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In spin Hall nano-oscillators (SHNOs), pure spin currents drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and may mutually synchronize. Here, we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 × 2 to 8 × 8 nano-constrictions, observed both electrically and using micro-Brillouin light scattering microscopy. On short time scales, where the auto-oscillation linewidth $$\Delta f$$ is governed by white noise, the signal quality factor, $$Q=f/\Delta f$$, increases linearly with the number of mutually synchronized nano-constrictions (N), reaching 170,000 in the largest arrays. We also show that SHNO arrays exposed to two independently tuned microwave frequencies exhibit the same synchronization maps as can be used for neuromorphic vowel recognition. Our demonstrations may hence enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and ultra-fast neuromorphic computing. Synchronization of oscillators can be used to carry out cognitive tasks. Large two-dimensional arrays of synchronized spin Hall nano-oscillators have now been demonstrated, and may in future enable neuromorphic computing on the nanoscale.

We investigate the origin of the experimentally observed varying current-frequency nonlinearity of the propagating spin wave mode in nanocontact spin torque oscillators. Nominally identical devices with 100 nm diameter are characterized by electrical microwave measurements and show large variation in the generated frequency as a function of drive current. This quantitative and qualitative device-to-device variation is described in terms of continuous and discontinuous nonlinear transitions between linear current intervals. The thin-film grain microstructure in our samples is determined using atomic force and scanning electron microscopy to be on the scale of 30 nm. Micromagnetic simulations show that the reflection of spin waves against the grain boundaries results in standing wave resonance configurations. For a simulated device with a single artificial grain, the frequency increases linearly with the drive current until the decreased wavelength eventually forces another spin wave antinode to be formed. This transition results in a discontinuous step in the frequency versus current relation. Simulations of complete, randomly generated grain microstructures additionally shows continuous nonlinearity and a resulting device-to-device variation in frequency that is similar to the experimental levels. The impact of temperature from 4 to 300 K on the resonance mode-transition nonlinearity and frequency noise is investigated using simulations and it is found that the peak levels of the spectral linewidth as a function of drive current agree quantitatively with typical levels found in experiments at room temperature. The impact of the grain microstructure on the localized oscillation modes is also investigated.

Reliable in situ control of spin wave (SW) excitation between localized and propagating SW modes is of great interest for both fundamental and applied spintronics and magnonics. While spin-transfer-torque-generated SWs can typically be tuned directly via the driving current, the frequency of the highest intensity SWs, achieved in the strongly self-localized magnetic droplet soliton, is virtually current independent, as the droplet frequency is given by the intrinsic material properties. Here, we demonstrate, using micromagnetic simulations, how the droplet frequency can be efficiently tuned by an applied voltage through the effect of electric field (E-field)-dependent perpendicular magnetic anisotropy (PMA). It is found that as the PMA decreases, the droplet begins to distort and eventually collapses to give way to propagating SWs. However, due to the geometrically confined structures, the radially propagating SWs are reflected by the periphery boundary of the sample, and then the forward and backward SWs superpose to produce a series of standing SWs. The node number of the standing SWs strongly depends on the sample size as well as the applied E field. These findings provide a deeper understanding of magnetic excitation properties, which will be helpful for designing advanced spintronic devices.

Synchronization of large spin Hall nano-oscillator (SHNO) arrays is an appealing approach toward ultrafast non-conventional computing. However, interfacing to the array, tuning its individual oscillators and providing built-in memory units remain substantial challenges. Here, we address these challenges using memristive gating of W/CoFeB/MgO/AlOx-based SHNOs. In its high resistance state, the memristor modulates the perpendicular magnetic anisotropy at the CoFeB/MgO interface by the applied electric field. In its low resistance state the memristor adds or subtracts current to the SHNO drive. Both electric field and current control affect the SHNO auto-oscillation mode and frequency, allowing us to reversibly turn on/off mutual synchronization in chains of four SHNOs. We also demonstrate that two individually controlled memristors can be used to tune a four-SHNO chain into differently synchronized states. Memristor gating is therefore an efficient approach to input, tune and store the state of SHNO arrays for non-conventional computing models.

