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Vibrating sample magnetometery (VSM) combined with Brillouin light scattering (BLS) were used to investigate the Dzyaloshinskii-Moriya interaction (iDMI), the perpendicular magnetic anisotropy (PMA) and the damping in ${\mathrm{Co}}_{0.5}{\mathrm{Fe}}_{0.5}$-based systems grown by sputtering on $\mathrm{Si}/{\mathrm{SiO}}_{2}$ substrates, using Pt or Cu buffer layers and Hf capping layer of variable thickness $(0\ensuremath{\le}{t}_{\mathrm{Hf}}\ensuremath{\le}2\phantom{\rule{0.28em}{0ex}}\mathrm{nm})$. VSM measurements revealed a significant decrease of the areal magnetic moment at saturation as ${t}_{\mathrm{Hf}}$ increases, most likely due to the increase of the magnetic dead layer thickness at CoFe/Hf interface up to $0.73\ifmmode\pm\else\textpm\fi{}0.06\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ for ${t}_{\mathrm{Hf}}=2\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$. Damping measurements allowed concluding to the weaker spin pumping contribution by the CoFe/Hf interface compared to Pt/CoFe. The analysis of the ${t}_{\mathrm{Hf}}$ dependence of damping within a model considering the contribution of each interface allowed us to determine the spin diffusion length of Hf, found to be 1.7 nm. The Hf thickness dependence of iDMI and PMA constants revealed significant (weak) contribution of the CoFe/Hf interface to PMA (iDMI). The surface iDMI constant of CoFe/Hf interface was estimated to be $(\ensuremath{-}0.37\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}{10}^{--7}\phantom{\rule{0.28em}{0ex}}\mathrm{erg}/\mathrm{cm}$. This suggests that the iDMI sign of Hf and Pt are opposite, and an additive behavior can be obtained when they are placed in opposite sides of the CoFe layer, allowing thus to strengthen the iDMI, needed for some applications. Quadratic correlations between PMA and iDMI constants and linear dependence of damping versus PMA constant were obtained confirming their relationship with the spin-orbit coupling.

In ${\mathrm{Ta/(Co,Fe)B/HfO}}_{2}$ stacks, a gate voltage drives, in a nonvolatile way, the system from an underoxidized state exhibiting in-plane anisotropy (IPA) to an optimum oxidation level resulting in perpendicular anisotropy (PMA) and further into an overoxidized state with IPA. The $\mathrm{IPA}\phantom{\rule{0.1em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.1em}{0ex}}\mathrm{PMA}$ regime is found to be significantly faster than the $\mathrm{PMA}\phantom{\rule{0.1em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.1em}{0ex}}\mathrm{IPA}$ regime, whereas only the latter shows full reversibility under the same gate voltages. The effective damping parameter also shows a marked dependence with gate voltage in the $\mathrm{IPA}\phantom{\rule{0.1em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.1em}{0ex}}\mathrm{PMA}$ regime, going from 0.029 to 0.012, and only a modest increase to 0.014 in the $\mathrm{PMA}\phantom{\rule{0.1em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.1em}{0ex}}\mathrm{IPA}$ regime. The existence of two magnetoionic regimes has been linked to a difference in the chemical environment of the anchoring points of oxygen species added to underoxidized or overoxidized layers. Our results show that multiple magnetoionic regimes can exist in a single device and that their characterization is of great importance for the design of high-performance spintronics devices.

Microstrip line ferromagnetic resonance (MS-FMR) and Brillouin light scattering (BLS) in the Damon-Eshbach geometry were used to investigate the perpendicular magnetic anisotropy (PMA), the damping and the interfacial Dzyaloshinskii-Moriya (iDMI) interaction in ferromagnetic $(\mathrm{FM})/\mathrm{Ta}{\mathrm{O}}_{x}\text{\ensuremath{-}}\mathrm{based}$ systems as a function of the ferromagnetic ($\mathrm{FM}=\mathrm{Co}$ or ${\mathrm{Co}}_{8}{\mathrm{Fe}}_{72}{\mathrm{B}}_{20}$) and the $\mathrm{Ta}{\mathrm{O}}_{x}$ thicknesses (oxidation level). The analysis of the experimental FMR and BLS data has shown that the effective magnetization, the Gilbert damping parameter \ensuremath{\alpha} and the iDMI are inversely proportional to the CoFeB and the Co films thickness. The BLS investigation of the iDMI variation versus the $\mathrm{Ta}{\mathrm{O}}_{x}$ thickness and oxidation level reveals a contribution of $\mathrm{FM}/\mathrm{Ta}{\mathrm{O}}_{x}$ mediated by the presence of a Rashba field at this interface. Finally, we evidenced a correlation between iDMI and PMA by varying the Cu spacer thickness in the $\mathrm{Pt}/\mathrm{Cu}/\mathrm{Co}/\mathrm{Ta}{\mathrm{O}}_{x}$ system and we showed that both PMA and iDMI are localized at the first atomic monolayers of the Pt/Co interface. The observed non-linear dependence of PMA versus iDMI constant is attributed to similar interface orbital hybridizations involved in both quantities.

