2021

M. Bassotti, R. Silvani and G. Carlotti, "From the spin eigenmodes of isolated Nel skyrmions to the magnonic bands of a skyrmionic crystal: a micromagnetic study as a function of the strength of both the interfacial Dzyaloshinskii-Moriya and the exchange constants", IEEE Magnetics Letters (Published 16.12.2021)

DOI: 10.1109/LMAG.2021.3136152

Abstract:

The presence of interfacial Dzyaloshinskii-Moriya interaction (DMI) may lead to the appearance of Nel skyrmions in ferromagnetic films. These topologically protected structures, whose diameter is as small as a few nanometers, can be nowadays stabilized at room temperature and have been proposed for the realization of artificial magnonic crystals and new spintronic devices, such as racetrack memories. In this perspective, it is of utmost importance to analyze their dynamical properties in the GHz range, i.e. in the operation range of current communication devices. Here we exploited the software MuMax3 to calculate the dynamics of Nel skyrmions in the range between 1 and 30 GHz, considering first the eigenmodes of an isolated skyrmion, then the case of two interacting skyrmions and finally a linear chain, representing a one-dimensional magnonic crystal, whose magnonic band structure has been calculated as a function of the strength of both the DMI- and the exchange-constants, namely D and A. The magnonic bands can be interpreted as derived from the eigenmodes of isolated skyrmions, even if hybridization and anti-crossing phenomena occur for specific ranges of values of D and A. Therefore, varying the latter parameters, for instance by a proper choice of the materials and thicknesses, may enable one to fine-tune the permitted and forbidden frequency interval of the corresponding magnonic crystal.

R.Silvania, M. Kuepferling, S. Tacchi and G. Carlotti, "Impact of the interfacial Dzyaloshinskii-Moriya interaction on the band structure of one-dimensional artificial magnonic crystals: A micromagnetic study", Journal of Magnetism and Magnetic Materials 539 (2021): 168342, (Published 01.12.2021)

DOI: 10.1016/j.jmmm.2021.168342

open access: https://arxiv.org/abs/2112.05360

Abstract:

We present the results of a systematic micromagnetic study of the effect of the Dzyaloshinskii-Moriya interaction (DMI) on the spin wave band structure of two one-dimensional magnonic crystals (MCs), both with the same periodicity p = 300 nm, but different implementation of the DMI modulation. In the first system the artificial periodicity was achieved by modulating the interfacial DMI constant D, while in the second system also the sample morphology was modulated. Due to the folding property of the band structure in the dispersion relations of the magnonic crystals it is possible to extend the sensitivity of Brillouin light scattering towards weak DMI strength (D in the range from 0 to 0.5 mJ/m²), by measuring the frequency splitting of folded modes in high-order artificial Brillouin zones, since the splitting increases almost linearly with the band index. For relatively large values of the DMI (D in the range from 1.0 to 2.0 mJ/m²) the spin waves dispersion relations present flat modes for positive wavevectors, separated by forbidden frequency gaps whose amplitude depend on the value of D. These frequency gaps are more pronounced for the sample with morphology modulation. The non-reciprocal, localised, spatial profiles of these modes in both MCs are discussed with reference to spin waves in plain films and in isolated stripes of the same thickness.

J. Chen, H. Yu and G. Gubbiotti, "Unidirectional spin-wave propagation and devices", Journal of Physics D: Applied Physics 55.12 (2021): 123001 (Published 12.11.2021)

DOI: 10.1088/1361-6463/ac31f4

Abstract:

Unidirectional information transport plays a key role in optics, microwave technology, electronic logic circuits and devices. Spin waves (SWs) are considered to be a promising candidate for the next-generation logic devices, which have many advantages such as low-energydissipation and compatibility with radio-frequency-based electronic devices. Unidirectional SWs have been demonstrated in magnetic thin films theoretically and experimentally, offering a great opportunity to realize unidirectional transport of spin information. In this article, we review several methods for emitting and measuring unidirectional SWs, such as using the nonreciprocity provided by magnetostatic surface SWs and interfacial Dzyaloshinskii–Moriya interactions. Unidirectional SWs can also be excited by magnetic nanowire arrays as well as spatially defined spin textures. Finally, we review some magnonic logic devices based on unidirectional SWs, such as spin-wave diodes.