Short wavelength exchange-dominated propagating spin waves will enable magnonic devices to operate at higher frequencies and higher data transmission rates. While giant magnetoresistance (GMR)-based magnetic nanocontacts are efficient injectors of propagating spin waves, the generated wavelengths are 2.6 times the nano-contact diameter, and the electrical signal strength remains too weak for applications. Here we demonstrate nano-contact-based spin wave generation in magnetic tunnel junctions and observe large-frequency steps consistent with the hitherto ignored possibility of second- and third-order propagating spin waves with wavelengths of 120 and 74 nm, i.e., much smaller than the 150-nm nanocontact. Mutual synchronization is also observed on all three propagating modes. These higher-order propagating spin waves will enable magnonic devices to operate at much higher frequencies and greatly increase their transmission rates and spin wave propagating lengths, both proportional to the much higher group velocity., Nano-contact-based spin wave generation may enable high-frequency magnonic devices but has been limited to long wavelengths and weak signal strengths. Here the authors demonstrate high-order short-wavelength propagating spin waves with increased transmission rates and propagation lengths in magnetic tunnel junction stacks.

Propagating spin waves generated by a metal-based spin Hall nano-oscillator for highly energy-efficient spin wave technology., Spin-orbit torque (SOT) can drive sustained spin wave (SW) auto-oscillations in a class of emerging microwave devices known as spin Hall nano-oscillators (SHNOs), which have highly nonlinear properties governing robust mutual synchronization at frequencies directly amenable to high-speed neuromorphic computing. However, all demonstrations have relied on localized SW modes interacting through dipolar coupling and/or direct exchange. As nanomagnonics requires propagating SWs for data transfer and additional computational functionality can be achieved using SW interference, SOT-driven propagating SWs would be highly advantageous. Here, we demonstrate how perpendicular magnetic anisotropy can raise the frequency of SOT-driven auto-oscillations in magnetic nanoconstrictions well above the SW gap, resulting in the efficient generation of field and current tunable propagating SWs. Our demonstration greatly extends the functionality and design freedom of SHNOs, enabling long-range SOT-driven SW propagation for nanomagnonics, SW logic, and neuromorphic computing, directly compatible with CMOS technology.

The spin Hall effect in a non-magnetic metal with spin–orbit coupling injects transverse spin currents into adjacent magnetic layers, where the resulting spin transfer torque can drive spin wave auto-oscillations. Such spin Hall nano-oscillators (SHNOs) hold great promise as extremely compact and broadband microwave signal generators and magnonic spin wave injectors. Here we show that SHNOs can also be mutually synchronized with unprecedented efficiency. We demonstrate mutual synchronization of up to nine individual SHNOs, each separated by 300 nm. Through further tailoring of the connection regions we can extend the synchronization range to 4 μm. The mutual synchronization is observed electrically as an increase in the power and coherence of the microwave signal, and confirmed optically using micro-Brillouin light scattering microscopy as two spin wave regions sharing the same spectral content, in agreement with our micromagnetic simulations.

We demonstrate sustained coherent emission of spin waves in NiFe films using rapid demagnetization from high repetition rate femtosecond laser pulse trains. As the pulse separation is shorter than the magnon decay time, magnons having a frequency equal to a multiple of the 1 GHz repetition-rate are coherently amplified. Using scanning micro-Brillouin Light Scattering (BLS) we observe this coherent amplification as strong peaks spaced 1 GHz apart. The BLS counts vs. laser power exhibit a stronger than parabolic dependence consistent with counts being proportional to the square of the magnetodynamic amplitude, and the demagnetization pulse strength being described by a Bloch law. Spatial spin wave mapping demonstrates how both localized and propagating spin waves can be excited, and how the propagation direction can be directly controlled. Our results demonstrate the versatility of BLS spectroscopy for rapid demagnetization studies and enable a new platform for photo-magnonics where sustained coherent spin waves can be utilized., Comment: 7 pages, 7 figures

Time-resolved scanning Kerr microscopy (TRSKM) was used to study precessional magnetization dynamics induced by a radio frequency (RF) current within a ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$/Py(5 nm)/Pt(6 nm)/Au(150 nm) spin Hall nano-oscillator structure. The Au layer was formed into two needle-shaped electrical contacts that concentrated the current in the center of a Py/Pt mesa of 4 $\ensuremath{\mu}\mathrm{m}$ diameter. Due to the spin Hall effect, current within the Pt layer drives a spin current into the Py layer, exerting a spin transfer torque (STT). By injecting RF current and exploiting the phase sensitivity of TRSKM and the symmetry of the device structure, the STT and Oersted field torques have been separated and spatially mapped. The STT and torque due to the in-plane Oersted field are observed to exhibit minima at the device center that is ascribed to spreading of RF current that is not observed for DC current. Torques associated with the RF current may destabilize the position of the self-localized bullet mode excited by the DC current and inhibit injection locking. The present study demonstrates the need to characterize both DC and RF current distributions carefully.