We report the results of the experimental investigation of magnonic Bloch modes in the presence of asymmetric dispersion induced by the interfacial Dzyaloshinskii-Moriya interaction by means of Brillouin light-scattering technique. It was realized in a specially designed ultrathin CoFeB/Pt periodic structure consisting of an array of rectangular nanostrips separated by half-etched grooves. The proposed theory based on the coupled mode approach explains the major features observed experimentally, such as Brillouin zone folding and the asymmetry of the magnonic band-gap points in the reciprocal $k$ space.

We study the optical and magneto-optical properties of low-concentration arrays of ultrathin nickel nanowires by means of Brillouin spectroscopy of thermal magnons. Brillouin spectroscopy in such quasitransparent magneto-optical structures is dominated by the Bragg phase synchronism mechanism. At variance with ultrathin cobalt nanowire arrays, the Stokes/anti-Stokes scattering pattern is practically symmetrical. This feature is attributed to their peculiar optical properties.

We present a complete calculation of spin waves in magnetic stacks, including the interfacial Dzyaloshinskii-Moriya interaction (iDMI) as a boundary condition, and discuss the influence of interlayer coupling and magnetic anisotropy on the spin-wave nonreciprocity. We show that the usual simple approach relating the iDMI strength to the slope of the spin-wave nonreciprocity versus the spin-wave number, in the case of a thin ferromagnetic film in contact with a heavy metal exhibiting a strong-orbit coupling, is not valid in many more complex structures. In the case of stacks made of identical magnetic layers, an analytical method allowed us to check that the effect of iDMI on the entire structure is captured by including the total thickness of the ferromagnetic layers. The experimental data obtained for some systems by means of Brillouin light scattering are analyzed through the presented models.

The interfacial Dzyaloshinskii-Moriya interaction (IDMI) is investigated in Co2FeAl (CFA) ultrathin films of various thicknesses (0.8 nm ≤ tCFA ≤ 2nm) grown by sputtering on Si substrates, using Pt, W, Ir, and MgO buffer or/and capping layers. Vibrating sample magnetometry reveals that the magnetization at saturation (Ms) for the Pt- and Ir-buffered films is higher than the usual Ms of CFA due to the proximity-induced magnetization (PIM) in Ir and Pt estimated to be 19% and 27%, respectively. The presence of PIM in these materials is confirmed using x-ray resonant magnetic reflectivity. Moreover, while no PIM is induced in W, higher PIM is obtained with Pt when it is used as a buffer layer rather than a capping layer. Brillouin light scattering in the Damon-Eshbach geometry is used to investigate the thickness dependences of the IDMI constants from the spin-wave nonreciprocity and the perpendicular anisotropy field versus the annealing temperature. The IDMI sign is found to be negative for Pt / CFA and Ir / CFA, while it is positive for W / CFA. The thickness dependence of the effective IDMI constant for stacks involving Pt and W shows the existence of two regimes similar to that of the perpendicular anisotropy constant due to the degradation of the interfaces as the CFA thickness approaches a critical thickness. The surface IDMI and anisotropy constants of each stack are determined for the thickest samples where a linear thickness dependence of the effective IDMI constant and the effective magnetization are observed. The interface anisotropy and IDMI constants investigated for the Pt / CFA / MgO system show different trends with the annealing temperature. The decrease of the IDMI constant with increasing annealing temperature is probably due to the electronic structure changes at the interfaces, while the increase of the interface anisotropy constant is coherent with the interface quality and disorder enhancement.

