arXiv subjects

Riccardo Hertel

Publications and source records attributed to Riccardo Hertel.

At least 19 recordsLinked to original sources

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

The Role of Flexoelectric Coupling and Chemical Strains in the Emergence of Polar Chiral Nano-Structures

This review examines the conditions that lead to the formation of flexo-sensitive chiral polar structures in thin films and core-shell ferroelectric nanoparticles. It also analyzes possible mechanisms by which the flexoelectric effect impacts the polarization structure in core-shell ferroelectric nanoparticles. Special attention is given to the role of the anisotropic flexoelectric effect in forming a unique type of polarization states with distinct chiral properties, referred to as "flexons". In the first part of the review, we study the influence of the flexoelectric coupling on the polarity, chirality and branching of metastable labyrinthine domain structures in uniaxial ferroelectric core-shell nanoparticles. We reveal that the transition from sinuous branched domain stripes to spiral-like domains occurs gradually as the flexoelectric coupling strength is increased. Our findings indicate that the joint action of flexoelectric effect and chemical strains, termed as "flexo-chemical" coupling, can significantly influence the effective Curie temperature, polarization distribution, domain morphology, and chirality in multiaxial ferroelectric core-shell nanoparticles. Furthermore, we demonstrate that the combination of flexo-chemical coupling and screening effects leads to the appearance and stabilization of a chiral polarization morphology in nanoflakes of van der Waals ferrielectrics. In the second part of the review, we discuss several advanced applications of flexo-sensitive chiral polar structures in core-shell ferroelectric nanoparticles for nanoelectronics elements and cryptography. We underline the possibilities of the flexoelectric control of multiple-degenerated labyrinthine states, which may correspond to a differential negative capacitance (NC) state stabilized in the uniaxial ferroelectric core by the presence of a screening shell.

cond-mat.mtrl-sci↗

arXiv2025

Topological characterization of Hopfions in finite-element micromagnetics

Topological magnetic structures, such as Hopfions, are central to three-dimensional magnetism, but their characterization in complex geometries remains challenging. We introduce a robust finite-element method for calculating the Hopf index in micromagnetic simulations of three-dimensional nanostructures. By employing the Biot-Savart form for the vector potential, our approach ensures gauge-invariant results, even in multiply connected geometries like tori. A novel variance-based correction scheme significantly reduces numerical errors in highly inhomogeneous textures, achieving accurate Hopf index values with fast mesh-dependent convergence. We validate the method using an analytically defined Hopfion structure and demonstrate its ability to detect topological transitions through a simulation of a Hopfion's field-induced destruction into a toron, marked by an abrupt change in the Hopf index. This method enables precise quantification of topological features in complex three-dimensional magnetic textures forming in finite-element micromagnetic simulations, offering a powerful tool for advancing topological magnetism studies in general geometries.

cond-mat.mes-hall↗

arXiv2024

Numerical Calculation of the Hopf Index for 3D Magnetic Textures

To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterisation has proven essential. In particular, while the skyrmion number is a well-established topological invariant for 2D magnetic textures, the Hopf index serves as a key topological descriptor for 3D magnetic structures. In this work, we present and compare various methods for numerically calculating the Hopf index, provide implementations, and offer a detailed analysis of their accuracy and computational efficiency. Additionally, we identify and address common pitfalls and challenges associated with the numerical computation of the Hopf index, offering insights for improving the robustness of these techniques.

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

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

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

Investigation of Spin-Wave Dynamics in Gyroid Nanostructures

A new concept in magnonics studies the dynamics of spin waves (SWs) in three-dimensional nanosystems. It is a natural evolution from conventionally used planar systems to explore magnetization configurations and dynamics in 3D nanostructures with lengths near intrinsic magnetic scales. In this work, we perform broadband ferromagnetic resonance (BBFMR) measurements and micromagnetic simulations of nanoscale magnetic gyroids - a periodic chiral structure consisting entirely of chiral triple junctions. Our results show unique properties of the network, such as the localization of the SW modes, evoking their topological properties, and the substantial sensitivity to the direction of the static magnetic field. The presented results open a wide range of applications in the emerging field of 3D magnonic crystals and spintronics.

