Magnetic Nanodisks Research Articles

Radial-spin-wave-mode-assisted vortex-core magnetization reversals

The dynamic behaviors of vortex-core magnetization reversals in soft magnetic nanodisks driven by oscillating magnetic fields applied perpendicularly to the disk plane were studied by means of micromagnetic numerical simulations. It was found that when the field frequencies are tuned to the eigenfrequencies of radial spin-wave modes, the threshold field amplitudes required for vortex-core switching are an order of magnitude smaller than those of static perpendicular fields. The reversal mechanism and associated underlying physics are completely different from those of vortex-antivortex-pair-mediated core reversals. The results reflect the achievement of an alternative efficient means of ultrafast vortex-core switching.

Magnetic behavior of a nano-disk constrained in an antiferromagnetic substrate

In this work we report a numerical Monte Carlo study of the behavior of a magnetic nano-disk put over an antiferromagnetic substrate. Three approaches were considered for describe the substrate: (1) A stacked antiferromagnetic configuration, (2) an Ising like arrangement and (3) Heisenberg like spins. For the Heisenberg case we still have considered an easy-plane and an easy-axis symmetry of the substrate. The hysteresis loop for the nano-disk is obtained by considering the three cases. The signature of the vortex in the nano-disk appears as small jumps in the hysteresis curve. Exchange bias effects are observed since the substrate has an easy axis symmetry.

Normal modes of coupled vortex gyration in two spatially separated magnetic nanodisks

We found from analytical derivations and micromagnetic numerical simulations that there exist two distinct normal modes in apparently complex vortex gyrotropic motions in two dipolar-coupled magnetic nanodisks. The normal modes have characteristic higher and lower single angular eigenfrequencies with their own elliptical orbits elongated along the x (bonding axis) and y axes, respectively. The superposition of the two normal modes results in coupled vortex gyrations, which depend on the relative vortex-state configuration in a pair of dipolar-coupled disks. This normal-mode representation is a simple means of understanding the observed complex vortex gyrations in two or more dipolar-interacting disks of various vortex-state configurations.

Spin-transfer torque and current-induced vortex superlattices in nanomagnets

Influence of the spin-transfer torque on the vortex state magnetic nanodisk is studied numerically via the Slonczewski-Berger mechanism. The existence of a critical current is determined for the case of same-directed electrical current, its spin polarization, and the polarity of the vortex. The critical current separates two regimes: (i) deformed but static vortex state and (ii) essentially dynamic state under which the spatiotemporal periodic structures can appear. The structure is a stable vortex-antivortex lattice. Symmetry of the lattice depends on the applied current value, and for high currents (close to saturation) only square lattices are observed. General relations for size of the stable lattice are obtained analytically.

Tunable Distribution of Magnetic Nanodiscs in an Array of Electrodeposited Multilayered Nanowires

Co-Ni-Cu/Cu multilayered nanowire arrays were electrodeposited in polyester track etched (PETE) nanoporous template with appropriate hydrophilic properties in a single bath. The array of multilayered nanowires can provide a three-dimensional accumulation of magnetic nanodiscs in a non-magnetic media. Magnetic properties and microstructure of multilayered nanowires with different copper layer thickness were studied. Using different characterization techniques including X-ray diffraction (XRD), transmission electron microscope (TEM), magnetic force microscopy and magnetization curves, we observe the formation of unique sharply interfaced multisegmented magnetic/nonmagnetic nanowires in a range of spacing thickness from 0.7 nm to 26 nm. MFM shows that the filling of nanopores happens uniformly during electrodeposition in the form of nanowires, while TEM examinations confirm the formation of precise multilayered structure. TEM also reveals the formation of sharp interfaces between the segments with a polycrystalline superlattice structure. XRD interestingly shows that satellite peaks appear around (111) main Bragg reflection. The magnetization curves at 20 K of the array show a relative rotation of easy axis direction from out of the plane to in the plane, as the spacing Cu layer thickness ( t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cu</sub> ) increases in a range of 0.7-26 nm. The variation of measured coercivity in different bi-layer thicknesses likely shows the intention of the structure to form discrete magnetic segments as the non-magnetic spacer layer becomes thicker. However, the variation of coercivity and squareness implies the existence of strong interaction between the segments. A study on the remanent magnetization at 20 K for t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Co-Ni-Cu</sub> =3.3 nm with a range of tCu reveals the existence of demagnetising interactions within each array suggesting the anti-ferromagnetic coupling between Co-Ni-Cu layers.

