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This study introduces a method for the characterization of the magnetoelectric coupling in nanoscale Pb(Zr,Ti)O3/CoFeB thin film composites based on propagating spin-wave spectroscopy. Finite element simulations of the strain distribution in the devices indicated that the magnetoelastic effective field in the CoFeB waveguides was maximized in the Damon - Eshbach configuration. All-electrical broadband propagating spin-wave transmission measurements were conducted on Pb(Zr,Ti)O3/CoFeB magnetoelectric waveguides with lateral dimensions down to 700 nm. The results demonstrated that the spin-wave resonance frequency can be modulated by applying a bias voltage to Pb(Zr,Ti)O3. The modulation is hysteretic due to the ferroelastic behavior of Pb(Zr,Ti)O3. An analytical model was then used to correlate the change in resonance frequency to the induced magnetoelastic field in the magnetostrictive CoFeB waveguide. We observe a hysteresis magnetoelastic field strength with values as large as 5.61 mT, and a non-linear magnetoelectric coupling coefficient with a maximum value of 1.69 mT/V., Comment: This project has received funding from the European Union's Horizon Europe research and innovation programme under grant agreement No 101070536 - project MandMEMS

We study experimentally the processes of parametric excitation in microscopic magnetically saturated disks of nanometer-thick Yttrium Iron Garnet. We show that, depending on the relative orientation between the parametric pumping field and the static magnetization, excitation of either degenerate or non-degenerate magnon pairs is possible. In the latter case, which is particularly important for applications associated with the realization of computation in the reciprocal space, a single-frequency pumping can generate pairs of magnons whose frequencies correspond to different eigenmodes of the disk. We show that, depending on the size of the disk and the modes involved, the frequency difference in a pair can vary in the range 0.1-0.8 GHz. We demonstrate that in this system, one can easily realize a practically important situation where several magnon pairs share the same mode. We also observe the simultaneous generation of up to six different modes using a fixed-frequency monochromatic pumping. Our experimental findings are supported by numerical calculations that allow us to unambiguously identify the excited modes. Our results open new possibilities for the implementation of reciprocal-space computing making use of low damping magnetic insulators., Comment: 18 pages, 4 figures

Magnonic nano-devices exploit magnons -- quanta of spin waves -- to transmit and process information within a single integrated platform that has the potential to outperform traditional semiconductor-based electronics for low power applications. The main missing cornerstone of this information nanotechnology is an efficient scheme for the direct amplification of propagating spin waves. The recent discovery of spin-orbit torque provided an elegant mechanism for propagation losses compensation. While partial compensation of the spin-wave damping has allowed for spin-wave signal modulation, true amplification - the exponential increase in the spin-wave intensity during propagation - has so far remained elusive. Here we evidence the operating conditions to achieve unambiguous amplification using clocked nanoseconds-long spin-orbit torque pulses in sub-micrometer wide magnonic waveguides, where the effective magnetization has been engineered to be close to zero to suppress the detrimental magnon-magnon scattering. As a result, we achieve an exponential increase in the intensity of propagating spin waves up to 500 % at a propagation distance of several micrometers. These results pave the way towards the implementation of energy efficient, cascadable magnonic architectures for wave-based information processing and complex on-chip computation., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Nature Communications, and is available online at https://doi.org/10.1038/s41467-024-45783-1

Thin garnet films are becoming central for magnon-spintronics and spin-orbitronics devices as they show versatile magnetic properties together with low magnetic losses. These fields would benefit from materials in which heat does not affect the magnetization dynamics, an effect known as the non-linear thermal frequency shift. In this study, low damping Bi substituted Iron garnet (Bi:YIG) ultra-thin films have been grown using Pulsed Laser Deposition. Through a fine tuning of the growth parameters, the precise control of the perpendicular magnetic anisotropy allows to achieve a full compensation of the dipolar magnetic anisotropy. Strikingly, once the growth conditions are optimized, varying the growth temperature from 405 {\deg}C to 475 {\deg}C as the only tuning parameter induces the easy-axis to go from out-of-plane to in-plane. For films that are close to the dipolar compensation, Ferromagnetic Resonance measurements yield an effective magnetization $\mu _{0}M_{eff} (T)$ that has almost no temperature dependence over a large temperature range (260 K to 400 K) resulting in an anisotropy temperature exponent of 2. These findings put Bi:YIG system among the very few materials in which the temperature dependence of the magnetic anisotropy varies at the same rate than the saturation magnetization. This interesting behavior is ascribed phenomenologically to the sizable orbital moment of $Bi^{3+}$., Comment: 15 pages 4 figures and supplemental Material

