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Massimiliano d'Aquino

Publications and source records attributed to Massimiliano d'Aquino.

At least 19 recordsLinked to original sources
arXiv2026

Nonlinear interaction theory for parametrically-excited spin-wave modes in confined micromagnetic systems

We present a general theoretical approach for the quantitative description of parametric excitation of spin-wave modes in confined micromagnetic systems. This type of problem belongs to a broader class of nonlinear modal dynamics that arise across many areas of physics and engineering. The ferromagnetic sample is driven by parallel pumping with an external applied magnetic field having two tones at different frequencies, which are able to trigger parametric instability of two resonant modes. The two excited spin-wave modes interact in a strongly nonlinear fashion giving rise to quasiperiodicity, hysteresis and non-commutativity of steady-state oscillation regimes. To disentangle such a complex variety of dynamics, we develop a reduced-order model based on magnetization normal modes that is amenable of appropriate analytical treatment, leading to quantitative description of parametric instability thresholds, post-instability steady-state amplitude saturation and complete determination of phase diagrams for steady-state oscillation regimes. We have performed validation of the theory using numerical simulations. The phase diagrams allow to predict and explain all the features of the nonlinear interaction between the parametrically-excited spin-wave modes and can be directly compared with experimental results.

cond-mat.mes-hall↗
arXiv2026

Radio-frequency assisted switching in perpendicular magnetic tunnel junctions

Spin-transfer torque magnetic random-access memory (STT-MRAM) relies on nanoscale magnetic tunnel junctions (MTJs) as its fundamental building blocks. Next-generation STT-MRAM requires strategies that simultaneously improve switching energy efficiency and device endurance. Here, we present the first study of perpendicular STT-MRAM writing assisted by radio-frequency (RF) spin torque. We show that applying a small-amplitude RF pulse prior to a direct-current (DC) writing pulse enhances the MTJ switching probability, with the efficiency gain increasing at lower RF frequencies. This RF+DC writing scheme enables shorter DC pulses, thereby improving device endurance. Analytical and numerical modeling qualitatively reproduces the experimental trends, while quantitative discrepancies indicate that realistic MTJ properties beyond idealized models play an important role in RF-assisted switching.

cond-mat.mes-hall↗
arXiv2026

Nonlinear mode interactions under parametric excitation in a YIG microdisk

A pair of quantized spin-wave modes is driven by two-tone parallel pumping in a YIG microdisk. The nonlinear dynamics is experimentally investigated by probing the resulting steady state, which is found to critically depend on the chosen pair of modes, the detuning between the pump frequencies and the modes parametric resonance, as well as the temporal sequence of the two rf tones. A general theory of parametric excitation in confined structures based on magnetization normal modes is developed and quantitatively accounts for the observed dependence and non-commutative behaviors, which emerge from the interplay between the self and mutual nonlinear frequency shifts of the spin-wave modes. Owing to its high degree of external controllability and scalability to larger sets of modes, this dynamical system provides a model platform for exploring nonlinear phenomena and a promising route toward rf driven state mapping relevant to neuromorphic and unconventional computing.

cond-mat.mes-hall↗
arXiv2025

Rotating Spin Wave Modes in Nanoscale Möbius Strips

Curved and topologically nontrivial magnetic structures offer new pathways to control spin-wave behavior beyond planar geometries. Here, we study spin-wave dynamics in Möbius-shaped soft-magnetic nanostrips using micromagnetic simulations. By comparing single-, double-, and triple-twisted Möbius strips to a topologically trivial bent ring, we isolate the roles of helical twist and non-orientable topology. Möbius geometries exhibit non-degenerate mode doublets associated with counterpropagating spin waves, in contrast to the standing-wave doublets in the trivial case. This splitting arises from a twist-induced geometric (Berry) phase that breaks propagation symmetry, producing non-reciprocal dispersion relations. The Möbius topology further imposes antisymmetric boundary conditions, resulting in half-integer wavelength quantization. Local RF excitation allows for the selective generation of spin waves with defined frequency and direction. An analytical model reproduces the dispersion behavior with excellent agreement. These results highlight how geometric and topological design can be leveraged to engineer spin-wave transport in three-dimensional magnonic systems.