Off-centred immobile magnetic vortex under influence of spin-transfer torque

Formation of the ‘dip’ structure which foregoes switching of magnetic vortex polarity is studied numerically in magnetic nanodisc. A new method based on influence of the spin-transfer torque is used. The method allows one to obtain the dip structure for immobile vortex which significantly improves studying accuracy in comparison with the case of moving vortex. Free out-of-plane vortices as well as in-plane vortices pinned on hole defects are considered. It is shown that the process of the dip formation is different for free and pinned vortices and direction of the dip does not directly depend on the vortex polarity.

Polarization-selective vortex-core switching by tailored orthogonal Gaussian-pulse currents

We experimentally demonstrate low-power-consumption vortex-core switching in magnetic nanodisks using tailored rotating magnetic fields that are produced with orthogonal and unipolar Gaussian-pulse currents. Optimal width of the orthogonal pulses and their time delay are found to be determined only by the angular eigenfrequency {\omega}_D for a given vortex-state disk of its polarization p, such that {\sigma} = 1/{\omega}_D and {\Delta}t = {\pi}p/2{\omega}_D, as studied from analytical and micromagnetic numerical calculations. The estimated optimal pulse parameters are in good agreements with the experimentally found results. This work provides a foundation for energy-efficient information recording in vortex-core cross-point architecture.

Fundamental design paradigms for systems of three interacting magnetic nanodiscs

The magnetic properties of a system of three interacting magnetic elliptical disks are examined. For the various levels of uniaxial anisotropy investigated a complicated series of phase transitions exist. These are marked by the critical lines of stability that are demonstrated in an applied magnetic field plane diagram.

Vortices in Low-Dimensional Magnetic Systems

Vortices are objects that are important to describe several physical phenomena. There are many examples of such objects in nature as in a large variety of physical situations like in fluid dynamics, superconductivity, magnetism, and biology. Historically, the interest in magnetic vortex-like excitations begun in the 1960s. That interest was mainly associated with an unusual phase-transition phenomenon in two-dimensional magnetic systems. More recently, direct experimental evidence for the existence of magnetic vortex states in nano-disks was found. The interest in such model was renewed due to the possibility of the use of magnetic nano-disks as bit elements in nano-scale memory devices. The goal of this study is to review some key points for the understanding of the vortex behavior and the progress that have been done in the study of vortices in low-dimensional magnetic systems.

Magnetic vortex formation and gyrotropic mode in nanodisks

The superparamagnetic limit imposes a restriction on how far the miniaturization of electronic devices can reach. Recently it was shown that magnetic thin films with nanoscale dimensions can exhibit a vortex as its ground state. The vortex can lower its energy by developing an out-of-plane magnetization perpendicular to the plane of the film, the z direction, which can be “up” or “down.” Because the vortex structure is very stable this twofold degeneracy opens up the possibility of using a magnetic nanodisk as a bit of memory in electronic devices. The manipulation of the vortex and a way to control the core magnetization is a subject of paramount importance. Recent results have suggested that the polarity of a vortex core could be switched by applying a pulsed magnetic field in the plane of the disk. Another important effect induced by an external magnetic field due to the component out-of-plane in vortex-core is the gyrotropic mode. The gyrotropic mode is the elliptical movement around the disk center executed by the vortex-core under the influence of a magnetic field. In the present work we used numerical simulations to study the ground state as well as the dynamical behavior of magnetic vortices in thin nanodisks. We have considered a model where the magnetic moments interact through exchange (−J∑S⃗i⋅S⃗j) and dipolar potentials {D∑[S⃗i⋅S⃗j−3(S⃗i⋅r̂ij)×(S⃗j⋅r̂ij)]/rij3}. We have investigated the conditions for the formation of the vortex-core with and without an out-of-plane magnetization as a function of the strength of the dipole interaction D and of the size and thickness of the magnetic nanodisk. Our results were consistent with the existence of two vortex phases separated by a crossover line [(Dc−D)α]. We have observed that Dc does not depend on the radius of nanodisk but depends on its thickness. The exponent α was found to be α≈0.55(2). The gyrotropic motion is studied by applying an external magnetic field parallel to the plane of the magnetic nanodisk. Our results show that there is a minimum value for the modulus of the out-of-plane vortex-core magnetization, from which we can excite the gyrotropic mode. This minimum value depends on the thickness of the nanodisk. This result suggest that an experimental way to improve the stability of the process of switching may be through the thickness control. We also observed that the gyrotropic mode frequency increases with the aspect ratio, which is in qualitatively accordance with theoretical and experimental results. Finally, we present theoretical results for Permalloy nanodisks obtained from our model, which are also in good agreement with experimental results.