We present the parametric excitation of spin-wave modes in YIG micro-disks via parallel pumping. Their spectroscopy is performed using magnetic resonance force microscopy (MRFM), while their spatial profiles are determined by micro-focus Brillouin light scattering (BLS). We observe that almost all the fundamental eigenmodes of an in-plane magnetized YIG micro-disk, calculated using a micromagnetic eigenmode solver, can be excited using the parallel pumping scheme, as opposed to the transverse one. The comparison between the MRFM and BLS data on one side, and the simulations on the other side, provides the complete spectroscopic labeling of over 40 parametrically excited modes. Our findings could be promising for spin-wave-based computation schemes, in which the amplitudes of a large number of spin-wave modes have to be controlled., Comment: 6 pages, 4 figures

Spintronic nano-synapses and nano-neurons perform complex cognitive computations with high accuracy thanks to their rich, reproducible and controllable magnetization dynamics. These dynamical nanodevices could transform artificial intelligence hardware, provided that they implement state-of-the art deep neural networks. However, there is today no scalable way to connect them in multilayers. Here we show that the flagship nano-components of spintronics, magnetic tunnel junctions, can be connected into multilayer neural networks where they implement both synapses and neurons thanks to their magnetization dynamics, and communicate by processing, transmitting and receiving radio frequency (RF) signals. We build a hardware spintronic neural network composed of nine magnetic tunnel junctions connected in two layers, and show that it natively classifies nonlinearly-separable RF inputs with an accuracy of 97.7%. Using physical simulations, we demonstrate that a large network of nanoscale junctions can achieve state-of the-art identification of drones from their RF transmissions, without digitization, and consuming only a few milliwatts, which is a gain of more than four orders of magnitude in power consumption compared to currently used techniques. This study lays the foundation for deep, dynamical, spintronic neural networks.

Extracting information from radiofrequency (RF) signals using artificial neural networks at low energy cost is a critical need for a wide range of applications from radars to health. These RF inputs are composed of multiples frequencies. Here we show that magnetic tunnel junctions can process analogue RF inputs with multiple frequencies in parallel and perform synaptic operations. Using a backpropagation-free method called extreme learning, we classify noisy images encoded by RF signals, using experimental data from magnetic tunnel junctions functioning as both synapses and neurons. We achieve the same accuracy as an equivalent software neural network. These results are a key step for embedded radiofrequency artificial intelligence., Comment: 9 pages, 5 figures

The main limitation in order to exploit spin torque nano-oscillators (STNOs) in various potential applications is their large phase noise. In this work, we demonstrate its efficient reduction by a highly reconfigurable, compact, specifically on-chip designed PLL based on custom integrated circuits. First, we thoroughly study the parameter space of the PLL+STNO system experimentally. Second, we present a theory which describes the locking of a STNO to an external signal in a general sense. In our developed theory, we do not restrict ourselves to the case of a perfect phase locking but also consider phase slips and the corresponding low offset frequency $1/f^2$ noise, so far the main drawback in such systems. Combining experiment and theory allows us to reveal complex parameter dependences of the system's phase noise. The results provide an important step for the optimization of noise properties and thus leverage the exploitation of STNOs in prospective real applications.

