Gyrotropic Mode Research Articles

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.

Bandwidth broadening and asymmetric softening of collective spin waves in magnonic crystals

We investigate the dependence on the applied field of the frequency/wavevector dispersion relations of collective spin waves in arrays of dots, close to a magnetic transition. In particular, we focus on the low frequency “soft” modes in three different cases: end modes in the transition between two different saturated states in ellipses, fundamental mode in the saturated-to-vortex transition in disks, and gyrotropic mode in the vortex-to-saturated transition in disks. Noteworthy, the spin waves with nonzero Bloch wavevector along the direction of the applied field happen to soften earlier than spin waves with a Bloch wavevector along different directions, and this feature is responsible for an asymmetric broadening of the bandwidth along the different lattice directions. This is particularly useful in magnonic/spin-logic device research, if different binary digits are associated to modes with the same cell function but different propagation directions.

Intensity inversion of vortex gyrotropic modes in thick ferromagnetic nanodots

Vortex gyrotropic modes in ferromagnetic nanostructures can be described as flexure oscillations of the vortex core line with different number of nodes n along the dot thickness. By conducting broadband ferromagnetic resonance measurements in the absence of external magnetic field on Ni80Fe20 circular nanodots with radius R = 150 nm and thickness 50 ≤ L ≤ 100 nm, we established that above L = 70 nm the intensity of more complicated n = 1 vortex mode is unexpectedly higher than the one of n = 0 mode. The observed behavior is explained on the basis of the inhomogeneous vortex mode phase profiles extracted from micromagnetic simulations. The phase difference of vortex core gyrations at the top and bottom dot faces is essentially different from 0 and π. The difference is increasing with increase in the dot aspect ratio L/R for the 0th order mode, whereas an inverse relationship is observed for the 1st order mode. The analytical theory indicates that this phase difference has magnetostatic origin.

Current-driven gyrotropic mode of a magnetic vortex as a nonisochronous auto-oscillator

Current-driven gyrotropic mode of a magnetic vortex as a nonisochronous auto-oscillator

Response to noise of a vortex based spin transfer nano-oscillator

We investigate experimentally and analytically the impact of thermal noise on the sustained gyrotropic mode of vortex magnetization in spin transfer nano-oscillators and its consequence on the linewidth broadening due to the different nonlinear contributions. Performing time domain measurements, we are able to extract separately the phase noise and the amplitude noise at room temperature for several values of dc current and perpendicular field. For a theoretical description, we extend the general model of nonlinear auto-oscillators to the case of vortex core dynamics and provide analytical expressions of the parameters describing the response to noise of the system. From the analysis of our experimental results, we demonstrate the major role of the amplitude-to-phase noise conversion on the linewidth broadening, and propose several solutions to increase even more the spectral coherence of vortex-based spin transfer nano-oscillators.

Vortex Core Reversal Due to Spin Wave Interference

In this Letter we address spin wave dynamics involved in fast and selective vortex core polarity reversal by rotating magnetic field bursts. In a first example we explain the origin of the delayed switching for excitations with short bursts of only one period duration as an interference effect between spin wave modes. Second, when the vortex core is initially no longer at rest but in gyrotropic motion, the magnetization dynamics become more complicated and the interaction of spin waves with the vortex core leads to a variety of nonlinear effects. Our analysis allows us to explain the experimentally observed switching diagram for simultaneous excitation of spin waves and gyrotropic mode.

Micromagnetic simulations of magnetic normal modes in elliptical nanomagnets with a vortex state

Combined methods of micromagnetic simulation and Fourier analysis are employed to study the gyrotropic magnetic excitations triggered by a short in-plane Gaussian field pulse in ellipse-shaped Permalloy elements with a vortex state. We observed a series of vortex-core azimuthal magnetic normal modes. The frequency of gyrotropic mode increases with the element thickness up to 40 nm, and then a dip appears in the frequency for thickness varying from 40 to 60 nm.

Probing the Anharmonicity of the Potential Well for a Magnetic Vortex Core in a Nanodot

The anharmonicity of the potential well confining a magnetic vortex core in a nanodot is measured dynamically with a magnetic resonance force microscope (MRFM). The stray field of the MRFM tip is used to displace the equilibrium core position away from the nanodot center. The anharmonicity is then inferred from the relative frequency shift induced on the eigenfrequency of the vortex core translational mode. An analytical framework is proposed to extract the anharmonic coefficient from this variational approach. Traces of these shifts are recorded while scanning the tip above an isolated nanodot, patterned out of a single crystal FeV film. We observe a +10% increase of the eigenfrequency when the equilibrium position of the vortex core is displaced to about one-third of its radius. This calibrates the tunability of the gyrotropic mode by external magnetic fields.