Optimal control of vortex-core polarity by resonant microwave pulses

In a vortex-state magnetic nano-disk, the static magnetization is curling in the plane, except in the core region where it is pointing out-of-plane, either up or down leading to two possible stable states of opposite core polarity p. Dynamical reversal of p by large amplitude motion of the vortex core has recently been demonstrated experimentally,raising fundamental interest for potential application in magnetic storage devices. Here we demonstrate coherent control of p by single and double microwave pulse sequences, taking advantage of the resonant vortex dynamics in a perpendicular bias magnetic field. Optimization of the microwave pulse duration required to switch p allows to experimentally infer the characteristic decay time of the vortex core in the large oscillation regime. It is found to be more than twice shorter than in the small oscillation regime, raising the fundamental question of the non-linear behaviour of magnetic dissipation.

Dynamics of 1-D Chains of Magnetic Vortices in Response to Local and Global Excitations

We report the magnetic vortex dynamics of 1-D chains of nanomagnetic disks under a time-dependent magnetic field localized at one end of the chain. The transmission of the peak amplitude of the gyrotropic excitation mode of the vortex core along the chain has been actively controlled by manipulating the geometry and condition of preparation of the magnetic ground states of the chains. The transmission is maximum for direct magnetostatic coupling and identical chirality of the nanodisks with geometric asymmetry. Dynamics of the optimized system under a global excitation field has also been investigated to understand the role of magnetostatic interaction in the energy transfer under the local excitation field. The observations are particularly important for the design of fast spin logic systems and the magnonic crystals.

Diagram for vortex formation in quasi-two-dimensional magnetic dots

The existence of nonlinear objects of the vortex type in two-dimensional magnetic systems presents itself as one of the most promising candidates for the construction of nanodevices, useful for storing data, and for the construction of reading and writing magnetic heads. The vortex appears as the ground state of a magnetic nanodisk whose magnetic moments interact via the dipole-dipole potential {D∑[S⃗i⋅S⃗j−3(S⃗i⋅r̂ij)×(S⃗j⋅r̂ij)]/rij3} and the exchange interaction (−J∑S⃗i⋅S⃗j). In this work it is investigated the conditions for the formation of vortices in nanodisks in triangular, square, and hexagonal lattices as a function of the size of the lattice and of the strength of the dipole interaction D. Our results show that there is a “transition” line separating the vortex state from a capacitorlike state. This line has a finite size scaling form depending on the size, L, of the system as Dc=D0+1/A(1+BL2). This behavior is obeyed by the three types of lattices. Inside the vortex phase it is possible to identify two types of vortices separated by a constant, D=Dc, line: An in-plane and an out-of-plane vortex. We observed that the out-of-plane phase does not appear for the triangular lattice. In a two layer system the extra layer of dipoles works as an effective out-of-plane anisotropy inducing a large Sz component at the center of the vortex. Also, we analyzed the mechanism for switching the out-of-plane vortex component. Contrary to some reported results, we found evidences that the mechanism is not a creation-annihilation vortex anti-vortex process.

