Giulio Siracusano

A generalized tool for accurate time-domain separation of excited modes in spin-torque oscillators

We propose and develop an advanced signal processing technique that, combined with micromagnetic simulations, is able to deeply describe the non-stationary behavior of spin-torque oscillators, both in terms of time domain and spatial distribution of the magnetization dynamics. The Hilbert-Huang Transform is used for the identification of the time traces of each oscillation in a multimode excitation and enhanced with masking signals and the Ensemble Empirical Mode Decomposition. We emphasize that the technique developed here is general and can be used for any physical non-linear system in the presence of multimode dynamical excitation or intermittence.

Self-Modulated Soliton Modes Excited in a Nanocontact Spin-Torque Oscillator

Self-modulated bubble-like solitons, namely droplets, recently observed in spin-torque nanooscillators with a perpendicular free layer, are promising for applications in spintronics, magnonics, and magnetic logic devices. This letter presents a micromagnetic analysis on soliton dynamics. Our results identify the role of physical parameters (i.e., external field, saturation magnetization, and exchange constant) in achieving experimental findings such as hysteretic, linear and nonlinear spin-wave excitations. The modes with different excitation frequencies have nonuniform spatial distributions of power, and the power of frequency sidebands is mostly located near the outer border of the nanocontact. At high currents, a wavelet-based analysis highlights that the magnetoresistive signal due to the sideband modes is not stationary, providing a possible origin of the asymmetric sidebands observed in spintronic self-modulators. We also identify the thermal field as the key ingredient for the excitation of linear modes in a subcritical regime.

Time-domain study of frequency-power correlation in spin-torque oscillators

This paper describes a numerical experiment, based on full micromagnetic simulations of current-driven magnetization dynamics in nanoscale spin valves, to identify the origins of spectral linewidth broadening in spin torque oscillators. Our numerical results show two qualitatively different regimes of magnetization dynamics at zero temperature: regular (single-mode precessional dynamics) and chaotic. In the regular regime, the dependence of the oscillator integrated power on frequency is linear, and consequently the dynamics is well described by the analytical theory of current-driven magnetization dynamics for moderate amplitudes of oscillations. We observe that for higher oscillator amplitudes, the functional dependence of the oscillator integrated power as a function of frequency is not a single-valued function and can be described numerically via introduction of nonlinear oscillator power. For a range of currents in the regular regime, the oscillator spectral linewidth is a linear function of temperature. In the chaotic regime found at large current values, the linewidth is not described by the analytical theory. In this regime we observe the oscillator linewidth broadening, which originates from sudden jumps of frequency of the oscillator arising from random domain wall nucleation and propagation through the sample. This intermittent behavior is revealed through a wavelet analysis that gives superior description of the frequency jumps compared to several other techniques.

Nonstationary magnetization dynamics driven by spin transfer torque

This paper shows that the presence of two dynamical regimes, characterized by different precessional axes, is the origin of the nonmonotonic behavior of the output integrated power for large-amplitude magnetization precession driven by spin-polarized current in nanoscale exchange-biased spin valves. In particular, an abrupt loss in the integrated output power exists at the transition current between those two regimes. After the introduction of a time-frequency analysis of magnetization dynamics based on the wavelet transform, we performed a numerical experiment by means of micromagnetic simulations. Our results predicted that, together with a modulation of the frequency of the main excited mode of the magnetization precession, at high nonlinear dynamical regime the instantaneous output power of the spin-torque oscillator can disappear and then reappear at nanosecond scale.

Intrinsic synchronization of an array of spin-torque oscillators driven by the spin-Hall effect

This paper micromagnetically studies the magnetization dynamics driven by the spin-Hall effect in a Platinum/Permalloy bi-layer. For a certain field and current range, the excitation of a uniform mode, characterized by a power with a spatial distribution in the whole ferromagnetic cross section, is observed. We suggest to use the ferromagnet of the bi-layer as basis for the realization of an array of spin-torque oscillators (STOs): the Permalloy ferromagnet will act as shared free layer, whereas the spacers and the polarizers are built on top of it. Following this strategy, the frequency of the uniform mode will be the same for the whole device, creating an intrinsic synchronization. The synchronization of an array of parallely connected STOs will allow to increase the output power, as necessary for technological applications.