A. Sud, S. Tacchi, D. Sagkovits, C. Barton, M. Sall, L. H. Diez, E. Stylianidis, N. Smith, L. Wright, S. Zhang, X. Zhang, D. Ravelosona, G. Carlotti, H. Kurebayashi, O. Kazakova and M. Cubukcu, "Tailoring interfacial effect in multilayers with Dzyaloshinskii–Moriya interaction by helium ion irradiation", Sci Rep 11, 23626 (Published 12.06.2021)

DOI: 10.1038/s41598-021-02902-y

Abstract:

We show a method to control magnetic interfacial effects in multilayers with Dzyaloshinskii–Moriya interaction (DMI) using helium (He+) ion irradiation. We report results from SQUID magnetometry, ferromagnetic resonance as well as Brillouin light scattering results on multilayers with DMI as a function of irradiation fluence to study the effect of irradiation on the magnetic properties of the multilayers. Our results show clear evidence of the He+ irradiation effects on the magnetic properties which is consistent with interface modification due to the effects of the He+ irradiation. This external degree of freedom offers promising perspectives to further improve the control of magnetic skyrmions in multilayers, that could push them towards integration in future technologies.

A. Magni, V. Basso, A. Sola, G. Soares, N. Meggiato, M. Kuepferling, W. Skowroński, S. Łazarski, K. Grochot, M. V. Khanjani, J. Langer and B. Ocker ,"Spin Hall magnetoresistance and spin orbit torque efficiency in Pt/FeCoB bilayers", IEEE Transactions on Magnetics (Published 28.05.2021)

DOI: 10.1109/TMAG.2021.3084866

Abstract:

The spin Hall magnetoresistance (SMR) of Pt/FeCoB bilayers with in-plane magnetocrystalline anisotropy was analysed with respect to a second order effect in the sensing current which acts, through the spin Hall effect in Pt, as a torque on the magnetization of the ferromagnetic layer and changes slightly its configuration. This leads to a small current dependent shift of the SMR curves in field that allows, in structures with a multidomain state (e.g. Hall bars), the determination of the sign of the magnetic remanence. The SMR measurements were performed as a function of the Pt thickness and the spin Hall angle, the diffusion length and the field-like and damping like SOT efficiency were determined. The results were compared with the values obtained from harmonic Hall voltage and SOT-ferromagnetic resonance (FMR) measurements and show a good agreement.

B. Sakar, S. Sibylle; A. Fernández Scarioni, F. Garcia-Sanchez, İ. Öztoprak, H. W. Schumacher and O.Öztürk, "A Ti/Pt/Co Multilayer Stack for Transfer Function Based Magnetic Force Microscopy Calibrations" Magnetochemistry 7, no. 6: 78. (Published 21.05.2021)

DOI: 10.3390/magnetochemistry7060078

Open Access: https://arxiv.org/abs/2201.09763.

Abstract:

Magnetic force microscopy (MFM) is a widespread technique for imaging magnetic structures with a resolution of some 10 nanometers. MFM can be calibrated to obtain quantitative (qMFM) spatially resolved magnetization data in units of A/m by determining the calibrated point spread function of the instrument, its instrument calibration function (ICF), from a measurement of a well-known reference sample. Beyond quantifying the MFM data, a deconvolution of the MFM image data with the ICF also corrects the smearing caused by the finite width of the MFM tip stray field distribution. However, the quality of the calibration depends critically on the calculability of the magnetization distribution of the reference sample. Here, we discuss a Ti/Pt/Co multilayer stack that shows a stripe domain pattern as a suitable reference material. A precise control of the fabrication process, combined with a characterization of the sample micromagnetic parameters, allows reliable calculation of the sample’s magnetic stray field, proven by a very good agreement between micromagnetic simulations and qMFM measurements. A calibrated qMFM measurement using the Ti/Pt/Co stack as a reference sample is shown and validated, and the application area for quantitative MFM measurements calibrated with the Ti/Pt/Co stack is discussed.

K. Szulc, S. Mendisch, M. Mruczkiewicz, F. Casoli, M. Becherer, and G. Gubbiotti, "Nonreciprocal spin-wave dynamics in Pt/Co/W/Co/Pt multilayers", Physical Review B 103.13 (2021): 134404, (Published 05.04.2021)

DOI: 10.1103/PhysRevB.103.134404

open access: https://arxiv.org/abs/2112.11206

Abstract:

We present a detailed study of the spin-wave dynamics in single Pt/Co/W and double Pt/Co/W/Co/Pt ferromagnetic layer systems. The dispersion of spin waves was measured by wave-vector-resolved Brillouin light scattering spectroscopy while the in-plane and out-of-plane magnetization curves were measured by alternating gradient field magnetometry. The interfacial Dzyaloshinskii-Moriya interaction induced nonreciprocal dispersion relation was demonstrated for both single and double ferromagnetic layers and explicated by numerical simulations and theoretical formulas. The results indicate the crucial role of the order of layers deposition on the magnetic parameters. A significant difference between the perpendicular magnetic anisotropy constant in double ferromagnetic layer systems conduces to the decline of the interlayer interactions and different dispersion relations for the spin-wave modes. Our study provides a significant contribution to the realization of the multifunctional nonreciprocal magnonic devices based on ultrathin ferromagnetic/heavy-metal layer systems.