Vortex mode dynamics and bandwidth tunability in a two-dimensional array of interacting magnetic disks

We calculate the spin wave spectrum and band diagram of a planar array of interacting disks in the vortex state at zero and finite applied field. We found that the circular polarization of modes depends on the Bloch wavevector k, and that the apparent spin wave profile can change as k increases from Γ to zone boundary as a consequence of the array periodicity, although the cell function remains the same. Focusing on the gyrotropic mode, we found that application of an external field can reduce or enhance the mode bandwidth, and hence slow down or boost the information carrier propagation along orthogonal directions.

Magnetic vortex behavior and its dynamics in nanomagnets in the presence of impurities

Using spin dynamics simulations we study and present a model for pointlike magnetic impurities in nano-magnets based on the exchange coupling between these pointlike impurities and their neighbors. We observed two possible types of impurities, acting as pinning (attractive) or scatter (repulsive) sites. A gaussian profile was observed for the interaction potential energy ranging up to two lattice parameters. Using the known values of the parameters for Permalloy-79 we have calculated the interaction energy of the vortex core with a single defect. We estimated the interaction range as approximately 10 nm. Both results agree quite well with experimental measurements. Also, we study the influence of magnetic impurities in the frequency of the gyrotropic mode in nanodisks of Permalloy-79. We observed fluctuations in the frequency which is in agreement with recent experimental results.

Spin-transfer torque induced vortex dynamics in Fe/Ag/Fe nanopillars

We report on the experimental and analytical work on spin-transfer torque induced vortex dynamics in metallic nanopillars with in-plane magnetized layers. We study nanopillars with a diameter of 150 nm, containing two Fe layers with a thickness of 15 nm and 30 nm, respectively, separated by a 6 nm Ag spacer. The sample geometry is such that it allows for the formation of magnetic vortices in the Fe discs. As confirmed by micromagnetic simulations, we are able to prepare states where one magnetic layer is homogeneously magnetized while the other contains a vortex. We experimentally show that in this configuration spin-transfer torque can excite vortex dynamics and analyse their dependence on a magnetic field applied in the sample plane. The centre of gyration is continuously dislocated from the disc centre, and the potential changes its shape with field strength. The latter is reflected in the field dependence of the excitation frequency. In the second part we propose a novel mechanism for the excitation of the gyrotropic mode in nanopillars with a perfectly homogeneously magnetized in-plane polarizing layer. We analytically show that in this configuration the vortex can absorb energy from the spin-polarized electric current if the angular spin-transfer efficiency function is asymmetric. This effect is supported by micromagnetic simulations.

Magnetic vortex core reversal by rotating magnetic fields generated on micrometer length scales

AbstractUnidirectional switching of the magnetic vortex core can be achieved in micron‐sized ferromagnetic platelets by excitation of the gyrotropic mode of the vortex structure with in‐plane rotating magnetic fields. Circulating fields with a switchable sense of rotation (clockwise, CW or counter clockwise, CCW) have been generated on a micrometer length scale at frequencies up to 1 GHz by two orthogonal electric RF currents with 90° phase shift flowing through crossed but not isolated striplines. Decoupling of these currents is realized by balanced symmetric RF sources. The amplitudes of the rotating magnetic fields and their spatial distributions are calculated and the stripline geometry is discussed. By taking advantage of this technique, unidirectional vortex core reversal by excitation with CW or CCW rotating magnetic fields has been observed by time resolved scanning transmission X‐ray microscopy. An area with reversed magnetization, the “dip,” was observed near the vortex core before vortex core reversal.

Dynamics of Coupled Vortices in a Pair of Ferromagnetic Disks

We here experimentally demonstrate that gyration modes of coupled vortices can be resonantly excited primarily by the ac current in a pair of ferromagnetic disks with variable separation. The sole gyration mode clearly splits into higher and lower frequency modes via dipolar interaction, where the main mode splitting is due to a chirality sensitive phase difference in gyrations of the coupled vortices, whereas the magnitude of the splitting is determined by their polarity configuration. These experimental results show that the coupled pair of vortices behaves similar to a diatomic molecule with bonding and antibonding states, implying a possibility for designing the magnonic band structure in a chain or an array of magnetic vortex oscillators.