Phase diagram of magnetic nanodisks measured by scanning electron microscopy with polarization analysis

Phase diagram of magnetic nanodisks measured by scanning electron microscopy with polarization analysis

Influence of the Dzyaloshinskii-Moriya interaction on vortex states in magnetic nanodisks

Curling magnetic vortices with chiral rotation sense and polarity of the core magnetization can exist in magnetic circular nanostructures. Broken mirror symmetry at surfaces/interfaces of magnetic nanostructures induces chiral Dzyaloshinskii-Moriya interactions which may strongly affect the magnetic properties. Using a micromagnetic approach, we investigate the influence of these chiral interactions on the vortex states in magnetic nanodisks. We calculate numerically the shape, size, and stability of the vortices in equilibrium as functions of magnetic field and the material and geometrical parameters. As a result, under the influence of the chiral magnetic interactions vortices of opposite chirality should have different sizes. We provide detailed numerical analysis of this effect, which can be applied to measure the strength of the induced Dzyaloshinskii-Moriya coupling in magnetic thin film elements.

Controlling spin vortex states in magnetic nanodisks by magnetic field pulses

We present the principles of the switching of the polarity and chirality of a magnetic nanodisk by external in-plane field pulses. We show that to switch the polarity requires a field pulse of a sufficient amplitude. On the other hand, to switch the chirality requires a pulse with a smaller amplitude and with a precisely chosen duration. Both phenomena together form the full control of the vortex state.

Theory of vortex states in magnetic nanodisks with induced Dzyaloshinskii-Moriya interactions

Broken inversion symmetry in magnetic nanostructures induces Dzyaloshinskii-Moriya couplings. In the presence of surfaces/interfaces the magnetism of magnetic nanodisks can be essentially affected by these chiral couplings. Within a micromagnetic approach we calculate the equilibrium sizes and shape of the vortices as functions of magnetic field, the material, and the geometrical parameters of nanodisks. It was found that the Dzyaloshinskii-Moriya coupling can considerably increase sizes of vortices with ``right'' chirality and suppress vortices with opposite chirality. This allows to form a bistable system of vortices with the same chirality as a basic element for storage applications.

Simulations of the dynamic switching of vortex chirality in magnetic nanodisks by a uniform field pulse

We present a possibility to switch the chirality of a spin vortex occurring in a magnetic nanodisk by applying a uniform in-plane field pulse, based on optimizing its strength and duration. The related spin-dynamical process, investigated by micromagnetic simulations, consists of several stages. After applying the field, the original vortex is expelled from the disk, after which two C-shaped states oscillate between each other. The essence of the method is based on turning the field off at a suitably chosen moment for which the orientation of the C-state will evolve into the nucleation of a vortex with the desirable chirality. This idea simply uses the information about the original chirality present inside the nanodisk during the dynamic process before losing it in saturation, and can thus be regarded as analogous to the recent studies on the polarity switching.

Bistability of Vortex Core Dynamics in a Single Perpendicularly Magnetized Nanodisk

Microwave spectroscopy of individual vortex-state magnetic nanodisks in a perpendicular bias magnetic field H is performed using a magnetic resonance force microscope. It reveals the splitting induced by H on the gyrotropic frequency of the vortex core rotation related to the existence of the two stable polarities of the core. This splitting enables spectroscopic detection of the core polarity. The bistability extends up to a large negative (antiparallel to the core) value of the bias magnetic field Hr, at which the core polarity is reversed. The difference between the frequencies of the two stable rotational modes corresponding to each core polarity is proportional to H and to the ratio of the disk thickness to its radius. Simple analytic theory in combination with micromagnetic simulations give a quantitative description of the observed bistable dynamics.

Predicted defect-induced vortex core switching in thin magnetic nanodisks

We investigate the influence of artificial defects (small holes) inserted into magnetic nanodisks on the vortex core dynamics. One and two holes (antidots) are considered. In general, the core falls into the hole; but, in particular, we would like to note an interesting phenomenon not yet observed, which is the vortex core switching induced by the vortex hole interactions. It occurs for the case with only one hole and for very special conditions involving the hole size and position as well as the disk size. Any small deformation in the disk geometry such as the presence of a second antidot completely changes the vortex dynamics, and the vortex core eventually falls into one of the defects. After trapped, the vortex center still oscillates with a very high frequency and small amplitude around the defect center.