R. Silvani, M. Alunni, S. Tacchi and G. Carlotti, "Effect of the Interfacial Dzyaloshinskii–Moriya Interaction on the Spin Waves Eigenmodes of Isolated Stripes and Dots Magnetized In-Plane: A Micromagnetic Study",Applied Sciences 11.7 (2021): 2929, (Published 25.03.2021)

DOI: 10.3390/app11072929

Abstract:

The influence of the Dzyaloshinskii–Moriya interaction (DMI) on the eigenmodes of magnetic nanostructures is attracting interest for both fundamental reasons and prospects in applications. In this study, the characteristics of spin waves eigenmodes in either long stripes or elliptical dots magnetized in-plane, with lateral dimensions of the order of 100 nm, are analyzed by micromagnetic simulations in presence of a sizeable DMI. Using the GPU-accelerated software MuMax3, we show that the eigenmodes spectrum is appreciably modified by the DMI-induced non-reciprocity in spin-waves propagation: the frequencies of the eigenmodes are red-shifted and their spatial profiles appreciable altered due to the lack of stationary character in the direction orthogonal to the magnetization direction. As a consequence, one finds a modification of the expected cross-section of the different modes in either ferromagnetic resonance or Brillouin light scattering experiments, enabling one to detect modes that would remain invisible without DMI. In this respect, the modifications of the spectrum can be directly connected to a quantitative estimation of the DMI constant. Moreover, it is seen that for sufficiently large values of the DMI constant, the low-frequency odd eigenmode changes its profile and becomes soft, reflecting the transition of the ground state from uniform to chiral.

A. Fernández Scarioni, C. Barton, H. Corte-León, S. Sievers, X. Hu, F. Ajejas, W. Legrand, N. Reyren, V. Cros, O. Kazakova, and H. W. Schumacher, "Thermoelectric Signature of Individual Skyrmions", Physical Review Letters 126.7 (2021): 077202, (Published 16.02.2021)

DOI: 10.1103/PhysRevLett.126.077202

open access: arXiv:2001.10251

Abstract:

We experimentally study the thermoelectrical signature of individual skyrmions in chiral Pt/Co/Ru multilayers. Using a combination of controlled nucleation, single skyrmion annihilation, and magnetic field dependent measurements the thermoelectric signature of individual skyrmions is characterized. The observed signature is explained by the anomalous Nernst effect of the skyrmion’s spin structure. Possible topological contributions to the observed thermoelectrical signature are discussed. Such thermoelectrical characterization allows for noninvasive detection and counting of skyrmions and enables fundamental studies of topological thermoelectric effects on the nanoscale.

A. Aqeel, J. Sahliger, T. Taniguchi, S. Mändl, D. Mettus, H. Berger, A. Bauer, M. Garst, C. Pfleiderer, and C. H. Back, "Microwave spectroscopy of the low-temperature skyrmion state in Cu2OSeO3", Physical Review Letters 126.1 (2021): 017202, (Published 06.01.2021)

DOI: 10.1103/PhysRevLett.126.017202

open access: arXiv:2011.07826

Abstract:

In the cubic chiral magnet Cu2OSeO3 a low-temperature skyrmion state (LTS) and a concomitant tilted conical state are observed for magnetic fields parallel to ⟨100⟩. Here, we report on the dynamic resonances of these novel magnetic states. After promoting the nucleation of the LTS by means of field cycling, we apply broadband microwave spectroscopy in two experimental geometries that provide either predominantly in-plane or out-of-plane excitation. By comparing the results to linear spin-wave theory, we clearly identify resonant modes associated with the tilted conical state, the gyrational and breathing modes associated with the LTS, as well as the hybridization of the breathing mode with a dark octupole gyration mode mediated by the magnetocrystalline anisotropies. Most intriguingly, our findings suggest that under decreasing fields the hexagonal skyrmion lattice becomes unstable with respect to an oblique deformation, reflected in the formation of elongated skyrmions.

