United States

Tailoring and control of electromagnetic properties of synthetic magnetic structures is advantageous for high frequency applications, such as shielding materials in magnetic recording, where characterisation in the gigahertz frequency range is necessary to determine parameters for simulations and aid component design. In such applications it is desirable to have a high saturation magnetisation, low coercivity, high permeability and close to zero magnetostriction. Meeting almost all these requirements, NiFe is the material of choice for many high frequency applications.&lt;br/&gt;We present a systematic study of the ferromagnetic resonance (FMR) and spin wave properties of Ni&lt;sub&gt;x&lt;/sub&gt;Fe&lt;sub&gt;100-x&lt;/sub&gt; alloy thin superlattice films of the form n[Ni&lt;sub&gt;x&lt;/sub&gt;Fe&lt;sub&gt;100-x&lt;/sub&gt;/Ni&lt;sub&gt;y&lt;/sub&gt;Fe&lt;sub&gt;100-y&lt;/sub&gt;], where n is the number of bilayers. Films were fabricated by planar magnetron sputtering and the effects of deposition conditions were investigated. Magnetic and material properties were measured using FMR [1], vibrating sample magnetometer and x-ray diffraction, with the aim to determine any relation between microstructure and the static and dynamic magnetic properties.&lt;br/&gt;Layer compositions within the bilayers have been chosen with particular interest in fcc/bcc layer combinations such as Ni&lt;sub&gt;80&lt;/sub&gt;Fe&lt;sub&gt;20&lt;/sub&gt;/Ni&lt;sub&gt;20&lt;/sub&gt;Fe&lt;sub&gt;80&lt;/sub&gt;, which may have benefits for some static properties such as high magnetisation and low magnetostriction [2]. Studies on single layers have shown dramatic changes in FMR response across the fcc-bcc boundary near x = 40, figure 1. However, for bilayer films it was found that increasing the thickness of the bcc Ni&lt;sub&gt;20&lt;/sub&gt;Fe&lt;sub&gt;80&lt;/sub&gt; layer in the structure increased the resonant frequency but did not significantly reduce the FMR signal, figure 2.

![](https://assets.underline.io/uploads/markdown_image/1/image/2d9c99cff6d1c85880be60efcc3b4eb1.jpg)

Fig. 1: FMR spectra of 100nm NixFe100-x single layer thin films with x varying from 10 to 60. Note that all measurements were performed at an applied field H=253Oe. XRD is inset.

![](https://assets.underline.io/uploads/markdown_image/1/image/80e55db23ea15b0120ab8fa67c4beb0e.jpg)

Fig. 2: FMR spectra of Ni80Fe20(60-t nm)/Ni20Fe80(t nm) thin films with t varying from 50 to 10. Note that all measurements were performed at an applied field of 253Oe. XRD is inset.




2022 Joint MMM-INTERMAG

Ferromagnetic Resonance of Tuneable Low Magnetostrictive NixFe100-x Superlattice Structures for High Frequency Application

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Tailoring and control of electromagnetic properties of synthetic magnetic structures is advantageous for high frequency applications, such as shielding materials in magnetic recording, where characterisation in the gigahertz frequency range is necessary to determine parameters for simulations and aid component design. In such applications it is desirable to have a high saturation magnetisation, low coercivity, high permeability and close to zero magnetostriction. Meeting almost all these requirements, NiFe is the material of choice for many high frequency applications. We present a systematic study of the ferromagnetic resonance (FMR) and spin wave properties of NixFe100-x alloy thin superlattice films of the form n[NixFe100-x/NiyFe100-y], where n is the number of bilayers. Films were fabricated by planar magnetron sputtering and the effects of deposition conditions were investigated. Magnetic and material properties were measured using FMR [1], vibrating sample magnetometer and x-ray diffraction, with the aim to determine any relation between microstructure and the static and dynamic magnetic properties. Layer compositions within the bilayers have been chosen with particular interest in fcc/bcc layer combinations such as Ni80Fe20/Ni20Fe80, which may have benefits for some static properties such as high magnetisation and low magnetostriction [2]. Studies on single layers have shown dramatic changes in FMR response across the fcc-bcc boundary near x = 40, figure 1. However, for bilayer films it was found that increasing the thickness of the bcc Ni20Fe80 layer in the structure increased the resonant frequency but did not significantly reduce the FMR signal, figure 2.

![](https://assets.underline.io/uploads/markdown_image/1/image/2d9c99cff6d1c85880be60efcc3b4eb1.jpg)

Fig. 1: FMR spectra of 100nm NixFe100-x single layer thin films with x varying from 10 to 60. Note that all measurements were performed at an applied field H=253Oe. XRD is inset.

