Bistability of vortex core dynamics in a single perpendicularly magnetized nanodisk

Scanning Spin Probe Based on Magnonic Vortex Quantum Cavities

Performing nanoscale scanning electron paramagnetic resonance (EPR) requires three essential ingredients: First, a static magnetic field together with field gradients to Zeeman split the electronic energy levels with spatial resolution; second, a radio frequency (rf) magnetic field capable of inducing spin transitions; finally, a sensitive detection method to quantify the energy absorbed by spins. This is usually achieved by combining externally applied magnetic fields with inductive coils or cavities, fluorescent defects, or scanning probes. Here, we theoretically propose the realization of an EPR scanning sensor merging all three characteristics into a single device: the vortex core stabilized in ferromagnetic thin-film discs. On one hand, the vortex ground state generates a significant static magnetic field and field gradients. On the other hand, the precessional motion of the vortex core around its equilibrium position produces a circularly polarized oscillating magnetic field, which is enough to produce spin transitions. Finally, the spin-magnon coupling broadens the vortex gyrotropic frequency, suggesting a direct measure of the presence of unpaired electrons. Moreover, the vortex core can be displaced by simply using external magnetic fields of a few mT, enabling EPR scanning microscopy with large spatial resolution. Our numerical simulations show that, by using low damping magnets, it is theoretically possible to detect single spins located on the disc's surface. Vortex nanocavities could also attain strong coupling to individual spin molecular qubits with potential applications to mediate qubit-qubit interactions or to implement qubit readout protocols.

Size driven barrier to chirality reversal in electric control of magnetic vortices in ferromagnetic nanodiscs

New high density storage media and spintronic devices come about with a progressing demand for the miniaturization of ferromagnetic structures. Vortex ordering of magnetic dipoles in such structures has been repeatedly observed as a stable state, offering the possibility of chirality in these states as a means to store information at high density. Electric pulses and magnetoelectric coupling are attractive options to control the chirality of such states in a deterministic manner. Here, we demonstrate the chirality reversal of vortex states in ferromagnetic nanodiscs via pulsed electric fields using a micromagnetic approach and focus on the analysis of the energetics of the reversal process. A strong thickness dependence of the chirality reversal in the nanodiscs is found that emanates from the anisotropy of the demagnetizing fields. Our results indicate that chiral switching of the magnetic moments in thin discs can give rise to a transient vortex-antivortex lattice not observed in thicker discs. This difference in the chirality reversal mechanism emanates from profoundly different energy barriers to overcome in thin and thicker discs. We also report the polarity-chirality correlation of a vortex that appears to depend on the aspect ratio of the nanodiscs.

Spin-wave spectroscopy of individual ferromagnetic nanodisks

The increasing demand for nanoscale magnetic devices requires development of 3D magnetic nanostructures. In this regard, focused electron beam induced deposition (FEBID) is a technique of choice for direct-writing of complex nano-architectures with applications in nanomagnetism, magnon spintronics, and superconducting electronics. However, intrinsic properties of nanomagnets are often poorly known and can hardly be assessed by local optical probe techniques. Here, an original spatially resolved approach is demonstrated for spin-wave spectroscopy of individual circular magnetic elements with sample volumes down to about 10-3 μm3. The key component of the setup is a coplanar waveguide whose microsized central part is placed over a movable substrate with well-separated CoFe-FEBID nanodisks which exhibit standing spin-wave resonances. The circular symmetry of the disks allows for the deduction of the saturation magnetization and the exchange stiffness of the material using an analytical theory. A good correspondence between the results of analytical calculations and micromagnetic simulations is revealed, indicating a validity of the used analytical model going beyond the initial thin-disk approximation used in the theoretical derivation. The presented approach is especially valuable for the characterization of direct-write magnetic elements opening new horizons for 3D nanomagnetism and magnonics.

Chaos in Magnetic Nanocontact Vortex Oscillators

We present an experimental study of spin-torque driven vortex self-oscillations in magnetic nanocontacts. We find that, above a certain threshold in applied currents, the vortex gyration around the nanocontact is modulated by relaxation oscillations, which involve periodic reversals of the vortex core. This modulation leads to the appearance of commensurate but also, more interestingly here, incommensurate states, which are characterized by devil's staircases in the modulation frequency. We use frequency- and time-domain measurements together with advanced time-series analyses to provide experimental evidence of chaos in incommensurate states of vortex oscillations, in agreement with theoretical predictions.

Probing Phase Coupling Between Two Spin-Torque Nano-Oscillators with an External Source

Phase coupling between auto-oscillators is central for achieving coherent responses such as synchronization. Here we present an experimental approach to probe it in the case of two dipolarly coupled spin-torque vortex nano-oscillators using an external microwave field. By phase locking one oscillator to the external source, we observe frequency pulling on the second oscillator. From coupled phase equations we show analytically that this frequency pulling results from concerted actions of oscillator-oscillator and source-oscillator couplings. The analysis allows us to determine the strength and phase shift of coupling between two oscillators, yielding important information for the implementation of large interacting oscillator networks.

Coupled gyration modes in one-dimensional skyrmion arrays in thin-film nanostrips as new type of information carrier

We report on a micromagnetic numerical simulation study of dynamic coupling between neighboring skyrmions periodically arranged in narrow-width nanostrips. We explored the coupled gyration modes and their characteristic dispersions in terms of the interdistance between the neighboring skyrmions. The application of perpendicular magnetic fields allows for the control and modification of the dispersion of the coupled gyration modes. The coupled gyration modes of individual skyrmions might provide a new type of information carrier in narrow-width straight and curved nanostrips, as driven by magnetic interactions in such continuous thin films.