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.

Injection locking of the gyrotropic vortex motion in a nanopillar

Spin-torque oscillators (STOs) are a promising application for the spin-transfer torque effect. The major challenge lies in pushing the STO’s microwave output power to useful levels, e.g., by operating an array of STOs in a synchronized, phase-locked mode. Our experiment on metallic, giant magnetoresistance-type nanopillars focuses on the influence of external high-frequency signals on the current-driven vortex dynamics and demonstrates the injection locking of the gyrotropic mode. We find a gap of about three orders of magnitude between the high-frequency power emitted by one oscillator and the power needed for phase-locking.

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.

Magnetic vortex dynamics in the presence of pinning

We have measured the frequency ${f}_{G}$ of the gyrotropic mode of a magnetic vortex formed in individual soft ferromagnetic disks with diameters from 600 nm to $2\text{ }\ensuremath{\mu}\text{m}$. For low excitation amplitudes, we observe fluctuations in ${f}_{G}$ as a function of applied magnetic field. The relationship between the applied field and the spatial displacement of the vortex core from the center of the disk indicates that the fluctuations are due to a distribution of nanoscale defects that pin the vortex core, which has a diameter of $\ensuremath{\sim}10\text{ }\text{nm}$. In the limit of high excitation amplitude, the gyrotropic frequency is independent of field, indicating that the core is depinned. In this limit ${f}_{G}={f}_{ideal}$ where ${f}_{ideal}$ is the frequency predicted by analytical models and micromagnetic simulations of ideal vortex behavior. We also find both experimentally and in simulations that the average frequency shift $⟨\ensuremath{\Delta}f⟩=⟨{f}_{\text{max}}\ensuremath{-}{f}_{ideal}⟩$ is independent of disk diameter. From this observation we argue that $\ensuremath{\Delta}f$ for a particular fluctuation is proportional to the interaction energy ${W}_{P}$ of the vortex core with a single nanoscale defect and estimate the average energy to be ${W}_{P}/e\ensuremath{\approx}2\text{ }\text{eV}$ for the defects in these sputtered permalloy films.

Precise probing spin wave mode frequencies in the vortex state of circular magnetic dots

We report on detailed broadband ferromagnetic resonance measurements of azimuthal and radial spin wave excitations in circular Permalloy dots in the vortex ground state. Dots with aspect ratio (β=height over radius) varied from 0.03 to 0.1 were explored. The frequency splitting of two lowest azimuthal modes was observed. The experimentally observed dependence of the frequency splitting on β was reasonably well described by dynamic splitting model accounting the spin waves and vortex gyrotropic mode interaction.

Spin-transfer torque driven magnetic antivortex dynamics by sudden excitation of a spin-polarized dc

Spin dynamics of antivortices excited by sudden action of a spin-polarized dc is reported. Two main excitation modes are found with increased current density, involving a translational (gyrotropic) mode and a core reversal mode. The former mode can be described by Thiele’s equation, which accounts for the orbital distortion in view of the modified restoring force by nontrivial structures nucleated at sample edges. The final states of the system in the translational mode are obtained, being either a domain wall state or a vortex state, depending on the current density. The frequency of gyromotion is dependent on dot sizes. Within a threshold radius, the off-centered antivortex can freely relax back to the dot center.

Soft spin modes and magnetic transitions in trilayered nanodisks in the vortex state

We present calculations of spin dynamics of a trilayered cylindrical nanodot with circular cross section, which is made of two permalloy disks with the same diameter (200 nm) and different thicknesses (20 and 10 nm), separated by a nonmagetic 10 nm thick spacer. The calculations are performed within the framework of the dynamical matrix method. Due to the different layer thicknesses, the ground state of this system at zero applied field is the vortex configuration in both layers. This system is the ideal one to investigate the dynamics of vortex modes in multilayered dots: we calculate doublets of gyrotropic, radial, and azimuthal modes, which are in phase and out-of-phase in the two layers. The dependence of these modes on vortex polarity and node number is investigated. The modes are studied as a function of a tangential magnetic field. The transition to the saturated state occurs at different critical fields for the two layers. In the proximity of these critical points, the magnetization discontinuities are related to the occurrence of soft modes.