inhomogeneous current distribution, allowing us to detect the local domain structure. By focusing on the chirality-dependent magneto-resistance change due to the vortex nucleation, we can clearly detect the vortex nucleation position, leading to the chirality determination. The reliability of the developed detection method has been confirmed by the magneto-resistance measurement with symmetrically configured electrodes.

Curvature induced chirality symmetry breaking in vortex core switching phenomena

The interplay between magnetic vortex polarity, chirality, and the curvature of the underlying surface results in a dependence of the vortex polarity switching efficiency on the vortex chirality. The switching is studied numerically by applying a short Gauss pulse of the external magnetic field to a spherical cap within its cut plane. The minimum field intensity required for the switching essentially depends on the vortex chirality and it does not depend on the initial vortex polarity. This effect decreases with the curvature radius increasing and it vanishes in the planar limit.

Linear Eсkman friction in the mechanism of the cyclone-anticyclone vortex asymmetry and in a new theory of rotating superfluid

The observed experimental and natural phenomenon of cyclone-anticyclone vortex asymmetry implies that a relatively more stable and showing a longer life, as well as a relatively more intense mode of rotation with an anticyclonic circulation direction (opposite to the direction of rotation of the medium as a whole) is realized as compared with an oppositely directed rotation of the cyclonic vortex mode. Until now, however, it was not a success to identify a universal triggering mechanism responsible for the formation of the corresponding breaking of chiral vortex symmetry. In this paper we reveal the said linear universal instability mechanism of breaking of chiral symmetry in the sign of vortex circulation in the rotating medium in the presence of linear Eckman friction. Results Obtained is a condition for the linear dissipative - centrifugal instability (DCI), which leads (only when considering the external linear Eckman friction for an abovethreshold value of rotation frequency of the underlying boundary surface of fluid) to the breaking of chiral symmetry in the Lagrangian fluid particle dynamics and the corresponding realization of the cyclone-anticyclone vortex asymmetry. Conclusion A new non-stationary solution to the problem for the disc which carries out weak axial-torsional oscillations in fluid with the frequency which are superimposed on its rotation with the previously considered frequency 0 ω in connection with the experimental data on the rotating superfluid helium II (see [ 16, 17 ]) has been found. It gives the possibility to conclude that the effects of external, linear on velocity, friction forces must be important to include into consideration for the solve of any fundamental problems of hydrodynamics in bounded systems (as for the blood dynamics in cardiovascular system, for example).

Effect of Dzyaloshinskii–Moriya interaction on magnetic vortex

The effect of the Dzyaloshinskii–Moriya (DM) interaction on the vortex in magnetic microdisk was investigated by micro-magnetic simulation based on the Landau–Lifshitz–Gilbert equation. Our results show that the DM interaction modifies the size of the vortex core, and also induces an out-of-plane magnetization component at the edge and inside the disk. The DM interaction can destabilizes one vortex handedness, generate a bias field to the vortex core and couple the vortex polarity and chirality. This DM-interaction-induced coupling can therefore provide a new way to control vortex polarity and chirality.

Magnetization reversal in asymmetric trilayer dots: effect of the interlayer magnetostatic coupling

The spin structure and magnetization reversal in Co/insulator/Fe trilayer nanodots are investigated by micromagnetic simulations. The vortex and C-state are found and the magnetization reversal is dominated by the shape asymmetry of the dots, which is produced by cutting off a fraction of the circular dot. The vortex chirality is thus controlled by the magnetic field direction. On the other hand, the magnetostatic interaction between the top and bottom magnetic layers has interesting influence on the dot reversal process, where the magnetocrystalline anisotropy direction of the Co layer is allowed to vary within the layer plane. The combined effect of these two aspects is discussed on the base of dot coercivity, remanent magnetization, vortex nucleation and annihilation, and the bias of the Fe layer hysteresis loop. While leading to a new S-state in circle dots, the interlayer interaction facilitates the formation of C-state in asymmetric dots, which reduces the vortex nucleation field. The bias effect of all dots is decreased with the deviation of the Co layer easy axis from the field direction. Unlike the circle and semicircle dots, the field range of the vortex state in other asymmetric dots increases with the angle between the cutting direction and the Co layer anisotropy. Additionally, vortex ranges in less asymmetric dots even larger than that in the circle dots are evidenced unexpectedly. Therefore, the control of the vortex chirality and enhancement of the vortex range are found simultaneously.

Controlling vortex chirality and polarity by geometry in magnetic nanodots

The independent control of both vortex chirality and polarity is a significant challenge in magnetic devices based on nano-sized magnetic vortex structures. By micromagnetic simulations here, we show that in soft ferromagnetic nanodots with an adequate modulated thickness, the desired combination of chirality and polarity can be achieved just by changing the direction of the in-plane applied magnetic field. Despite the complex behavior, the vortex chirality and polarity control can be summarized in two simple rules that can thus become a useful tool for designing magnetic devices.

Control of the polarity of magnetization vortex by torsion

The switching behavior of vortex polarity in a circular ferromagnetic nanodot subjected to torsion is investigated by using a real space phase field model, which explicitly includes the coupling between magnetization and mechanical strain. It is found that the vortex polarity of the nanodot can be switched by torsion when the sign of the torsion is opposite to that of vortex chirality whereas switching does not take place if the sign of torsion is the same as that of vortex chirality. The magneto-elastic coupling and demagnetization field play a decisive role in the polarity switching, which involves an intriguing interplay of magnetization, strain, and demagnetization. The results suggest another way to control vortex polarity by mechanical torsion other than magnetic field and electric current.