Non-stationary excitation of two localized spin-wave modes in a nano-contact spin torque oscillator

We measure and simulate micromagnetically a framework based upon a nano-contact spin torque oscillator where two distinct localized evanescent spin-wave modes can be detected. The resulting frequency spectrum is composed by two peaks, corresponding to the excited modes, which lie below the ferromagnetic resonance frequency, and a low-frequency tail, which we attribute to the non-stationary switching between these modes. By using Fourier, wavelet, and Hilbert-Huang transforms, we investigate the properties of these modes in time and spatial domains, together with their spatial distribution. The existence of an additional localized mode (which was neither predicted by theory nor by previous numerical and experimental findings) has to be attributed to the large influence of the current-induced Oersted field strength which, in the present setup, is of the same order of magnitude as the external field. As a further consequence, the excited spin-waves, contrarily to what usually assumed, do not possess cylindrical symmetry: the Oersted field induces these modes to be excited at the two opposite sides of the region beneath the nano-contact.

Spin-Hall nano-oscillator with oblique magnetization and Dzyaloshinskii-Moriya interaction as generator of skyrmions and nonreciprocal spin-waves

Spin-Hall oscillators (SHO) are promising sources of spin-wave signals for magnonics applications, and can serve as building blocks for magnonic logic in ultralow power computation devices. Thin magnetic layers used as “free” layers in SHO are in contact with heavy metals having large spin-orbital interaction, and, therefore, could be subject to the spin-Hall effect (SHE) and the interfacial Dzyaloshinskii-Moriya interaction (i-DMI), which may lead to the nonreciprocity of the excited spin waves and other unusual effects. Here, we analytically and micromagnetically study magnetization dynamics excited in an SHO with oblique magnetization when the SHE and i-DMI act simultaneously. Our key results are: (i) excitation of nonreciprocal spin-waves propagating perpendicularly to the in-plane projection of the static magnetization; (ii) skyrmions generation by pure spin-current; (iii) excitation of a new spin-wave mode with a spiral spatial profile originating from a gyrotropic rotation of a dynamical skyrmion. These results demonstrate that SHOs can be used as generators of magnetic skyrmions and different types of propagating spin-waves for magnetic data storage and signal processing applications.

Micromagnetic simulations of persistent oscillatory modes excited by spin-polarized current in nanoscale exchange-biased spin valves

We perform three-dimensional micromagnetic simulations of current-driven magnetization dynamics in nanoscale exchange biased spin valves that take account of (i) back action of spin-transfer torque on the pinned layer, (ii) nonlinear damping, and (iii) random thermal torques. Our simulations demonstrate that all these factors significantly impact the current-driven dynamics and lead to a better agreement between theoretical predictions and experimental results. In particular, we observe that at a nonzero temperature and a subcritical current, the magnetization dynamics exhibits nonstationary behavior in which two independent persistent oscillatory modes are excited which compete for the angular momentum supplied by spin-polarized current. Our results show that this multimode behavior can be induced by combined action of thermal and spin transfer torques.

Micro-focused Brillouin light scattering study of the magnetization dynamics driven by Spin Hall effect in a transversely magnetized NiFe nanowire

We employed micro-focused Brillouin light scattering to study the amplification of the thermal spin wave eigenmodes by means of a pure spin current, generated by the spin-Hall effect, in a transversely magnetized Pt(4nm)/NiFe(4nm)/SiO2(5nm) layered nanowire with lateral dimensions 500x2750 nm2. The frequency and the cross section of both the center (fundamental) and the edge spin wave modes have been measured as a function of the intensity of the injected dc electric current. The frequency of both modes exhibits a clear redshift while their cross section is greatly enhanced on increasing the intensity of the injected dc. A threshold-like behavior is observed for a value of the injected dc of 2.8 mA. Interestingly an additional mode, localized in the central part of the nanowire, appears at higher frequency on increasing the intensity of the injected dc above the threshold value. Micromagnetic simulations were used to quantitatively reproduce the experimental results and to investigate the complex non-linear dynamics induced by the spin-Hall effect, including the modification of the spatial profile of the spin wave modes and the appearance of the extra mode above the threshold.

A variation-aware simulation framework for hybrid CMOS/spintronic circuits

In this paper, a variation-aware simulation framework is introduced for hybrid circuits comprising MOS transistors and spintronic devices (e.g., magnetic tunnel junction-MTJ). The simulation framework is based on one-time characterization via micromagnetic multi-domain simulations, as opposed to most of existing frameworks based on single-domain analysis. As further distinctive capability, stochastic variations of the MTJ switching are explicitly incorporated through a Skew Normal distribution, which is adjusted to fit micromagnetic simulations. The framework is implemented in the form of Verilog-A look-up table based model, which assures easy integration with commercial circuit design tools, and very low computational effort. The framework is applied to non-volatile Flip-FIops as case study with 10,000 Monte Carlo runs.