2020

S. Finizio, S. Wintz, S. Mayr, A. J. Huxtable, M. Langer, J. Bailey, G. Burnell,C. H. Marrows, and  J. Raabe, "Time-resolved visualization of the magnetization canting induced by field-like spin–orbit torques", Applied Physics Letters 117.21 (2020): 212404, (Published 25.11.2020)

DOI: 10.1063/5.0029816

Abstract:

We report on the use of time-resolved scanning transmission x-ray microscopy imaging for the visualization of the dynamical canting of the magnetization induced by field-like spin–orbit torques in a perpendicularly magnetized microwire. In particular, we show how the contributions to the dynamical canting of the magnetization arising from the field-like spin–orbit torque can be separated from the heating-induced effects on the magnetization of the microwire. This method will allow for the imaging of the dynamical effects of spin–orbit torques in device-like structures and buried layers.

W. Lin, B. Yang, A. P. Chen, X. Wu, R. Guo, S. Chen, L. Liu, Q. Xie, X. Shu, Y. Hui, G. Moog Chow, Y. Feng, G. Carlotti, S. Tacchi, H. Yang, and J. Chen, "Perpendicular Magnetic Anisotropy and Dzyaloshinskii-Moriya Interaction at an Oxide/Ferromagnetic Metal Interface", Physical Review Letters 124.21 (2020): 217202, (Published 26.05.2020)

DOI: 10.1103/PhysRevLett.124.217202

open access: arXiv:2006.14268

Abstract:

We report on the study of both perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii-Moriya interaction (DMI) at an oxide/ferromagnetic metal (FM) interface, i.e., BaTiO3 (BTO)/CoFeB. Thanks to the functional properties of the BTO film and the capability to precisely control its growth, we are able to distinguish the dominant role of the oxide termination (TiO2 vs BaO) from the moderate effect of ferroelectric polarization in the BTO film, on the PMA and DMI at an oxide/FM interface. We find that the interfacial magnetic anisotropy energy of the BaO−BTO/CoFeB structure is 2 times larger than that of the TiO2−BTO/CoFeB, while the DMI of the TiO2−BTO/CoFeB interface is larger. We explain the observed phenomena by first principles calculations, which ascribe them to the different electronic states around the Fermi level at oxide/ferromagnetic metal interfaces and the different spin-flip process. This study paves the way for further investigation of the PMA and DMI at various oxide/FM structures and thus their applications in the promising field of energy-efficient devices.

S. Finizio, S. Wintz, S. Mayr,  A. J. Huxtable, M. Langer, J. Bailey, G. Burnell,  C. H. Marrows, and J. Raabe, "Current-induced dynamical tilting of chiral domain walls in curved microwires", Applied Physics Letters 116.18 (2020): 182404., (Published 06.05.2020)

DOI:10.1063/5.0005186

Abstract:

We report on the investigation of current-induced domain wall motion of Néel domain walls in perpendicularly magnetized microwires with curved geometries in the flow regime. The investigation was performed by time-resolved scanning transmission x-ray microscopy. In particular, we studied the dynamical tilting of the Néel domain walls, observing that an asymmetric behavior in the domain wall tilt appears upon an inversion of the polarity of the current pulse driving the motion, an effect not predicted by state-of-the-art theories and micromagnetic modeling.

S. Pöllath, T. Lin, N. Lei, W. Zhao, J. Zweck, C. H. Back, "Spin structure relation to phase contrast imaging of isolated magnetic Bloch and Néel skyrmions", Ultramicroscopy 212 (2020), (Published 27.02.2020)

DOI: 10.1016/j.ultramic.2020.112973

open access: arXiv:2002.12469

Abstract:

Magnetic skyrmions are promising candidates for future storage devices with a large data density. A great variety of materials have been found that host skyrmions up to the room-temperature regime. Lorentz microscopy, usually performed in a transmission electron microscope (TEM), is one of the most important tools for characterizing skyrmion samples in real space. Using numerical calculations, this work relates the phase contrast in a TEM to the actual magnetization profile of an isolated Néel or Bloch skyrmion, the two most common skyrmion types. Within the framework of the used skyrmion model, the results are independent of skyrmion size and wall width and scale with sample thickness for purely magnetic specimens. Simple rules are provided to extract the actual skyrmion configuration of pure Bloch or Néel skyrmions without the need of simulations. Furthermore, first differential phase contrast (DPC) measurements on Néel skyrmions that meet experimental expectations are presented and showcase the described principles. The work is relevant for material sciences where it enables the engineering of skyrmion profiles via convenient characterization.