Spin Hall nano-oscillators (SHNOs) generate highly tunable microwave signals at room temperature, and beyond that, the ability of constriction-based SHNOs to phase lock with each other makes them candidates for neuromorphic computing devices. However, most practical applications require operation in only a weak magnetic field, or none at all, so a deeper understanding of SHNO dynamics in weak fields is needed. Here angle-resolved measurements of constriction-based SHNOs under weak in-plane fields reveal both a linearlike spin-wave mode and a bullet soliton, and intrinsic frequency doubling allows output signals above 9 GHz, in fields as low as 40 mT.

Injection of a radio frequency (RF) current was used to phase lock the SHNO to the TRSKM. The out of plane magnetization was detected by means of the polar magneto optical Kerr effect (MOKE). However, longitudinal MOKE images were dominated by an artifact arising from the edges of the Au NCs. Time resolved imaging revealed the simultaneous excitation of a non-linear `bullet' mode at the centre of the device, once the DC current exceeded a threshold value, and ferromagnetic resonance (FMR) induced by the RF current. However, the FMR response observed for sub-critical DC current values exhibits an amplitude minimum at the centre, which is attributed to spreading of the RF spin current due to the reactance of the device structure. This FMR response can be subtracted to yield images of the bullet mode. As the DC current is increased above threshold, the bullet mode appears to increase in size, suggesting increased translational motion. The reduced spatial overlap of the bullet and FMR modes, and this putative translational motion, may impede the injection locking and contribute to the reduced locking range observed within NC-SHNO devices. This illustrates a more general need to control the geometry of an injection-locked oscillator so that the autonomous dynamics of the oscillator exhibit strong spatial overlap with those resulting from the injected signal.

Magnetic droplets are nontopological dynamical solitons that can be nucleated in nanocontact based spin torque nano-oscillators (STNOs) with perpendicular magnetic anisotropy free layers. While theory predicts that the droplet should be of the same size as the nanocontact, its inherent drift instability has thwarted attempts at observing it directly using microscopy techniques. Here, we demonstrate highly stable magnetic droplets in all-perpendicular STNOs and present the first detailed droplet images using scanning transmission X-ray microscopy. In contrast to theoretical predictions, we find that the droplet diameter is about twice as large as the nanocontact. By extending the original droplet theory to properly account for the lateral current spread underneath the nanocontact, we show that the large discrepancy primarily arises from current-in-plane Zhang-Li torque adding an outward pressure on the droplet perimeter. Electrical measurements on droplets nucleated using a reversed current in the antiparallel state corroborate this picture.

We use micromagnetic simulations to map out and compare, the linear and auto-oscillating modes in constriction-based spin Hall nano-oscillators as a function of applied magnetic field with varying magnitude and out-of-plane angle. We demonstrate that for all possible applied field configurations the auto-oscillations emerge from the localized linear modes of the constriction. For field directions tending towards the plane, these modes are of the so-called "edge" type, i.e. localized at the opposite sides of the constriction. When the magnetization direction instead approaches the film normal, the modes transform to the so-called "bulk" type, i.e. localized inside the constriction with substantially increased precession volume, consistent with the re-distribution of the magnetic charges from the sides to the top and bottom surfaces of the constriction. In general, the threshold current of the corresponding auto-oscillations increases with the applied field strength and decreases with its out-of-plane angle, consistent with the behavior of the internal field and in good agreement with a macrospin model. A quantitative agreement is then achieved by taking into account the strongly non-uniform character of the system via a mean-field approximation. Both the Oe field and the spin transfer torque from the drive current increase the localization and decrease the frequency of the observed mode. Furthermore, the anti-symmetric Oe field breaks the lateral symmetry, favoring the localized mode at one of the two constriction edges, in particular for large out-of-plane field angles where the threshold current is significantly increased and the edge demagnetization is suppressed., Comment: 8 pages, 7 figures