The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D) eigenvalue problem is studied in a general sense in mathematical physics, and has in the last decade successively reached the scope of experiments. In coupled systems, it gives rise to unique physical phenomena, which enable novel approaches for the development of seminal types of highly sensitive sensors. Here, we demonstrate at room temperature the emergence of EPs in coupled spintronic nanoscale oscillators and hence exploit the system's non-hermiticity. We describe the observation of amplitude death of self-oscillations and other complex dynamics, and develop a linearized non-hermitian model of the coupled spintronic system, which properly describes the main experimental features. Interestingly, these spintronic nanoscale oscillators are deployment-ready in different applicational technologies, such as field, current or rotation sensors, radiofrequeny and wireless devices and, more recently, novel neuromorphic hardware solutions. Their unique and versatile properties, notably their large nonlinear behavior, open up unprecedented perspectives in experiments as well as in theory on the physics of exceptional points. Furthermore, the exploitation of EPs in spintronics devises a new paradigm for ultrasensitive nanoscale sensors and the implementation of complex dynamics in the framework of non-conventional computing.

Multiferroics offer an elegant means to implement voltage-control and on the fly reconfigurability in microscopic, nanoscaled systems based on ferromagnetic materials. These properties are particularly interesting for the field of magnonics, where spin waves are used to perform advanced logical or analogue functions. Recently, the emergence of nano-magnonics {\color{black} is expected to} eventually lead to the large-scale integration of magnonic devices. However, a compact voltage-controlled, on demand reconfigurable magnonic system has yet to be shown. Here, we introduce the combination of multiferroics with ferromagnets in a fully epitaxial heterostructure to achieve such voltage-controlled and reconfigurable magnonic systems. Imprinting a remnant electrical polarization in thin multiferroic $\mathrm{BiFeO_3}$ with a periodicity of $500\,\mathrm{nm}$ yields a modulation of the effective magnetic field in the micron-scale, ferromagnetic $\mathrm{La_{2/3}Sr_{1/3}MnO_3}$ magnonic waveguide. We evidence the magneto-electrical coupling by characterizing the spin wave propagation spectrum in this artificial, voltage induced, magnonic crystal and demonstrate the occurrence of a robust magnonic bandgap with $>20 \,\mathrm{dB}$ rejection.

Vortex based spin torque nano oscillators (STVOs) can present more complex dynamics than the spin torque induced gyrotropic (G) motion of the vortex core. The respective dynamic modes and the transition between them can be controlled by experimental parameters such as the applied dc current. An interesting behavior is the stochastic transition from the G- to a dynamic C-state occurring for large current densities. Moreover, the C-state oscillations exhibit a constant active magnetic volume. We present noise measurements in the different dynamic states that allow accessing specific properties of the stochastic transition, such as the characteristic state transition frequency. Furthermore,we confirm, as theoretically predicted, an increase of flicker noise with $I_{dc}^2$ when the oscillation volume remains constant with the current. These results bring insight into the potential optimization of noise properties sought for many potential rf applications with spin torque oscillators. Furthermore, the investigated stochastic characteristics open up new potentialities, for instance in the emerging field of neuromorphic computing schemes.

Artificial neural networks are a valuable tool for radio-frequency (RF) signal classification in many applications, but digitization of analog signals and the use of general purpose hardware non-optimized for training make the process slow and energetically costly. Recent theoretical work has proposed to use nano-devices called magnetic tunnel junctions, which exhibit intrinsic RF dynamics, to implement in hardware the Multiply and Accumulate (MAC) operation, a key building block of neural networks, directly using analogue RF signals. In this article, we experimentally demonstrate that a magnetic tunnel junction can perform multiplication of RF powers, with tunable positive and negative synaptic weights. Using two magnetic tunnel junctions connected in series we demonstrate the MAC operation and use it for classification of RF signals. These results open the path to embedded systems capable of analyzing RF signals with neural networks directly after the antenna, at low power cost and high speed., Comment: 10 pages, 4 figures