cond-mat.mes-hall↗
arXiv2025

Nonreciprocal inertial spin-wave dynamics in twisted magnetic nanostrips

We develop a theoretical framework for inertial spin-wave dynamics in three-dimensional twisted soft-magnetic nanostrips, where curvature and torsion couple with magnetic inertia to generate terahertz (THz) magnetic oscillations. The resulting spin-wave spectra exhibit pronounced nonreciprocity due to effective symmetry breaking arising from geometric chirality and inertial effects. We show that this behavior is governed by a curvature-induced geometric (Berry) phase, which we analytically capture through compact expressions for dispersion relations and spectral linewidths in both nutational (THz) and precessional (GHz) regimes. Topological variations, including Möbius and helical geometries, impose distinct wavenumber quantization rules, elucidating the role of topology in spin-wave transport. These results position twisted magnetic strips as a viable platform for curvilinear THz magnonics and nonreciprocal spintronic applications.

cond-mat.mes-hall↗
arXiv2025

Self-modulation instability in high power ferromagnetic resonance of BiYIG nanodisks

We study the high power ferromagnetic resonance (FMR) of perpendicularly magnetized BiYIG nanodisks where the uniaxial anisotropy almost compensates the shape anisotropy. We observe a strong saturation of the averaged magnetization upon moderately increasing the amplitude of the rf field and a broadening of the FMR line towards lower and higher magnetic field. Full micromagnetic simulations reveal that a self-modulation of the dynamic magnetization is responsible of this behavior. To get more insight into this unstable dynamics, it is analysed in terms of normal modes. The number of modes involved is found to rapidly increase above the critical threshold. Still, a normal modes model taking into account only a few of them and their mutual nonlinear couplings allows us to qualitatively reproduce the observed phenomenon. The normal modes analysis and micromagnetic simulations also predict a Suhl-like instability at larger excitation power when it is slowly increased from low values, and bistability. Using two-tone spectroscopy, we directly measure the self-modulation spectrum and provide experimental evidence of bistable dynamics. These findings open some perspectives of using high dimensional dynamics in magnetic nanostructures for unconventional information processing.

cond-mat.mes-hall↗
arXiv2024

Quantum Micromagnetic Theory of Magnons in Finite Nanostructures

This paper presents a quantum field theoretical formalism for studying magnons in finite nanostructures with arbitrary shapes and spatially nonuniform ground states. It extends the classical micromagnetic formalism by introducing a micromagnetic Hamiltonian quantum operator, which incorporates exchange, Dzyaloshinsky-Moriya, anisotropy, magnetostatic, and Zeeman energies. The nonuniformity of the ground state is handled by pointwise aligning the quantization axis of the magnetization field operator with the classical ground state. The Hamiltonian is expanded in the large spin-number limit and truncated to retain only terms quadratic in the components of the magnetization operator transverse to the quantization axis. This quadratic Hamiltonian is used to derive the linear quantum Landau-Lifshitz equation. By diagonalizing this equation under appropriate boundary and normalization conditions, a discrete set of magnon creation and annihilation operators is obtained, enabling a complete description of the magnon spectrum. Finally, the theory is applied to study the effects of temperature and shape on low-temperature thermal equilibrium fluctuations of magnons in thin ferromagnetic nanodisks.

cond-mat.mes-hall↗
arXiv2024

Analytical solutions for ultra-fast precessional switching in inertial magnetization dynamics

Here we consider the magnetization dynamics in ferromagnetic nanoparticles or films driven by external magnetic field pulses directed transverse to the initial equilibrium state. The excitation pulse drives large-angle ultra-fast magnetization dynamics that may eventually end up in the reversed equilibrium realizing successful precessional switching. We consider ultra-short pulse duration (fractions of picosecond) and large external field intensities (several Tesla) which may be relevant for the realization of faster energy-efficient memory cells. For such short time scales, we include inertial effects in the theoretical description by considering the inertial Landau-Lifshitz-Gilbert equation which requires to be treated as a system of singularly perturbed ODEs for small values of the inertia. By using suitable perturbation approach based on multiple time scales analysis, we develop an approximate closed-form solution for the switching dynamics as well as formulas for switching time and its safety tolerances to obtain the successful switching as function of physical parameters of the particle and strength of magnetic inertia. The developed analytical solution is validated by numerical simulations.

math.DS↗
arXiv2024

Mode-resolved micromagnetics study of parametric spin wave excitation in thin-film disks