Thermal fluctuations play an increasingly important role in micromagnetic research relevant for various biomedical and other technological applications. Until now, it was deemed necessary to use a time stepping algorithm with a fixed time step in order to perform micromagnetic simulations at nonzero temperatures. However, Berkov and Gorn have shown that the drift term which generally appears when solving stochastic differential equations can only influence the length of the magnetization. This quantity is however fixed in the case of the stochastic Landau-Lifshitz-Gilbert equation. In this paper, we exploit this fact to straightforwardly extend existing high order solvers with an adaptive time stepping algorithm. We implemented the presented methods in the freely available GPU-accelerated micromagnetic software package MuMax3 and used it to extensively validate the presented methods. Next to the advantage of having control over the error tolerance, we report a twenty fold speedup without a loss of accuracy, when using the presented methods as compared to the hereto best practice of using Heun's solver with a small fixed time step., 9 pages, 9 figures

We present an efficient method to tailor propagating spin waves in quasi-confined systems. We use nanocontact spin-torque nano-oscillators based on NiFe/Cu/Co spin-valves and study the ferromagnetic and spin-wave resonances (FMR and SWR) of both layers. We employ homodyne-detected ferromagnetic resonance spectroscopy, resembling spin-torque FMR, to detect the magnetodynamics. The external field is applied in-plane, giving a parallel configuration of the magnetic layers, which do not provide any spin-transfer torque. Instead, the excitation is caused by the Oersted field. By varying the thickness of the bottom Cu electrode ( t Cu ) of the devices, we tune the current distribution in the samples, and thereby the Oersted field, which governs the spin wave characteristics. Both the average k-vector and the bandwidth of the SWR increases as t Cu increases.

We demonstrate the control of Gilbert damping in 65-nm-thick yttrium iron garnet (YIG) films using a spin-polarized current generated by a direct current through a nanocontact, spin filtered by a t ...

This work provides a detailed investigation of the measured in-plane field-swept homodyne-detected ferromagnetic resonance (FMR) spectra of an extended Co/Cu/NiFe pseudo spin valve stack using a nanocontact (NC) geometry. The magnetodynamics are generated by a pulse-modulated microwave current and the resulting rectified dc mixing voltage, which appears across the NC at resonance, is detected using a lock-in amplifier. Most notably, we find that the measured spectra of the NiFe layer are composite in nature and highly asymmetric, consistent with the broadband excitation of multiple modes. Additionally, the data must be fit with two Lorentzian functions in order to extract a reasonable value for the Gilbert damping of the NiFe. Aided by micromagnetic simulations, we conclude that (i) for in-plane fields the rf Oersted field in the vicinity of the NC plays the dominant role in generating the observed spectra, (ii) in addition to the FMR mode, exchange dominated spin waves are also generated, and (iii) the NC diameter sets the mean wavevector of the exchange dominated spin wave, in good agreement with the dispersion relation., 7 pages, 7 figures

A phenomenological equation called Landau-Lifshitz-Baryakhtar (LLBar) equation, which could be viewed as the combination of Landau-Lifshitz (LL) equation and an extra "exchange damping" term, was derived by Baryakhtar using Onsager's relations. We interpret the origin of this "exchange damping" as nonlocal damping by linking it to the spin current pumping. The LLBar equation is investigated numerically and analytically for the spin wave decay and domain wall motion. Our results show that the lifetime and propagation length of short-wavelength magnons in the presence of nonlocal damping could be much smaller than those given by LL equation. Furthermore, we find that both the domain wall mobility and the Walker breakdown field are strongly influenced by the nonlocal damping., Comment: 10 pages, 6 figures

In the last twenty years, numerical modeling has become an indispensable part of magnetism research. It has become a standard tool for both the exploration of new systems and for the interpretation of experimental data. In the last five years, the capabilities of micromagnetic modeling have dramatically increased due to the deployment of graphical processing units (GPU), which have sped up calculations to a factor of 200. This has enabled many studies which were previously unfeasible. In this topical review, we give an overview of this modeling approach and show how it has contributed to the forefront of current magnetism research.

In this work, a self-consistent thermodynamic approach to micromagnetism is presented. The magnetic degrees of freedom are modeled using the Landau-Lifshitz-Baryakhtar theory, that separates the different contributions to the magnetic damping, and thereby allows them to be coupled to the electron and phonon systems in a self-consistent way. We show that this model can quantitatively reproduce ultrafast magnetization dynamics in Nickel., 5 pages, 3 figures

We report a numerical implementation of the Landau-Lifshitz-Baryakhtar theory that dictates that the micromagnetic relaxation term obeys the symmetry of the magnetic crystal, i.e., replacing the single intrinsic damping constant with a tensor of corresponding symmetry. The effect of anisotropic relaxation is studied in a thin saturated ferromagnetic disk and an ellipse with and without uniaxial magnetocrystalline anisotropy. We investigate the angular dependence of the linewidth of magnonic resonances with respect to the given structure of the relaxation tensor. The simulations suggest that the anisotropy of the magnonic linewidth is determined by two factors: the projection of the relaxation tensor onto the plane of precession and the ellipticity of the latter.