$\mathrm{C}{\mathrm{o}}_{2}\mathrm{FeAl}$ (CFA) ultrathin films, of various thicknesses $(0.9\phantom{\rule{0.28em}{0ex}}\mathrm{nm}\ensuremath{\le}{t}_{\mathrm{CFA}}\ensuremath{\le}1.8\phantom{\rule{4pt}{0ex}}\mathrm{nm})$, have been grown by sputtering on Si substrates, using Ir as a buffer layer. The magnetic properties of these structures have been studied by vibrating sample magnetometry (VSM), miscrostrip ferromagnetic resonance (MS-FMR), and Brillouin light scattering (BLS) in the Damon-Eshbach geometry. VSM characterizations show that films are mostly in-plane magnetized and the saturating field perpendicular to the film plane increases with decreasing CFA thickness suggesting the existence of a perpendicular interface anisotropy. The presence of a magnetic dead layer of 0.44 nm has been detected by VSM. The MS-FMR with the magnetic field applied perpendicularly to the film plane has been used to determine the gyromagnetic factor. The BLS measurements reveal a pronounced nonreciprocal spin wave propagation, due to the interfacial Dzyaloshinskii-Moriya interaction (DMI) induced by the Ir interface with CFA, which increases with decreasing CFA thickness. The DMI sign has been found to be the same (negative) as that of Pt/Co, in contrast to the ab initio calculation on Ir/Co, where it is found to be positive. The thickness dependence of the effective DMI constant shows the existence of two regimes similarly to that of the perpendicular anisotropy constant. The surface DMI constant ${D}_{s}$ was estimated to be $\ensuremath{-}0.37\phantom{\rule{0.16em}{0ex}}\mathrm{pJ}/\mathrm{m}$ for the thickest samples, where a linear thickness dependence of the effective DMI constant has been observed.

Interface Dzyaloshinskii-Moriya interactions (iDMIs) in interlayer exchange coupled (IEC) Pt/${\mathrm{Co}}_{20}{\mathrm{Fe}}_{60}{\mathrm{B}}_{20}$(1.12 nm)/Ru/${\mathrm{Co}}_{20}{\mathrm{Fe}}_{60}{\mathrm{B}}_{20}$(1.12 nm) systems have been studied theoretically and experimentally. A vibrating sample magnetometer has been used to measure their magnetization at saturation and their interlayer exchange coupling constants. The latter are found to be of an antiferromagnetic nature for the investigated Ru range thickness ($0.5\text{--}1\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$). Their dynamic magnetic properties were studied using the Brillouin light scattering (BLS) technique. The BLS measurements reveal pronounced nonreciprocal spin-wave propagation. In contrast to the calculations for symmetrical IEC CoFeB layers, this experimental nonreciprocity is Ru thickness and thus coupling strength dependent. Therefore, to explain the experimental behavior, a theoretical model based on the perpendicular interface anisotropy difference between the bottom and top CoFeB layers has been developed. We show that the Ru thickness dependence of the spin-wave nonreciprocity is well reproduced by considering a constant iDMI and different perpendicular interfacial anisotropy fields between the top and bottom CoFeB layers. This anisotropy difference has been confirmed by the investigation of the CoFeB thickness dependence of the effective magnetization of Pt/CoFeB/Ru and Ru/CoFeB/MgO individual layers, where a linear behavior has been observed.

Spin waves in perpendicularly magnetized ${\text{Pt/Co/AlO}}_{x}/\text{Pt}$ ultrathin films with varying Co thicknesses (0.6--1.2 nm) have been studied with Brillouin light spectroscopy in the Damon-Eshbach geometry. The measurements reveal a pronounced nonreciprocal propagation, which increases with decreasing Co thickness. This nonreciprocity, attributed to an interfacial Dzyaloshinskii-Moriya interaction (DMI), is significantly stronger than asymmetries resulting from surface anisotropies for such modes. Results are consistent with an interfacial DMI constant ${D}_{\mathrm{s}}=\ensuremath{-}1.7\ifmmode\pm\else\textpm\fi{}0.11\phantom{\rule{0.28em}{0ex}}\text{pJ}$/m, which favors left-handed chiral spin structures. This suggests that such films below 1 nm in thickness should support chiral states such as skyrmions at room temperature.

Investigations of microwave properties of Ni-based inverse ferromagnetic opal-like film with the [111] axis of the fcc structure along the normal direction to the film have been carried out in the 2--18 GHz frequency band. We observed multiple spin wave resonances for the magnetic field applied perpendicular to the film, i.e., along the [111] axis of this artificial crystal. For the field applied in the film plane, a broad band of microwave absorption is observed, which does not contain a fine structure. The field ranges of the responses observed are quite different for these two magnetization directions. This suggests a collective magnetic ground state or shape anisotropy and collective microwave dynamics for this foam-like material. This result is in agreement with SQUID measurements of hysteresis loops for the material. Two different models for this collective behavior are suggested that satisfactorily explain the major experimental results.