Spin-torque resonant expulsion of the vortex core for an efficient radiofrequency detection scheme

It has been proposed that high-frequency detectors based on the so-called spin-torque diode effect in spin transfer oscillators could eventually replace conventional Schottky diodes due to their nanoscale size, frequency tunability and large output sensitivity. Although a promising candidate for information and communications technology applications, the output voltage generated from this effect has still to be improved and, more pertinently, reduces drastically with decreasing radiofrequency (RF) current. Here we present a scheme for a new type of spintronics-based high-frequency detector based on the expulsion of the vortex core in a magnetic tunnel junction (MTJ). The resonant expulsion of the core leads to a large and sharp change in resistance associated with the difference in magnetoresistance between the vortex ground state and the final C-state configuration. Interestingly, this reversible effect is independent of the incoming RF current amplitude, offering a fast real-time RF threshold detector.

Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators

Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spinwaves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighbouring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators. Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, as confirmed by an analytical model and micromagnetic simulations highlighting the physics at play in the synchronization process.

Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators

Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spinwaves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighbouring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators. Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, as confirmed by an analytical model and micromagnetic simulations highlighting the physics at play in the synchronization process.

Origin of spectral purity and tuning sensitivity in a spin transfer vortex nano-oscillator

We investigate the microwave characteristics of a spin transfer nano-oscillator (STNO) based on coupled vortices as a function of the perpendicular magnetic field H(⊥). Interestingly, we find that our vortex-based oscillator is quasi-isochronous independently of H(⊥) and for a dc current ranging between 18 and 25 mA. It means that the severe nonlinear broadening usually observed in STNOs can be suppressed on a broad range of bias. Still, the generation linewidth displays strong variations on H(⊥) (from 40 kHz to 1 MHz), while the frequency tunability in current remains almost constant (7  MHz/mA). This demonstrates that isochronicity does not necessarily imply a loss of frequency tunability, which is here governed by the current induced Oersted field. It is not sufficient either to achieve the highest spectral purity in the full range of H(⊥). We show that the observed linewidth broadenings are due to the excited mode interacting with a lower energy overdamped mode, which occurs at the successive crossings between harmonics of these two modes. These findings open new possibilities for the design of STNOs and the optimization of their performance.

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.

Spectroscopy and imaging of edge modes in Permalloy nanodisks

We report ferromagnetic resonance force microscopy of confined spin-wave modes with improved, 100 nm resolution. The ferromagnetic resonance spectra in Permalloy disks (diameters ranging from 100 to 750 nm) distinguish multiple edge modes, and the images reveal distinct precession patterns. The fundamental edge mode also provides a new, localized probe of the magnetic properties of the film edge; rotation of the applied field reveals large edge property variations in nominally circular disks. As a function of disk diameter, the number of observed edge modes agrees with modeling.

Magnetic vortex core reversal by excitation of spin waves

Micron-sized magnetic platelets in the flux-closed vortex state are characterized by an in-plane curling magnetization and a nanometer-sized perpendicularly magnetized vortex core. Having the simplest non-trivial configuration, these objects are of general interest to micromagnetics and may offer new routes for spintronics applications. Essential progress in the understanding of nonlinear vortex dynamics was achieved when low-field core toggling by excitation of the gyrotropic eigenmode at sub-GHz frequencies was established. At frequencies more than an order of magnitude higher vortex state structures possess spin wave eigenmodes arising from the magneto-static interaction. Here we demonstrate experimentally that the unidirectional vortex core reversal process also occurs when such azimuthal modes are excited. These results are confirmed by micromagnetic simulations, which clearly show the selection rules for this novel reversal mechanism. Our analysis reveals that for spin-wave excitation the concept of a critical velocity as the switching condition has to be modified.

Ultrafast magnetization dynamics of spintronic nanostructures

The ultrafast (sub-nanosecond) magnetization dynamics of ferromagnetic thin films and elements that find application in spintronic devices is reviewed. The major advances in the understanding of magnetization dynamics in the two decades since the discovery of giant magnetoresistance and the prediction of spin-transfer torque are discussed, along with the plethora of new experimental techniques developed to make measurements on shorter length and time scales. Particular consideration is given to time-resolved measurements of the magneto-optical Kerr effect, and it is shown how a succession of studies performed with this technique has led to an improved understanding of the dynamics of nanoscale magnets. The dynamics can be surprisingly rich and complicated, with the latest studies of individual nanoscale elements showing that the dependence of the resonant mode spectrum upon the physical structure is still not well understood. Finally, the article surveys the prospects for development of high-frequency spintronic devices and highlights areas in which further study of fundamental properties will be required within the coming decade.

Large microwave generation from current-driven magnetic vortex oscillators in magnetic tunnel junctions

Spin-polarized current can excite the magnetization of a ferromagnet through the transfer of spin angular momentum to the local spin system. This pure spin-related transport phenomenon leads to alluring possibilities for the achievement of a nanometer scale, complementary metal oxide semiconductor-compatible, tunable microwave generator that operates at low bias for future wireless communication applications. Microwave emission generated by the persistent motion of magnetic vortices induced by a spin-transfer effect seems to be a unique manner to reach appropriate spectral linewidth. However, in metallic systems, in which such vortex oscillations have been observed, the resulting microwave power is much too small. In this study, we present experimental evidence of spin-transfer-induced vortex precession in MgO-based magnetic tunnel junctions, with an emitted power that is at least one order of magnitude stronger and with similar spectral quality. More importantly and in contrast to other spin-transfer excitations, the thorough comparison between experimental results and analytical predictions provides a clear textbook illustration of the mechanism of spin-transfer-induced vortex precession.