We present a computational study of the parametric excitation of spin waves in thin film disks with a mode-resolved approach. The method involves projecting out the time-dependent magnetization, computed using micromagnetics simulations, onto the spatial profile of the eigenmodes that are obtained from the linearization of the equations of motion. Unlike spectral analysis in the frequency domain, the projection allows for the analysis of transient mode dynamics under parametric excitation. We apply this method to parallel pumping of quantized spin wave modes in in-plane magnetized thin-film disks, where phenomena such as frequency pulling, mutual phase locking, and higher-order magnon scattering processes are identified.

cond-mat.mes-hall↗
arXiv2023

Defect-sensitive High-frequency Modes in a Three-Dimensional Artificial Magnetic Crystal

Modern three-dimensional nanofabrication methods make it possible to generate arbitrarily shaped nanomagnets, including periodic networks of interconnected magnetic nanowires. Structurally similar to optical or acoustic metamaterials, these arrays could represent magnetic variants of such artificial materials. Using micromagnetic simulations, we investigate a three-dimensional array of interconnected magnetic nanowires with intersection points corresponding to atomic positions of a diamond lattice. The high-frequency excitation spectrum of this artificial magnetic crystal (AMC) is governed by its microstructure and, to a lesser extent, by the magnetic configuration. The magnetic system displays characteristics of three-dimensional artificial spin ice. It can contain Dirac-type magnetic defect structures, which modify the magnonic spectrum of the AMC similarly as defect sites in a natural diamond crystal influence optical absorption spectra. Our study opens new perspectives for applying such materials in high-density magnonic devices and shows that AMCs represent a promising category of magnonic materials with tunable properties.

cond-mat.mes-hall↗
arXiv2023

Midpoint geometric integrators for inertial magnetization dynamics

We consider the numerical solution of the inertial version of Landau-Lifshitz-Gilbert equation (iLLG), which describes high-frequency nutation on top of magnetization precession due to angular momentum relaxation. The iLLG equation defines a higher-order nonlinear dynamical system with very different nature compared to the classical LLG equation, requiring twice as many degrees of freedom for space-time discretization. It exhibits essential conservation properties, namely magnetization amplitude preservation, magnetization projection conservation, and a balance equation for generalized free energy, leading to a Lyapunov structure (i.e. the free energy is a decreasing function of time) when the external magnetic field is constant in time. We propose two second-order numerical schemes for integrating the iLLG dynamics over time, both based on implicit midpoint rule. The first scheme unconditionally preserves all the conservation properties, making it the preferred choice for simulating inertial magnetization dynamics. However, it implies doubling the number of unknowns, necessitating significant changes in numerical micromagnetic codes and increasing computational costs especially for spatially inhomogeneous dynamics simulations. To address this issue, we present a second time-stepping method that retains the same computational cost as the implicit midpoint rule for classical LLG dynamics while unconditionally preserving magnetization amplitude and projection. Special quasi-Newton techniques are developed for solving the nonlinear system of equations required at each time step due to the implicit nature of both time-steppings. The numerical schemes are validated on analytical solution for macrospin terahertz frequency response and the effectiveness of the second scheme is demonstrated with full micromagnetic simulation of inertial spin waves propagation in a magnetic thin-film.

physics.comp-ph↗
arXiv2023

Controlled Quasi-Latitudinal Solutions for ultra-fast Spin-Torque Precessional Magnetization Switching

The aim of the paper is to present a novel class of time-dependent controls to realize ultra-fast magnetization switching in nanomagnets driven by spin-torques produced by spin-polarized electric currents. Magnetization dynamics in such systems is governed by the Landau-Lifshitz-Slonczewski equation which describes the precessional motion of (dimensionless) magnetization vector on the unit-sphere. The relevant case of nanoparticles with uniaxial anisotropy having in-plane easy and intermediate axes and out-of-plane hard axis is considered. By exploiting the characteristic smallness of damping and spin-torque intensity, the aforementioned controls are constructed via suitable perturbative tools in a way to realise approximate \emph{latitudinal solutions} (i.e. motions on a sphere in which the out-of-plane magnetization component stays constant) with the effect to fast ``switch'' the system from one stationary state to another. The possibility to keep a (``small'') bounded value of the out-of-plane coordinate throughout this process of ``transfer'', turns out to be advantageous in the applications as it sensibly reduces the post-switching relaxation oscillations that may cause the failure of switching in real samples. Further relevant quantitative results on the behaviour of the solutions during the pre- and post-switching stages (termed ``expulsion'' and ``attraction'', respectively), are given as a byproduct. A selection of validating numerical experiments is presented alongside the corresponding theoretical results.