Dynamic dipolar interactions between spin wave eigenmodes of closely spaced nanomagnets determine the collective behavior of magnonic and spintronic metamaterials and devices. However, dynamic dipolar interactions are difficult to quantify since their effects must be disentangled from those of static dipolar interactions and variations in the shape, size, and magnetic properties of the nanomagnets. It is shown that when two imperfect nanoscale magnetic disks with similar but nonidentical modes are brought into close proximity, the effect of the dynamic dipolar interaction can be detected by considering the difference of the phase of precession within the two disks. Measurements show that the interaction is stronger than expected from micromagnetic simulations, highlighting both the need for characterization and control of magnetic properties at the deep nanoscale, and also the potential for improved control of collective magnetic phenomena. Our approach is equally applicable to other physical systems in which dynamic interactions are obscured by inhomogeneous broadening and static interactions.

An all-optical experiment long utilized to image phonons excited by ultrashort optical pulses has been applied to a magnetic sample. In addition to circular ripples due to surface acoustic waves, we observe an X-shaped pattern formed by propagating spin waves. The emission of spin waves from the optical pulse epicenter in the form of collimated beams is qualitatively reproduced by micromagnetic simulations. We explain the observed pattern in terms of the group velocity distribution of Damon-Eshbach magnetostatic spin waves in the reciprocal space and the wave vector spectrum of the focused ultrafast laser pulse.

A review is provided of recent time-resolved scanning Kerr microscopy experiments and micromagnetic simulations of magnetization dynamics in single nanomagnets, and in pairs of dipolar coupled nanomagnets. Two nanomagnet systems are presented. In a single 440 nm square, the effect of the pulsed field amplitude on the relative amplitudes of center- and edge-type confined spin wave modes is explored. In addition, the difference in the damping of dynamics observed in different magnetic ground states is discussed. In pairs of 300 nm disks, the relative effect of structural imperfections and static dipolar fields on the splitting of edge-modes is investigated as a function of disk separation.

We review the use of numerical micromagnetic simulations (“micromagnetics”) for investigations in magnonics, the study of spin waves and their quanta – magnons. We argue that, when used with suitable post-processing tools, micromagnetics provide the power and flexibility necessary both for interpretation of complex magnonic phenomena observed in realistic magnetic structures and devices and for prediction of novel effects. We foresee that the development of multiscale and multiphysics extensions of micromagnetic solvers will broaden both the scope of micromagnetic simulations in magnonics and the field of magnonics itself. For example, the extension of micromagnetics to solvers based on atomistic spin models will underpin application of the developed methodology to studies of phenomena involving both magnons and other fundamental excitations of the solid state. In a more distant perspective, it is highly intriguing to study spin waves in non-stationary conditions (i.e. in structures with time dependent material properties), such as those realized in experiments with samples under ultrafast optical pumping.

We present a method of calculation of the effective magnetic permeability of magnonic metamaterials containing arrays of magnetic inclusions of arbitrary shapes. The method fully takes into account the spectrum of spin waves confined in the inclusions. We evaluate the method by considering a particular case of a metamaterial formed by a stack of identical two-dimensional (2D) periodic hexagonal arrays of disk-shaped magnetic inclusions in a nonmagnetic matrix. Two versions of the method are considered. The first approach is based on a simple semianalytical theory that uses the numerically calculated susceptibility tensor of an isolated inclusion as input data for an analytical calculation in which the magnetodipole interaction between inclusions within each 2D array is taken into account. In the second approach, we employ micromagnetic packages with periodic boundary conditions to calculate the susceptibility of the whole 2D periodic array of such inclusions. The comparison of the two approaches reveals the necessity of retaining higher-order terms in the analytical calculation of the magnetodipole interaction via the multipole expansion. Models limited to the dipolar term can lead to remarkable underestimation of the effect of the magnetodipole interaction, in particular, for modes localized near the edge regions of inclusions. To calculate the susceptibility tensor of an isolated inclusion, we have implemented two different methods: (a) a method based on micromagnetic simulations, in which we have compared three different micromagnetic packages: the finite-element package nmag and the two finite differences packages oommf and micromagus, and (b) the modified dynamical matrix method (DMM). The comparison of the different micromagnetic packages and the DMM (based on the calculation of the susceptibility tensor of an isolated inclusion) demonstrate that their results agree to within 3%. Frequency regions in which the metamaterial is characterized by the negative permeability are identified. We speculate that the proposed methodology could be generalized to more complex arrangements of magnetic inclusions, e.g., to those with multiple periods or fractal arrangements, as well as to arrays of inclusions with a distribution of properties. � 2012 American Physical Society.