Performance of magnetoresistive sensors is today mainly limited by their 1/f low-frequency noise. Here, we study this noise component in vortex-based TMR sensors. We compare the noise level in different magnetization configurations of the device, i.e vortex state or uniform parallel or antiparallel states. We find that the vortex state is at least an order of magnitude noisier than the uniform states. Nevertheless, by activating the spin-transfer induced dynamics of the vortex configuration, we observe a reduction of the 1/f noise, close to the values measured in the AP state, as the vortex core has a lower probability of pinning into defect sites. Additionally, by driving the dynamics of the vortex core by a non-resonant rf field or current we demonstrate that the 1/f noise can be further decreased. The ability to reduce the 1/f low-frequency noise in vortex-based devices by leveraging their spin-transfer dynamics thus enhances their applicability in the magnetic sensors' landscape.

In the present study, we investigate a dynamical mode beyond the gyrotropic (G) motion of a magnetic vortex core in a confined magnetic disk of a nano-pillar spin torque nano oscillator. It is characterized by the in-plane circular precession associated to a C-shaped magnetization distribution. We show a transition between G and C-state mode which is found to be purely stochastic in a current-controllable range. Supporting our experimental findings with micromagnetic simulations, we believe that the results provide novel opportunities for the dynamic and stochastic control of STOs, which could be interesting to be implemented for example in neuromorphic networks.

The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape. However, in nonlinear oscillators, such as spin torque nano oscillators, the frequency spectrum can become particularly complex. This is specifically true when not only considering thermal but also colored $1/f$ flicker noise processes, which are crucial in the context of the oscillator's long term stability. In this study, we address the frequency spectrum of spin torque oscillators in the regime of large-amplitude steady oscillations experimentally and as well theoretically. We particularly take both thermal and flicker noise into account. We perform a series of measurements of the phase noise and the spectrum on spin torque vortex oscillators, notably varying the measurement time duration. Furthermore, we develop the modelling of thermal and flicker noise in Thiele equation based simulations. We also derive the complete phase variance in the framework of the nonlinear auto-oscillator theory and deduce the actual frequency spectrum. We investigate its dependence on the measurement time duration and compare with the experimental results. Long term stability is important in several of the recent applicative developments of spin torque oscillators. This study brings some insights on how to better address this issue.

The brain naturally binds events from different sources in unique concepts. It is hypothesized that this process occurs through the transient mutual synchronization of neurons located in different regions of the brain when the stimulus is presented. This mechanism of binding through synchronization can be directly implemented in neural networks composed of coupled oscillators. To do so, the oscillators must be able to mutually synchronize for the range of inputs corresponding to a single class, and otherwise remain desynchronized. Here we show that the outstanding ability of spintronic nano-oscillators to mutually synchronize and the possibility to precisely control the occurrence of mutual synchronization by tuning the oscillator frequencies over wide ranges allows pattern recognition. We demonstrate experimentally on a simple task that three spintronic nano-oscillators can bind consecutive events and thus recognize and distinguish temporal sequences. This work is a step forward in the construction of neural networks that exploit the non-linear dynamic properties of their components to perform brain-inspired computations.

Magnetic tunnel junctions are nanoscale spintronic devices with microwave generation and detection capabilities. Here we use the rectification effect called "spin-diode" in a magnetic tunnel junction to wirelessly detect the microwave emission of another junction in the auto-oscillatory regime. We show that the rectified spin-diode voltage measured at the receiving junction end can be reconstructed from the independently measured auto-oscillation and spin diode spectra in each junction. Finally we adapt the auto-oscillator model to the case of spin-torque oscillator and spin-torque diode and we show that accurately reproduces the experimentally observed features. These results will be useful to design circuits and chips based on spintronic nanodevices communicating through microwaves.