![](https://assets.underline.io/uploads/markdown_image/1/image/80e55db23ea15b0120ab8fa67c4beb0e.jpg)

Fig. 2: FMR spectra of Ni80Fe20(60-t nm)/Ni20Fe80(t nm) thin films with t varying from 50 to 10. Note that all measurements were performed at an applied field of 253Oe. XRD is inset.

technical paper

An interesting phenomenon occurs in submicron, magnetic vortex ground state particles as their thickness is increased, and the vortex becomes a fully-fledged three dimensional object. Although the ground state remains largely homogeneous through the thickness, one but needs to apply the smallest of excitation to see the emergent shearing of the magnetization texture and resonant modes associated with it [1,2]. Using the nanostencil fabrication technique[3] we obtained planar arrays of increasingly thick (up to 350 nm) magnetic particles, going beyond thicknesses studied previously. Not only do we observe the inversion of intensities of the modes, as high order modes become the most intense, we see also the complete disappearance of the homogeneous G0 mode, which marks a transition where the 2D dynamic solutions completely cease their existence, see the spectrum presented on Fig. 1. This new effect also goes toward a significant increase of the speed of dynamics in the system. In the course of study we place a special emphasis on taking the real, dome-like particle profiles into account, which, as we show, influence the spectra for thick particles significantly. The profiles used were attained with a help of atomic force microscopy. The realistic boundaries primarily tune the non-radiative standing spin wave modes[4] which in turn affect gyrational modes through hybridization. We observe this through the detailed, microscopic study of mode distributions such as the one on Fig. 2, by matching experimental spectra, and juxtaposing stationary trajectories (in the time domain).

![](https://assets.underline.io/uploads/markdown_image/1/image/8f782616bbfa5a82e7cffe9fbfba735f.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/fc47f4d3547c1babcc525b8c1162cc50.jpg)

High Order Gyromode Observation in Dome-like Nanoparticles

High Order Gyromode Observation in Dome-like Nanoparticles

All Optical Helicity Independent Switching (AO-HIS) of magnetization, using single femtosecond laser pulses, has been demonstrated in GdFeCo ferrimagnetic alloys for various concentrations [1] as well as in other structures with antiferromagnetic coupling, Gd/Co, [Tb/Co]n/Ta/CoFeB and Mn2RuxGa [2,3,4]. Up to now, AO-HIS has never been observed for ferromagnetic layers. However, it was shown that a single pulse magnetization reversal of a ferromagnet could be observed in a spin-valve structure [5]. The switching is then achieved by the ultrashort spin current pulse generated from the ultrafast demagnetization of GdFeCo [5,6]. In this work, we study Gdx(FeCo)1-x/Cu/FM spin-valve structures, where FM can be different ferromagnetic layers [7] and the composition x of the GdFeCo alloy is also changed [8]. By increasing the Gadolinium concentration x, we aim at increasing the spin current injected in the copper layer [6]. We show that this can reduce the laser fluence threshold required to observe the FM magnetization reversal. In particular, no AO-HIS of the GdFeCo layer is required and the threshold fluence for the FM layer is around 1.6 mJ/cm2 i.e. comparable to GdFeCo and Gd/Co multilayers [1,2] and smaller than what is achieved for Tb/Co/CoFeB [2] and Mn2RuxGa [3]. We also show that by changing the Curie temperature, the laser pulse duration and the Cu/FM interface, one can control the interaction between the spin current and the FM layer and so the laser fluence threshold. Finally, we measured the dynamics of the reversal of the FM layer, which happens in around a picosecond. We show a model, based on a recent theory for the ultrafast magnetization dynamics of ferromagnets [9], that explains this behavior. We thus designed spin-valve structures that could provide technological advantages regarding both speed and energy efficiency of data storage.