math.DS↗
arXiv2023

Interpretation of spin-wave modes in Co/Ag nanodot arrays probed by broadband ferromagnetic resonance

We present a detailed investigation of the magnetization dynamics in Co/Ag nanodots, which due to their size can support standing spin-wave (SSW) modes with complex spectral responses. To interpret the experimentally measured broadband vector network analyzer ferromagnetic resonance data, we compare the spectra of the nanoarray structure with those of the unpatterned Co/Ag film of identical thickness, which serves as a baseline for obtaining the general magnetic parameters of the system. Using a novel frequency domain, matrix-free simulation method of the dynamic response, we identify the nature of the excitation modes, which allows us to assess the boundary conditions for the nanodots. We find an excellent agreement between the calculated and experimental values for the frequencies of the fundamental (uniform-like) (011) mode. The existence of an edge-localized mode in the experiment has been confirmed and fits very well with theory and micromagnetic simulations, having the form of a flapping mode at the extrema of the nanodot in one of the in-plane directions. Its frequency is below the fundamental mode's frequency and has been shown to be a consequence of the imaginary wave vector for such localized SSW modes. Higher order SSW modes can be generated from the theory, which allows us to find a probable mode number for the second bulk SSW (201 or 221 or 131), which lies at frequencies above the fundamental mode.

cond-mat.mes-hall↗
arXiv2023

Degenerate and non-degenerate parametric excitation in YIG nanostructures

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.

cond-mat.mes-hall↗
arXiv2023

Magnetization dynamics in a three-dimensional interconnected nanowire array

Three-dimensional magnetic nanostructures have recently emerged as artificial magnetic material types with unique properties bearing potential for applications, including magnonic devices. Interconnected magnetic nanowires are a sub-category within this class of materials that is attracting particular interest. We investigate the high-frequency magnetization dynamics in a cubic array of cylindrical magnetic nanowires through micromagnetic simulations based on a frequency-domain formulation of the linearized Landau-Lifshitz-Gilbert equation. The small-angle high-frequency magnetization dynamics excited by an external oscillatory field displays clear resonances at distinct frequencies. These resonances are identified as oscillations connected to specific geometric features and micromagnetic configurations. The geometry- and configuration-dependence of the nanowire array's absorption spectrum demonstrates the potential of such magnetic systems for tuneable and reprogrammable magnonic applications.

cond-mat.mes-hall↗
arXiv2023

Micromagnetic study of inertial spin waves in ferromagnetic nanodots

Here we report the possibility to excite ultra-short spin waves in ferromagnetic thin-films by using time-harmonic electromagnetic fields with terahertz frequency. Such ultra-fast excitation requires to include inertial effects in the description of magnetization dynamics. In this respect, we consider the inertial Landau-Lifshitz-Gilbert (iLLG) equation and develop analytical theory for exchange-dominated inertial spin waves. The theory predicts a finite limit for inertial spin wave propagation velocity, as well as spin wave spatial decay and lifetime as function of material parameters. Then, guided by the theory, we perform numerical micromagnetic simulations that demonstrate the excitation of ultra-short inertial spin waves (20 nm long) propagating at finite speed in a confined magnetic nanodot. The results are in agreement with the theory and provide the order of magnitude of quantities observable in realistic ultra-fast dynamics experiments.

cond-mat.mes-hall↗
arXiv2023

Complete identification of spin-wave eigenmodes excited by parametric pumping in YIG microdisks

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.

physics.app-ph↗
arXiv2023

Micromagnetic frequency-domain simulation methods for magnonic systems

We present efficient numerical methods for the simulation of small magnetization oscillations in three-dimensional micromagnetic systems. Magnetization dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation, linearized in the frequency domain around a generic equilibrium configuration, and formulated in a special operator form that allows leveraging large-scale techniques commonly used to evaluate the effective field in time-domain micromagnetic simulations. By using this formulation, we derive numerical algorithms to compute the free magnetization oscillations (i.e., spin wave eigenmodes) as well as magnetization oscillations driven by ac radio-frequency fields for arbitrarily shaped nanomagnets. Moreover, semi-analytical perturbation techniques based on the computation of a reduced set of eigenmodes are provided for fast evaluation of magnetization frequency response and absorption spectra as a function of damping and ac field. We present both finite difference and finite element implementations and demonstrate their effectiveness on a test case. These techniques open the possibility to study generic magnonic systems discretized with several hundred thousand (or even millions) of computational cells in a reasonably short time.

physics.comp-ph↗