Spin-based electronics has evolved into a major field of research that broadly encompasses different classes of materials, magnetic systems, and devices. This review describes recent advances in spintronics that have the potential to impact key areas of information technology and microelectronics. We identify four main axes of research: nonvolatile memories, magnetic sensors, microwave devices, and beyond-CMOS logic. We discuss state-of-the-art developments in these areas as well as opportunities and challenges that will have to be met, both at the device and system level, in order to integrate novel spintronic functionalities and materials in mainstream microelectronic platforms., Comment: Review written by the SpinFactory European Consortium

Arrays of spin-torque nano-oscillators are promising for broadband microwave signal detection and processing, as well as for neuromorphic computing. In many of these applications, the oscillators should be engineered to have equally-spaced frequencies and equal sensitivity to microwave inputs. Here we design spin-torque nano-oscillator arrays with these rules and estimate their optimum size for a given sensitivity, as well as the frequency range that they cover. For this purpose, we explore analytically and numerically conditions to obtain vortex spin-torque nano-oscillators with equally-spaced gyrotropic oscillation frequencies and having all similar synchronization bandwidths to input microwave signals. We show that arrays of hundreds of oscillators covering ranges of several hundred MHz can be built taking into account nanofabrication constraints.

Low frequency noise close to the carrier remains little explored in spin torque nano oscillators. However, it is crucial to investigate as it limits the oscillator's frequency stability. This work addresses the low offset frequency flicker noise of a TMR-based spin-torque vortex oscillator in the regime of large amplitude steady oscillations. We first phenomenologically expand the nonlinear auto-oscillator theory aiming to reveal the properties of this noise. We then present a thorough experimental study of the oscillator's $1/f$ flicker noise and discuss the results based on the theoretical predictions. Hereby, we connect the oscillator's nonlinear dynamics with the concept of flicker noise and furthermore refer to the influence of a standard $1/f$ noise description based on the Hooge formula, taking into account the non-constant magnetic oscillation volume, which contributes to the magnetoresistance., Comment: 10 pages

Strongly out-of-equilibrium regimes in magnetic nanostructures exhibit novel properties, linked to the nonlinear nature of magnetization dynamics, which are of great fundamental and practical interest. Here, we demonstrate that field-driven ferromagnetic resonance can occur with substantial spatial coherency at unprecedented large angle of magnetization precessions, which is normally prevented by the onset of spin-wave instabilities and magnetization turbulent dynamics. Our results show that this limitation can be overcome in nanomagnets, where the geometric confinement drastically reduces the density of spin-wave modes. The obtained deeply nonlinear ferromagnetic resonance regime is probed by a new spectroscopic technique based on the application of a second excitation field. This enables to resonantly drive slow coherent magnetization nutations around the large angle periodic trajectory. Our experimental findings are well accounted for by an analytical model derived for systems with uniaxial symmetry. They also provide new means for controlling highly nonlinear magnetization dynamics in nanostructures, which open interesting applicative opportunities in the context of magnetic nanotechnologies.

Spin-torque nano-oscillators can emulate neurons at the nanoscale. Recent works show that the non-linearity of their oscillation amplitude can be leveraged to achieve waveform classification for an input signal encoded in the amplitude of the input voltage. Here we show that the frequency and the phase of the oscillator can also be used to recognize waveforms. For this purpose, we phase-lock the oscillator to the input waveform, which carries information in its modulated frequency. In this way we considerably decrease amplitude, phase and frequency noise. We show that this method allows classifying sine and square waveforms with an accuracy above 99% when decoding the output from the oscillator amplitude, phase or frequency. We find that recognition rates are directly related to the noise and non-linearity of each variable. These results prove that spin-torque nano-oscillators offer an interesting platform to implement different computing schemes leveraging their rich dynamical features.

A magnetic material combining low losses and large Perpendicular Magnetic Anisotropy (PMA) is still a missing brick in the magnonic and spintronic fields. We report here on the growth of ultrathin Bismuth doped Y$_{3}$Fe$_{5}$O$_{12}$ (BiYIG) films on Gd$_{3}$Ga$_{5}$O$_{12}$ (GGG) and substituted GGG (sGGG) (111) oriented substrates. A fine tuning of the PMA is obtained using both epitaxial strain and growth induced anisotropies. Both spontaneously in-plane and out-of-plane magnetized thin films can be elaborated. Ferromagnetic Resonance (FMR) measurements demonstrate the high dynamic quality of these BiYIG ultrathin films, PMA films with Gilbert damping values as low as 3 10$^{-4}$ and FMR linewidth of 0.3 mT at 8 GHz are achieved even for films that do not exceed 30 nm in thickness. Moreover, we measure Inverse Spin Hall Effect (ISHE) on Pt/BiYIG stacks showing that the magnetic insulator$'$s surface is transparent to spin current making it appealing for spintronic applications., Comment: 17 pages, 4 figures and 8 pages of Supp. informations

