Double Vortex States Research Articles

Multivortex Formation During Magnetization Reversal Process in Rectangular and Square CoFe Nanostructures

Shape- and thickness-dependent magnetization reversal process is investigated in CoFe nanostructures by micromagnetic simulations. The reversal is abrupt in the case of 10-nm and 20-nm thick rectangular and square nanostructures. Intermediate double vortex states are formed in rectangular nanostructures of thickness 30 to 60 nm when the field is applied along the longer dimension. Magnetization reversal along the shorter dimension happens through the formation of multivortex states. Similar type of reversal is observed in 40 to 60-nm thick square nanostructures of dimensions 225 nm and 335 nm.

Evolution of magnetic vortex formation in micron-sized disks

Automotive magnetic field sensing applications require a robust sensing concept. One way to meet the corresponding sensor requirements, such as a negligible hysteresis and a large linear working range, is to employ the vortex state. Consequently, the nucleation field Hn of the vortex state becomes a highly important sensor parameter. In this study, we examine different factors that affect Hn. Tunneling magnetoresistance spin-valve sensors with disk-shaped CoFeB free layers, which energetically favor the nucleation of the vortex state, are electrically characterized and compared with micromagnetic simulations. Phase transitions into intermediate magnetic states, such as various buckling states, the S-state, or the double vortex state, are extracted from hysteresis loops. The resulting phase diagrams show that the formation of the S-state only occurs below a thickness of approximately 25 nm, whereas the double vortex state nucleates frequently only above approximately 35 nm. Both the S- and double vortex states lower the nucleation field of the single vortex state compared to higher order buckling states. Understanding both the origin and the influence of the intermediate phases opens the way to designing a robust and reliable vortex sensor concept.

Comparative Study of Magnetization Reversal Process Between Elliptical and Rectangular CoFe Nanomagnets

The magnetization reversal process for elliptical and rectangular permendur (CoFe) nanostructures were compared using micromagnetic simulations. Single domain states were observed in 10 nm thick elliptical and rectangular nanomagnets. The magnetization reversal along the major and minor axis in 60 nm thick elliptical nanomagnets occurred through the formation of double vortex states. In rectangular nanomagnets, it occurred through the formation of single vortex state along 225 nm and double vortex state along 335 nm.

Spin Wave Excitations and Winter’s Magnons in Vertically Coupled Vortex State Permalloy Dots

Circular soft magnetic dots are the main elements of many proposed novel spintronics devices, capable of fascinating spin-based electronics applications, from extremely sensitive magnetic field sensors, to current-tunable microwave vortex oscillators. Here, we investigate static and broadband dynamic magnetization responses of vertically coupled Permalloy (Py) magnetic dots in the vortex state in layered nanopillars (experiment and simulations), which were explored as a function of in-plane magnetic field and interlayer separation. Under reduction of magnetic field from saturation for the field range just above vortex-vortex ground state. We observe a metastable double vortex state for each of the dots. In this state, novel kinds of spin waves (Winter’s magnons along domain walls between vortex cores and half-edge antivortex) are excited. For dipolarly coupled circular Py(25 nm)/Cu(20 nm)/Py(25 nm) trilayer nanopilars of diameter 600 nm, a small in-plane field splits the eigenfrequencies of azimuthal spin wave modes inducing an abrupt transition between acoustic (in-phase) and optic (out-of-phase) kinds of the low-lying coupled spin wave modes. Qualitatively similar changes (although more gradual and at higher values of in-plane fields) occur in the exchange coupled Py(25 nm)/Cu(1 nm)/Py(25 nm) trilayer nanopillars. These findings are in qualitative agreement with micromagnetic dynamic simulations.