Dynamic magnetic properties of arrays of Ni nanorods with a low aspect ratio have been investigated. It has been shown that the spectra of spin-wave resonances localized on nanorods with a low aspect ratio typically feature the presence of zones with high density of states resulting in a characteristic two-peak pattern of Stokes and anti-Stokes lines of magneto-optical (MO) Brillouin light scattering with pronounced Stokes--anti-Stokes (S-AS) asymmetry. A simple theoretical model based on the analysis of the elliptic character of the polarization of the optical wave interacting with a dipole magnetostatic wave has been proposed. It has been shown that the S-AS asymmetry is due entirely to the asymmetry of the MO interaction efficiency with respect to time reversal of the magnetic precession in a magnon.

${\text{Co}}_{2}\text{MnGe}$ films of different thicknesses (34, 55, and 83 nm) were grown by rf sputtering at $400\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ on single-crystal ${\text{Al}}_{2}{\text{O}}_{3}$ corundum substrates showing an in-plane $\mathbf{c}$ axis. Their dynamic magnetic properties were studied using conventional and microstrip line (MS) ferromagnetic resonances (FMRs), as well as Brillouin light scattering (BLS) techniques. The effective magnetizations and gyromagnetic factors are first deduced from the resonance spectra involving the uniform magnetic mode under in-plane and out-of-plane magnetic applied fields. The angular dependence of the frequency, measured under a weak in-plane magnetic applied field, then allows deriving of the parameters describing the in-plane magnetic anisotropy. In the 34- and 55-nm-thick films, its behavior is described assuming a magnetic energy density showing an orthorhombic symmetry with a twofold axis normal to the film and planar anisotropy axes at $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/4$ of the $\mathbf{c}$ axis of the substrate; however, due to the comparative deduced values of the pertinent coefficients, this energy density is predominantly tetragonal. In the thickest film (83 nm), one of the planar anisotropy axes is parallel to $\mathbf{c}$ and approximate tetragonal symmetry is no more observed. Moreover, the orthorhombic symmetry is not completely fulfilled and a small misalignment between the principal directions connected to the uniaxial and the fourfold energy terms appears. Finally, the perpendicular surface standing modes, which are observed in MS-FMR and in BLS spectra, allow evaluation of the exchange stiffness constant. Good agreement between BLS and MS-FMR measurements has been found.

Behavior of dipole-exchange spin waves (SWs) in the Damon-Eshbach geometry in a nanocomposite ${({\text{SiO}}_{2})}_{100\ensuremath{-}x}{\text{Co}}_{x}$ superferromagnetic $(x=80\text{ }\text{at}\text{.}\text{ }%)$ film has been studied by Brillouin light scattering. The measured value of the effective exchange constant turned out to be three times less than its value for the bulk cobalt. A qualitative theoretical model has been proposed to explain this reduction. It has been shown that the ``superspin'' approximation, identifying each nanoparticle with a ``magnetic point'' with no internal structure, is not sufficient to account for the description of the SW behavior of a concentrated nanocomposite medium.

Using Brillouin light scattering measurements, we have studied the properties of the spin waves in various arrays of Permalloy wires showing widths of 0.5, 1, and 1.5 \ensuremath{\mu}m. When the transferred in-plane wave vector ${\mathbf{\ensuremath{\kappa}}}_{\ensuremath{\parallel}},$ specified by the experimental setup, is perpendicular to the wires, a sampling of the Damon-Eshbach surface mode branch giving rise to a set of discrete dispersionless modes is observed. We attribute this behavior to a lateral quantization of the wave vector ${\mathbf{q}}_{\ensuremath{\parallel}}$ of the magnetic excitations. The frequency separation between two adjacent modes is found to decrease when the width D of the wires increases. However, this frequency dependence does not simply follow the expected one assuming the usual naive relation ${q}_{\ensuremath{\parallel},n}=n\ensuremath{\pi}/D,$ which would not allow one to give account of the behavior of the lowest mode $n=0.$ We have performed numerical calculations of the dynamical magnetization response functions of these rectangular cross section wires using the method of finite elements. The magnetic parameters used in these calculations were derived from the experimental Brillouin spectra of the unpatterned films. Both our experiments and our calculations agree with the results expected from the unpatterned film assuming the following discrete values: ${q}_{\ensuremath{\parallel},0}=0,$ ${q}_{\ensuremath{\parallel},n}=\ensuremath{\pi}(n+\ensuremath{\beta})/D.$ The zero value observed for the lowest mode $n=0$ simply results from the calculation and does not need for an additional hypothesis as previously proposed.