Substantial evidence indicates that the brain uses principles of non-linear dynamics in neural processes, providing inspiration for computing with nanoelectronic devices. However, training neural networks composed of dynamical nanodevices requires finely controlling and tuning their coupled oscillations. In this work, we show that the outstanding tunability of spintronic nano-oscillators can solve this challenge. We successfully train a hardware network of four spin-torque nano-oscillators to recognize spoken vowels by tuning their frequencies according to an automatic real-time learning rule. We show that the high experimental recognition rates stem from the high frequency tunability of the oscillators and their mutual coupling. Our results demonstrate that non-trivial pattern classification tasks can be achieved with small hardware neural networks by endowing them with non-linear dynamical features: here, oscillations and synchronization. This demonstration is a milestone for spintronics-based neuromorphic computing.

We report a study on spin conductance in ultra-thin films of Yttrium Iron Garnet (YIG), where spin transport is provided by propagating spin waves, that are generated and detected by direct and inverse spin Hall effects in two Pt wires deposited on top. While at low current the spin conductance is dominated by transport of thermal magnons, at high current, the spin conductance is dominated by low-damping non-equilibrium magnons thermalized near the spectral bottom by magnon-magnon interaction, with consequent a sensitivity to the applied magnetic field and a longer decay length. This picture is supported by microfocus Brillouin Light Scattering spectroscopy.

Neurons in the brain behave as non-linear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behavior to realize high density, low power neuromorphic computing will require huge numbers of nanoscale non-linear oscillators. Indeed, a simple estimation indicates that, in order to fit a hundred million oscillators organized in a two-dimensional array inside a chip the size of a thumb, their lateral dimensions must be smaller than one micrometer. However, despite multiple theoretical proposals, there is no proof of concept today of neuromorphic computing with nano-oscillators. Indeed, nanoscale devices tend to be noisy and to lack the stability required to process data in a reliable way. Here, we show experimentally that a nanoscale spintronic oscillator can achieve spoken digit recognition with accuracies similar to state of the art neural networks. We pinpoint the regime of magnetization dynamics leading to highest performance. These results, combined with the exceptional ability of these spintronic oscillators to interact together, their long lifetime, and low energy consumption, open the path to fast, parallel, on-chip computation based on networks of oscillators.

Spin transfer magnetization dynamics have led to considerable advances in Spintronics, including opportunities for new nanoscale radiofrequency devices. Among the new functionalities is the radiofrequency(rf) detection using the spin diode rectification effect in spin torque nano-oscillators (STNOs). In this study, we focus on a new phenomenon, the resonant expulsion of a magnetic vortex in STNOs. This effect is observed when the excitation vortex radius, due to spin torques associated to rf currents, becomes larger than the actual radius of the STNO. This vortex expulsion is leading to a sharp variation of the voltage at the resonant frequency. Here we show that the detected frequency can be tuned by different parameters; furthermore, a simultaneous detection of different rf signals can be achieved by real time measurements with several STNOs having different diameters. This result constitutes a first proof-of-principle towards the development of a new kind of nanoscale rf threshold detector.