Localized domain-wall excitations in patterned magnetic dots probed by broadband ferromagnetic resonance

We investigate the magnetization dynamics in circular Permalloy dots with spatially separated magnetic vortices interconnected by domain walls (double vortex state). We identify a novel type of quasi one-dimensional (1D) localized spin wave modes confined along the domain walls, connecting each of two vortex cores with two edge half-antivortices. Variation of the mode eigenfrequencies with the dot sizes is in quantitative agreement with the developed model, which considers a dipolar origin of the localized 1D spin waves or so-called Winter's magnons [J. M. Winter, Phys. Rev. 124, 452 (1961)]. These spin waves are analogous to the displacement waves of strings and could be excited in a wide class of patterned magnetic nanostructures possessing domain walls, namely in triangular, square, circular, or elliptic soft magnetic dots.

Nucleation of vortex pairs in exchange biased nanoelements

We report a theoretical investigation of interface effects in the magnetic order of interface biased iron and Permalloy™ elliptical nano-elements. Contrary to intuition, there is a partial pinning of the interface layer, favoring double vortex states along the hysteresis loop. Interface biasing affects the relative chirality and the distance of the vortices. Unbiased nanoelements may nucleate vortex pairs with the same chirality separated by an antivortex. For interface biased nanoelements the vortex pair forms with opposite chirality separated by a magnetic domain.

Spin re-orientation in magnetostatically coupledNi80Fe20 ellipsoidal nanomagnets

We investigate the influence of magnetostatic coupling on the spin configurations andmagnetization reversal mechanism in a one-dimensional linear chain of densely packedNi80Fe20 ellipsoidal nanomagnets arranged in two basic configurations (elements coupled alongthe major or minor axes). Using magnetic force microscopy (MFM) we observedthat for geometrically identical ellipsoidal nanomagnets the magnetic states atremanence are strongly dependent on the arrangement of the ellipsoid due tocompetition between the inherent shape and configuration anisotropies. When theelements are coupled along the major axis, the individual elements adopt a singledomain magnetic state at remanence for field applied along the linear chain. This isin contrast with a wide range of magnetic states (single vortex states, doublevortex states and modified single domain states) observed for elements coupledalong the minor axis and also isolated elements. We have conducted a detailedinvestigation on the magnetization reversal mechanisms for both configurationsand have correlated our experimental results with micromagnetic simulations.

Vortex phase boundaries from ferromagnetic resonance measurements in a patterned disc array

Using a recently developed broadband microwave measurement technique, we have studied the hysteretic appearance and disappearance with in-plane magnetic field of the uniform ferromagnetic resonance (FMR) mode of a patterned permalloy disk array. The observed features are consistent with our micromagnetic simulations (performed on an infinite array of such disks), which predict that on decreasing the magnetic field from a positively magnetized state at positive fields the array will: (i) pass continuously into a double-vortex state; (ii) followed by a discontinuous transition to a single-vortex state; and finally (iii) discontinuously into a negatively magnetized state at some negative field. The hysteretic counterpart occurs on reversing the field sweep and returning to positive fields. The FMR data are consistent with the hysteretic dc magnetization measurements performed earlier on samples patterned in an identical manner.

Effect of in situ FIB Trimming on the Spin Configurations of Hexagonal-Shaped Elements Characterized by SEMPA Imaging

We report on the effect of in situ focused ion beam (FIB) trimming on the spin configurations of the hexagonal-shaped elements, characterized by scanning electron microscopy with polarization analysis (SEMPA) imaging. The use of SEMPA and successive in situ FIB trimming makes it possible to study the effect of thickness on the spin configuration of a same hexagonal dot array, eliminating the effect of irregularity in edges caused by the fabrication processes. The results obtained indicate that there exists a transition of a single vortex state to a stable double vortex state when the thickness is reduced to below 8 nm. Micromagnetic modeling has been performed to investigate the effect of reductions in both the thickness and saturation magnetization due to FIB trimming.