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

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↗

arXiv2022

Impact of 3D curvature on the polarization orientation in non-Ising domain walls

Ferroelectric domain boundaries are quasi-two-dimensional functional interfaces with high prospects for nanoelectronic applications. Despite their reduced dimensionality, they can exhibit complex non-Ising polarization configurations and unexpected physical properties. Here, the impact of the three-dimensional (3D) curvature on the polarization profile of nominally uncharged 180° domain walls in LiNbO3 is studied using second-harmonic generation microscopy and 3D polarimetry analysis. Correlations between the domain wall curvature and the variation of its internal polarization unfold in the form of modulations of the Néel-like character, which we attribute to the flexoelectric effect. While the Néel-like character originates mainly from the tilting of the domain wall, the internal polarization adjusts its orientation due to the synergetic upshot of dipolar and monopolar bound charges and their variation with the 3D curvature. Our results show that curved interfaces in solid crystals may offer a rich playground for tailoring nanoscale polar states.

cond-mat.mtrl-sci↗

arXiv2022

Electric field control of labyrinth domain structures in core-shell ferroelectric nanoparticles

In the framework of the Landau-Ginzburg-Devonshire (LGD) approach, we studied the possibility of controlling the polarity and chirality of equilibrium domain structures by a homogeneous external electric field in a nanosized ferroelectric core covered with an ultra-thin shell of screening charge. Under certain screening lengths and core sizes, the minimum of the LGD energy, which consists of Landau-Devonshire energy, Ginzburg polarization gradient energy, and electrostatic terms, leads to the spontaneous appearance of stable labyrinth domain structures in the core. The labyrinths evolve from an initial polarization distribution consisting of arbitrarily small randomly oriented nanodomains. The equilibrium labyrinth structure is weakly influenced by details of the initial polarization distribution, such that one can obtain a quasi-continuum of nearly degenerate labyrinth structures, whose number is limited only by the mesh discretization density. Applying a homogeneous electric field to a nanoparticle with labyrinth domains, and subsequently removing it, allows inducing changes to the labyrinth structure, as the maze polarity is controlled by a field projection on the particle polar axis. Under specific conditions of the screening charge relaxation, the quasi-static dielectric susceptibility of the labyrinth structure can be negative, potentially leading to a negative capacitance effect. Considering the general validity of the LGD approach, we expect that an electric field control of labyrinth domains is possible in many spatially-confined nanosized ferroics, which can be potentially interesting for advanced cryptography and modern nanoelectronics.

cond-mat.mtrl-sci↗

arXiv2021

Chiral Polarization Textures Induced by the Flexoelectric Effect in Ferroelectric Nanocylinders

Polar chiral structures have recently attracted much interest within the scientific community, as they pave the way towards innovative device concepts similar to the developments achieved in nanomagnetism. Despite the growing interest, many fundamental questions related to the mechanisms controlling the appearance and stability of ferroelectric topological structures remain open. In this context, ferroelectric nanoparticles provide a flexible playground for such investigations. Here, we present a theoretical study of ferroelectric polar textures in a cylindrical core-shell nanoparticle. The calculations reveal a chiral polarization structure containing two oppositely oriented diffuse axial domains located near the cylinder ends, separated by a region with a zero-axial polarization. We name this polarization configuration "flexon" to underline the flexoelectric nature of its axial polarization. Analytical calculations and numerical simulation results show that the flexon's chirality can be switched by reversing the sign of the flexoelectric coefficient. Furthermore, the anisotropy of the flexoelectric coupling is found to critically influence the polarization texture and domain morphology. The flexon rounded shape, combined with its distinct chiral properties and the localization nature near the surface, are reminiscent of Chiral Bobber structures in magnetism. In the azimuthal plane, the flexon displays the polarization state of a vortex with an axially polarized core region, i.e., a meron. The flexoelectric effect, which couples the electric polarization and elastic strain gradients, plays a determining role in the stabilization of these chiral states. We discuss similarities between this interaction and the recently predicted ferroelectric Dyzaloshinskii-Moriya interaction leading to chiral polarization states.

cond-mat.mtrl-sci↗

arXiv2021

Flexo-Sensitive Polarization Vortices in Thin Ferroelectric Films

We consider theoretically the influence of the flexoelectric coupling on the spatial distribution and temperature behavior of spontaneous polarization for several types of stable domain structure in thin ferroelectric films, such as stripe domains and vortices.Finite element modelling (FEM) for BaTiO3 films and analytical calculations within the Landau-Ginzburg-Devonshire approach reveals that an out-of-plane polarization component can be very sensitive to the flexoelectric coupling for periodic quasi-2D stripe domains and 3D vortex-antivortex structures.However, the influence is rather different for these structures. The flexoelectric coupling increases significantly the amplitude of a small out-of-plane polarization component in the stripe domains, and the "up" or "down" direction of the component is defined by the sign of the flexoelectric coefficients.Concerning the vortex-antivortex pairs, their antivortices with in-plane anti-circulation have smooth wide dipolar cores through the entire film, whose shape and other features are almost insensitive to the coupling.The vortices with in-plane vorticity have spike-like cores with an out-of-plane quadrupolar moment induced by the flexoelectric coupling. The cores are located near the film-dead layer interfaces.FEM results corroborated by analytical calculations prove that a change of the flexoelectric coefficient sign leads to a reorientation of the core axial polarization, making the flexo-sensitive 3D vortices similar to the recently introduced "flexons" in cylindrical nanoparticles.The relatively wide temperature range (from 200 to 400 K) of the flexo-sensitive vortices' existence gives us the hope that they can be observed experimentally in thin ferroelectric films by scanning probe and nonlinear optical microscopy methods.