We use spin-torque resonance to probe simultaneously and separately the dynamics of a magnetic domain wall and of magnetic domains in a nanostripe magnetic tunnel junction. Thanks to the large associated resistance variations we are able to analyze quantitatively the resonant properties of these single nanoscale magnetic objects. In particular, we find that the magnetic damping of both domains and domain walls is doubled compared to the damping value of their host magnetic layer. We estimate the contributions to damping arising from dipolar couplings between the different layers in the junction and from the intralayer spin pumping effect. We find that they cannot explain the large damping enhancement that we observe. We conclude that the measured increased damping is intrinsic to large amplitudes excitations of spatially localized modes or solitons such as vibrating or propagating domain walls

Spin-orbit effects [1-4] have the potential of radically changing the field of spintronics by allowing transfer of spin angular momentum to a whole new class of materials. In a seminal letter to Nature [5], Kajiwara et al. showed that by depositing Platinum (Pt, a normal metal) on top of a 1.3 $\mu$m thick Yttrium Iron Garnet (YIG, a magnetic insulator), one could effectively transfer spin angular momentum through the interface between these two different materials. The outstanding feature was the detection of auto-oscillation of the YIG when enough dc current was passed in the Pt. This finding has created a great excitement in the community for two reasons: first, one could control electronically the damping of insulators, which can offer improved properties compared to metals, and here YIG has the lowest damping known in nature; second, the damping compensation could be achieved on very large objects, a particularly relevant point for the field of magnonics [6,7] whose aim is to use spin-waves as carriers of information. However, the degree of coherence of the observed auto-oscillations has not been addressed in ref. [5]. In this work, we emphasize the key role of quasi-degenerate spin-wave modes, which increase the threshold current. This requires to reduce both the thickness and lateral size in order to reach full damping compensation [8] , and we show clear evidence of coherent spin-orbit torque induced auto-oscillation in micron-sized YIG discs of thickness 20 nm.

We study translational, breathing and twisting resonant modes of transverse magnetic domain walls pinned at notches in ferromagnetic nanostrips. We demonstrate that a mode's sensitivity to notches depends strongly on the characteristics of that particular resonance. For example, the frequencies of modes involving lateral motion of the wall are the ones which are most sensitive to changes in the notch intrusion depth (especially at the narrower, more strongly confined end of the domain wall). In contrast, the breathing mode, whose dynamics are concentrated away from the notches is relatively insensitive to changes in the notches' sizes. We also demonstrate a sharp drop in the translational mode's frequency towards zero when approaching depinning which is found, using a harmonic oscillator model, to be consistent with a reduction in the local slope of the notch-induced confining potential at its edge., Comment: 11 pages, 10 figures, additional data and analysis

We report on an experimental study on the spin-waves relaxation rate in two series of nanodisks of diameter $\phi=$300, 500 and 700~nm, patterned out of two systems: a 20~nm thick yttrium iron garnet (YIG) film grown by pulsed laser deposition either bare or covered by 13~nm of Pt. Using a magnetic resonance force microscope, we measure precisely the ferromagnetic resonance linewidth of each individual YIG and YIG{\textbar}Pt nanodisks. We find that the linewidth in the nanostructure is sensibly smaller than the one measured in the extended film. Analysis of the frequency dependence of the spectral linewidth indicates that the improvement is principally due to the suppression of the inhomogeneous part of the broadening due to geometrical confinement, suggesting that only the homogeneous broadening contributes to the linewidth of the nanostructure. For the bare YIG nano-disks, the broadening is associated to a damping constant $\alpha = 4 \cdot 10^{-4}$. A 3 fold increase of the linewidth is observed for the series with Pt cap layer, attributed to the spin pumping effect. The measured enhancement allows to extract the spin mixing conductance found to be $G_{\uparrow \downarrow}= 1.55 \cdot 10^{14}~ \Omega^{-1}\text{m}^{-2}$ for our YIG(20nm){\textbar}Pt interface, thus opening large opportunities for the design of YIG based nanostructures with optimized magnetic losses., Comment: 4 pages, 3 figures

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 some 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 of the experiments, we extend the general model of nonlinear auto-oscillators to the case of vortex core dynamics and provide some analytical expressions of the response-to-noise of the system as the coupling coefficient between the phase and the amplitude of the vortex core dynamics due to the nonlinearities. 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 some solutions to improve the spectral coherence of vortex based spin transfer nano-oscillators., Comment: 9 pages, 4 figures