K. Zeissler, S. Finizio, C. Barton, A. Huxtable, J.Massey, J. Raabe, A. V. Sadovnikov, S. A. Nikitov, R. Brearton, T. Hesjedal, G. van der Laan, M. C. Rosamond, E. H. Linfield, G. Burnell and C. H. Marrows, "Diameter-independent skyrmion Hall angle in the plastic flow regime observed in chiral magnetic multilayers", Nature communications 11.1 (2020): 1-11, (Published: 22.01.2020)

DOI: 10.1038/s41467-019-14232-9

open access: arXiv:1908.04239

Abstract:

Magnetic skyrmions are topologically non-trivial nanoscale objects. Their topology, which originates in their chiral domain wall winding, governs their unique response to a motion-inducing force. When subjected to an electrical current, the chiral winding of the spin texture leads to a deflection of the skyrmion trajectory, characterized by an angle with respect to the applied force direction. This skyrmion Hall angle was believed to be skyrmion diameter-dependent. In contrast, our experimental study finds that within the plastic flow regime the skyrmion Hall angle is diameter-independent. At an average velocity of 6 ± 1 m/s the average skyrmion Hall angle was measured to be 9° ± 2°. In fact, in the plastic flow regime, the skyrmion dynamics is dominated by the local energy landscape such as materials defects and the local magnetic configuration.

2019

A. Casiraghi, H. Corte-León, M. Vafaee, F. Garcia-Sanchez, G. Durin, M.Pasquale, G. Jakob, M. Kläui and O. Kazakova, "Individual skyrmion manipulation by local magnetic field gradients", Communications Physics 2.1 (2019): 1-9, (Published: 15.11.2019)

DOI : 10.1038/s42005-019-0242-5

open access: arXiv:1903.00367

Abstract:

Magnetic skyrmions are topologically protected spin textures, stabilised in systems with strong Dzyaloshinskii-Moriya interaction (DMI). Several studies have shown that electrical currents can move skyrmions efficiently through spin-orbit torques. While promising for technological applications, current-driven skyrmion motion is intrinsically collective and accompanied by undesired heating effects. Here we demonstrate a new approach to control individual skyrmion positions precisely, which relies on the magnetic interaction between sample and a magnetic force microscopy (MFM) probe. We investigate perpendicularly magnetised X/CoFeB/MgO multilayers, where for X = W or Pt the DMI is sufficiently strong to allow for skyrmion nucleation in an applied field. We show that these skyrmions can be manipulated individually through the local field gradient generated by the scanning MFM probe with an unprecedented level of accuracy. Furthermore, we show that the probe stray field can assist skyrmion nucleation. Our proof-of-concepts results pave the way towards achieving current-free skyrmion control.

S. Saha, M. Zelent, S. Finizio, M. Mruczkiewicz, S. Tacchi, A. K. Suszka, S. Wintz, N. S. Bingham, J. Raabe, M. Krawczyk and L. J. Heyderman, "Formation of Néel-type skyrmions in an antidot lattice with perpendicular magnetic anisotropy", Phys. Rev. B 100, 144435 (Published: 25.10.2019)

DOI: 10.1103/PhysRevB.100.144435

open access: arXiv:1910.04515

Abstract:

Magnetic skyrmions are particlelike chiral spin textures found in magnetic films with out-of-plane anisotropy and are considered to be potential candidates as information carriers in next generation data storage devices. Despite intense research into the nature of skyrmions and their dynamic properties, there are several key challenges that still need to be addressed. In particular, the outstanding issues are the reproducible generation, stabilization, and confinement of skyrmions at room temperature. Here, we present a method for the capture of magnetic skyrmions in an array of defects in the form of an antidot lattice. We find that inhomogeneity in the total effective field produced by the antidot lattice is important for the formation of skyrmions which are mainly stabilized by the dipolar interaction. With micromagnetic simulations and scanning transmission x-ray microscopy we elucidate that the formation of skyrmions within the antidot lattice depends on the lattice constant and that, below a certain lattice constant, the skyrmion formation is suppressed. Based on our results we propose that, by varying the lattice constant, we can modify the probability of skyrmion formation in different parts of a sample by specific patterning. This provides another platform for experimental investigations of skyrmions and skyrmion-based devices.