We report a numerical study of the dispersion of collective magnonic modes in magnonic crystals formed by stacks of magnetostatically coupled magnetic nanoelements. The calculations reveal that the sign of the magnonic dispersion is determined by the spatial character and ellipticity of precession for the eigenmodes of the isolated elements that give rise to the magnonic bands. We identify a critical value of the ellipticity at which the dispersion of the collective magnonic modes changes sign. The critical value is independent of the magnetic parameters and shape of the elements but is a characteristic of their arrangement (superstructure).

We report a continuous medium theory of dispersion and scattering of spin waves propagating in thin nanowire magnonic waveguides with curved regions. Assuming that the static magnetization is aligned along the waveguide, the curvature leads to a “geometrical” effective magnetic field term that is proportional to the square of the ratio of the exchange length to the radius of curvature of the waveguide. The term is small enough to favor the use of bended nanowire waveguides in planar magnonic data architectures. However, a stronger (multiple) winding (e.g., within helical structures) could enable design of magnonic waveguides with desired properties.

We use time resolved scanning Kerr microscopy and analytical and numerical calculations to demonstrate coupling of uniform global microwave field to propagating spin waves for emerging magnonic architectures. The coupling is mediated by the local dynamic dipolar field produced by the magnetization of a resonantly driven all-metallic magnetic microwave-to-spin-wave transducer. The local dipolar field can exceed that of the incident microwave field by one order of magnitude. Our numerical simulations demonstrate the ability of the transducer to unidirectionally emit coherent exchange spin waves of nanoscale wavelengths with the emission direction programmed by the magnetic state of the transducer.

We have used micromagnetic simulations to demonstrate a method for controlling the amplitude and phase of spin waves propagating inside a magnonic waveguide. The method employs a nanomagnet formed on top of a magnonic waveguide. The function of the proposed device is controlled by defining the static magnetization direction of the nanomagnet. The result is a valve or phase shifter for spin waves, acting as the carrier of information for computation or data processing within the emerging spin wave logic architectures of magnonics. The proposed concept offers such technically important benefits as energy efficiency, non-volatility, and miniaturization.

Designers of nano-scale magnonic devices would benefit from methods of their evaluation that do not require one to access the microscopic level of description or to construct device prototypes. Here, we propose a numerical micromagnetics version of such a method, in which magnonic devices are considered as two-port linear networks and can therefore be described in terms of their s-parameters (i.e., reflection and transmission characteristics). In the micromagnetic model, the sample is composed from a magnonic device-under-test situated between input and output magnonic waveguides. First, dispersion relations and amplitudes of spin waves in the input and output waveguides are calculated from the simulations. The results are then compared to derive the s-parameters of the device-under-test. We use a simple rectangular magnetic nonuniformity, for which analytical results are readily obtained, to evaluate the efficiency and limitations of the technique in the sub-terahertz band.

Large amplitude magnetization dynamics of a single square nanomagnet have been studied by time-resolved Kerr microscopy. Experimental spectra revealed that only a single mode was excited for all bias field values. Micromagnetic simulations demonstrate that at larger pulsed field amplitudes the center mode dominates the dynamic response while the edge mode is almost completely suppressed. Controlled suppression of edge modes in a single nanomagnet has potential applications in the operation of nanoscale spin transfer torque oscillators and bistable switching devices for which the amplitude of the magnetization trajectory is often large and a more uniform dynamic response is desirable.

We report upon a theoretical study of collective magnonic modes in pairs of magnetic nano-elements with quasi-uniform magnetization. The mode spectrum and character are numerically computed for an individual isolated nano-element and then used to analytically calculate the splitting of the modes due to the inter-element magneto-dipole interaction. The results are compared with those obtained using direct simulations for the pairs of elements, yielding a generally good agreement. For the edge mode the interaction between the edges of the neighboring elements can exceed that between the edges of the same element, leading to softening of the mode profile and hence to the violation of the assumptions of the analytical approach. The softening has to be taken into account in the interpretation of dynamical studies of closely packed arrays of magnetic elements (magnonic crystals).