cond-mat.mtrl-sci↗

arXiv2021

Switchable Magnetic Frustration in Buckyball Nanoarchitectures

Recent progress in nanofabrication has led to the emergence of three-dimensional magnetic nanostructures as a vibrant field of research. This includes the study of three-dimensional arrays of interconnected magnetic nanowires with tunable artificial spin-ice properties. Prominent examples of such structures are magnetic buckyball nanoarchitectures, which consist of ferromagnetic nanowires connected at vertex positions corresponding to those of a C60 molecule. These structures can be regarded as prototypes for the study of the transition from two- to three-dimensional spin-ice lattices. In spite of their significance for three-dimensional nanomagnetism, little is known about the micromagnetic properties of buckyball nanostructures. By means of finite-element micromagnetic simulations, we investigate the magnetization structures and the hysteretic properties of several sub-micron-sized magnetic buckyballs. Similar to ordinary artificial spin ice lattices, the array can be magnetized in a variety of zero-field states with vertices exhibiting different degrees of magnetic frustration. Remarkably, and unlike planar geometries, magnetically frustrated states can be reversibly created and dissolved by applying an external magnetic field. This easiness to insert and remove defect-like magnetic charges, made possible by the angle-selectivity of the field-induced switching of individual nanowires, demonstrates a potentially significant advantage of three-dimensional nanomagnetism compared to planar geometries. The control provided by the ability to switch between ice-rule obeying and magnetically frustrated structures could be an important feature of future applications, including magnonic devices exploiting differences in the fundamental frequencies of these configurations.

cond-mat.mes-hall↗

arXiv2021

Geometrically constrained Skyrmions

Skyrmions are chiral swirling magnetization structures with nanoscale size. These structures have attracted considerable attention due to their topological stability and promising applicability in nanodevices, since they can be displaced with spin-polarized currents. However, for the comprehensive implementation of skyrmions in devices, it is imperative to also attain control over their geometrical position. Here we show that, through thickness modulations introduced in the host material, it is possible to constrain three-dimensional skyrmions to desired regions. We investigate skyrmion structures in rectangular FeGe platelets with micromagnetic finite element element simulations. First, we establish a phase diagram of the minimum-energy magnetic state as a function of the external magnetic field strength and the film thickness. Using this understanding, we generate preferential sites for skyrmions in the material by introducing dot-like "pockets" of reduced film thickness. We show that these pockets can serve as pinning centers for the skyrmions, thus making it possible to obtain a geometric control of the skyrmion position. This control allows stabilizing skyrmions at positions and in configurations that they would otherwise not attain. Our findings may have implications for technological applications in which skyrmions are used as units of information that are displaced along racetrack-type shift register devices.

cond-mat.mes-hall↗

arXiv2020

Flexo-Elastic Control Factors of Domain Morphology in Core-Shell Ferroelectric Nanoparticles: Soft and Rigid Shells

Within the framework of the Landau-Ginzburg-Devonshire approach we explore the impact of elastic anisotropy, electrostriction, flexoelectric couplings, and mismatch strain on the domain structure morphology in ferroelectric core-shell nanoparticles of spherical shape. We perform finite element modelling (FEM) for multiaxial ferroelectric nanoparticle cores covered with an elastically-isotropic soft or elastically-anisotropic rigid paraelectric shell, with and without mismatch strains. In the case of a core covered with a soft shell, the FEM results show that at room temperature a single polarization vortex with a dipolar kernel can be stable if the electrostriction coupling is weak. With increasing anisotropic electrostriction coupling, the vortex disappears and is replaced by complex flux-closure structures, which are formed in the equatorial plane and transform into an elongated vortex with a central 180-degree domain wall near the core poles. This complex domain morphology develops in the core due to the anisotropic electrostriction, and the flexoelectric coupling leads to an additional curvature and twist of the polarization isosurfaces. In contrast to this, FEM performed for a core covered with a rigid shell shows that, at room temperature, the anisotropic elastic properties of the shell can stabilize vortex-like structures with three flux-closure domains, which gradually cross in the equatorial plane of the core and transform into 120-degree domains near the core poles. The flexoelectric coupling leads to a noticeable curling of the flux-closure domain walls. A mismatch strain compensates the curling of the flux-closure domains in the core confined by the elastically-anisotropic rigid shell. Our analysis reveals different types of topological defects, namely Bloch point structures (BPS) and Ising lines, that form in a ferroelectric core covered with a soft or rigid shell.

cond-mat.mtrl-sci↗