Controlling Double Vortex States in Low-Dimensional Dipolar Systems

The reversal process of the chirality of each opposite vortex belonging to a double vortex state in ferromagnetic hysterons, via the application of in-plane magnetic fields, is reported. Simulations reveal that such a process involves the formation of four intermediate states, including original ones. Hysteresis loops can occur only in a counterclockwise fashion because of one of these intermediate states. Double vortex states can also be controlled by electric fields in ferroelectric nanostructures of different shapes, but with some key differences with respect to the ferromagnetic case.

Magnetization reversal via single and double vortex states in submicron Permalloy ellipses

The magnetization reversal mechanism in an array of submicron elliptical Permalloy elements with an aspect ratio 1.4:1 is investigated using the diffracted magneto-optic Kerr effect technique, Lorentz scanning transmission electron microscopy, and Lorentz transmission electron microscopy. The experimental results are interpreted from a comparison with micromagnetic simulations. The reversal mechanism is found to be dependent on the direction of the magnetic field and to occur via the formation of one or two vortices; the one vortex state is nucleated when the field is applied along the short axis. For the field applied along the long axis a mixture of one- and two-vortex states is observed at remanence.

Magnetization reversal process of the nanosized elliptical permalloy magnetic dots with various aspect ratios

We have studied systematically the reversal processes of nanosized elliptical dots with various aspect ratios, and found three states of magnetization reversal in micromagnetics simulation results: single vortex, double vortex and vortex-free reversal. Uncontrollable single and double vortex state was observed in dot with small aspect ratio, stable double vortex state in medium aspect ratio and vortex free reversal in large aspect ratio. These varieties of magnetization processes were unified in single vortex state when tilted field was applied.

High‐temperature magnetic stability of small magnetite particles

The stability of magnetic domain structures of small grains of magnetite were examined between room temperature and the Curie temperature using a high‐resolution three‐dimensional micromagnetic algorithm. At all times the minimum resolution used was determined by calculating the exchange length. Using an unconstrained model, the single domain (SD) to multidomain (MD) threshold grain size d0 was found to be nearly independent of temperature up to ∼450°C. Above this temperature, d0 was observed to rise sharply. Energy barriers between metastable domain states trapped in local energy minimums (LEM) were determined using a constrained algorithm. Three types of domain structure were considered: SD, vortex, and double vortex (effectively three domain), in a range of grain sizes with side length between 30 and 300 nm. In addition, the effect of varying shape was also considered by examining asymmetric grains with aspect ratios up to 1.4. From the numerical solutions energy barriers between LEM states were determined. It was found that MD grains 300 nm in size display higher stability than smaller SD grains (∼50 nm). Double vortex states were found to be less stable than single vortex states at nearly all temperatures. Blocking temperatures as function of grain size for both symmetric and asymmetric grains were determined and agree well with experimental results. Transdomain thermoremanence analysis indicated that there are a limited number of grain sizes and shapes which will nucleate domain wall‐type structures during cooling. Such nucleation events would cause the total measured remanence to decrease with cooling in conflict with Néel's analytical theory for remanence cooling behavior but in agreement with experimental observations.

Magnetic states of small cubic particles with uniaxial anisotropy

The lowest energy states in small cubic particles with uniaxial anisotropy are explored as a function of anisotropy strength and particle size. The investigations result in a phase diagram which contains the boundaries between the regions of one, two and three domains (flower, vortex and double vortex states). While the general features of the phase diagram are derived from energy estimates based on domain theory, the details are obtained using numerical micromagnetics. The two-domain and the three-domain phase can be subdivided into subphases. The comparison between different configurations revealed that a twisted vortex configuration with an S-shaped domain wall replaces the symmetric vortex with a straight wall at larger sizes. The three-domain phase contains two subphases which are symmetric with respect to (1 0 0) and (1 1 0) mirror planes, respectively. The transition from two to three domains occurs into the (1 1 0)-three-domain-state (diagonal state). This structure can be described as a configuration with two (quarter-) circular domain walls in two opposing corners. However, this configuration is energetically favored only in a small region within the phase diagram relative to the (1 0 0)-symmetry three-domain state with straight walls (sandwich state).