S. Pöllath, A. Aqeel, A. Bauer, C. Luo, H. Ryll, F. Radu, C. Pfleiderer, G. Woltersdorf and C. H. Back, "Ferromagnetic resonance with magnetic phase selectivity by means of resonant elastic x-ray scattering on a chiral magnet", Phys. Rev. Lett. 123, 167201 (Published: 14.10.2019)

DOI: 10.1103/PhysRevLett.123.167201

open access: arXiv:1909.08293

Abstract:

Cubic chiral magnets, such as Cu2OSeO3, exhibit a variety of non-collinear spin textures, including a trigonal lattice of spin whirls, so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at GHz frequencies, we probe the ferromagnetic resonance modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS-FMR, is carried out at distinct positions in reciprocal space, it allows to distinguish contributions originating from different magnetic states, providing information on the precise character, weight and mode mixing as a prerequisite of tailored excitations for applications.

S. Finizio, K. Zeissler, S. Wintz, S. Mayr, T. Weßels, A. J. Huxtable, G. Burnell, C. H. Marrows and J. Raabe, "Deterministic Field-Free Skyrmion Nucleation at a Nanoengineered Injector Device", Nano Lett. 2019, 19, 10, 7246-7255 (Published: 17.09.2019)

DOI: 10.1021/acs.nanolett.9b02840

open access: arXiv:1902.10435

Abstract:

Magnetic skyrmions are topological solitons promising for applications as encoders for digital information. A number of different skyrmion-based memory devices have been recently proposed. In order to demonstrate a viable skyrmion-based memory device, it is necessary to reliably and reproducibly nucleate, displace, detect, and delete the magnetic skyrmions, possibly in the absence of external applied magnetic fields, which would needlessly complicate the device design. While the skyrmion displacement and detection have both been thoroughly investigated, much less attention has been dedicated to the study of the skyrmion nucleation process and its sub-nanosecond dynamics. In this study, we investigate the nucleation of magnetic skyrmions from a dedicated nanoengineered injector, demonstrating the reliable magnetic skyrmion nucleation at the remnant state. The sub-nanosecond dynamics of the skyrmion nucleation process were also investigated, allowing us to shine light on the physical processes driving the nucleation.

Christian Back, Giovanni Carlotti, Arianna Casiraghi, Gianfranco Durin, Felipe Garcia-Sanchez, Michaela Kuepferling, Christopher Marrows, Gabriel Soaresand Silvia Tacchi, "Measuring Interfacial Dzyaloshinskii-Moriya Interaction: A Review", proceedings (Published: 05.09.2019)

DOI: 10.3390/proceedings2019026041

Giovanni Carlotti, "Pushing down the lateral dimension of single and coupled magnetic dots to the nanometric scale: characteristics and evolution of the spin-wave eigenmodes", Applied Physics Review 6 (3) 031304 (2019). (Published: 29.08.2019)

DOI: 10.1063/1.5110434

open access: arXiv:1908.11098

Abstract:

Planar magnetic nanoelements, either single- or multilayered, are exploited in a variety of current or forthcoming spintronic and/or ICT devices, such as read heads, magnetic memory cells, spin-torque nano-oscillators, nanomagnetic logic circuits, magnonic crystals, and artificial spin-ices. The lateral dimensions of the elemental magnetic components have been squeezed down during the last decade to a few tens of nanometers, but they are still an order of magnitude larger than the exchange correlation length of the constituent materials. This means that the spectrum of spin-wave eigenmodes, occurring in the gigahertz range, is relatively complex and cannot be described within a simple macrospin approximation. On the other hand, a detailed knowledge of the dynamical spectrum is needed to understand or to predict crucial characteristics of the devices. With this focused review, we aim at the analysis and the rationalization of the characteristics of the eigenmode spectrum of magnetic nanodots, paying special attention to the following key points: (i) Consider and compare the case of in-plane and out of-plane orientation of the magnetization, as well as of single- and multilayered dots, putting in evidence similarities and diversities, and proposing a unifying nomenclature and labeling scheme; (ii) Underline the evolution of the spectrum when the lateral size of magnetic dots is squeezed down from hundreds to tens of nanometers, as in current devices, with emphasis given to the occurrence of soft modes and to the change of spatial localization of the fundamental mode for in-plane magnetized dots; (iii) Extend the analysis from isolated elements to twins of dots, as well as to dense arrays of dipolarly interacting dots, showing how the discretized eigenmodes distinctive of the single element transform in finite-width frequency bands of spin waves propagating through the array.