Ultrafast Single Pulse All Optical Magnetization Switching of Ferromagnets

Graphene/ferromagnet interfaces have exhibited various unusual spin-orbit coupling(SOC) related effects despite very small SOC strength of graphene[1-3]. Here we have investigated femtosecond laser induced spin dynamics using an all-optical time-resolved magneto-optical Kerr effect(TR-MOKE) magnetometry in sputter-deposited CoFeB thin films on chemical-vapor-deposition grown single-layer graphene(SLG) by varying the thickness of CoFeB from 1.5 to 6 nm[4]. The ultrafast demagnetization time(τm) extracted using three-temperature modelling(Fig. 1(a)) show a monotonic variation with CoFeB thickness(Fig. 1(b)). The Gilbert damping parameter(α) is directly extracted from the decaying amplitude of precessional oscillation(Fig. 1(c)). We have modelled the CoFeB-thickness-dependent α to estimate the effective spin-mixing conductance(Geff) and two-magnon scattering coefficient(βTMS) for SLG/CoFeB interface(Fig. 1(d)) which revealed spin pumping(SP) [4] as the dominant contributor to modulation of α(Fig. 1(e)). Furthermore, we have observed an inverse relationship between τm and α for SLG/CoFeB heterostructures(Fig. 1(f)) due to the dominance of SP-induced nonlocal spin-transport mechanism[4]. To disentangle other possible interface contributions to the damping such as spin memory loss(SML), we have inserted a 1-nm-thick Cu spacer layer between the SLG and CoFeB. Negligible damping modulation by the insertion of Cu spacer between SLG and CoFeB confirms that additional effects like SML are absent in our system. In summary, this study has provided a qualitative understanding of different ultrafast spin manipulation mechanisms in a graphene-based heterostructure, which can lead towards the next-generation graphene-based ultrafast spintronics devices. AB acknowledges the financial assistance from S. N. Bose National Centre for Basic Sciences(SNBNCBS), India under Project SNB/AB/11-12/96 and SNB/AB/18-19/211. SNP, SM, SC and ArB acknowledge SNBNCBS for respective fellowship.

![](https://assets.underline.io/uploads/markdown_image/1/image/2365a212e2a849241df3b94e8286c456.jpg)

Fig. 1(a) Ultrafast demagnetization in SLG/CoFeB(d) (b) Evolution of τm with d (c) Precessional oscillations at H=3.59 kOe (d) Evolution of α fitted with a phenomenological model (e) Variation of 1/τm as a function of α (f) Contributions of SP and TMS to α.

Correlation between Femtosecond Laser Induced Spin Current and Spin Dynamics at the Single Layer Graphene/CoFeB Thin Films

Ultrafast generation of chiral magnetic order is one of the most sought-after technology for its potential application in next generation magnetic memory devices [1]. Recent experimental demonstration of generation of skyrmions with ultrafast laser pulses [2] has opened new horizons regarding the experimental feasibility of achieving this. In spite of such immense experimental achievement, the theoretical understanding of the underlying physics is still not very clear. Most of the existing studies tries to explain this with classical magnetisation dynamics only and thus completely miss the impact of the electronic interactions which plays crucial role in early sub-picosecond regime. More advanced TD-DFT based approaches are quite successful in explaining the fast dynamics in this regime, however, they are not quite fruitful in explaining the slow magnetisation dynamics which can last for several picoseconds. In this presentation we bridge this gap with the help of a quantum-classical hybrid approach which allows us to reveal the physics with a sub-femtosecond resolution and at the same time look at the steady state after several picoseconds [3]. We have successfully identified both the inherent and emergent interactions which drives the intertwined electronic and magnetic interaction leading to a stable chiral configuration and thus can predict their lifetime as well. We show here that the laser assisted dynamics is inherently different from the predictions of phenomenological two/three temperature model which has been widely used in modelling ultrafast demagnetisation. We show that the thermal re-population leads to formation of multiple domains with higher energy and less stability compared to smooth spiral formed by laser excitation. The final chiral configuration can be tuned both with laser and material parameters and formation can sustain at moderate temperature which makes our findings feasible for experimental realisation and thus would be instrumental in revealing the rich physics of ultrafast optical manipulation of the magnetisation.

![](https://assets.underline.io/uploads/markdown_image/1/image/17b5b1fc1f24b7f50457de2d6090ae8f.jpg)

Comparison of magnetisation dynamics excited by laser and thermal repopulation. Thermal excitation forms multiple domain where laser forms a smooth spiral configuration.

Imprinting chirality in collinear magnet with ultrafast laser

The discovery of helicity-independent all-optical switching1 as well as ps current-pulse driven magnetization reversal2 of a ferrimagnetic GdFeCo led to a significant development towards ultrafast magnetization reversal of a magnetic tunnel junction (MTJ) based memory element. Ultrafast switching of Co/Pt multilayers coupled with a GdFeCo has been observed within ~ 7 ps which occurs due to RKKY exchange coupling3. However, GdFeCo isn’t a desirable choice for a MTJ as it does not hold PMA for a patterned dot with a diameter less than a mm4. On the other hand, CoGd ferrimagnet can maintain its PMA down to 200 nm diameter4. In this work, we have experimentally observed the all-optical time-resolved magnetization dynamics of a “CoGd/Pt spacer (1 to 4 nm)/ [Co/Pt] multilayers” heterostructure. The magnetization of CoGd is reversed after 1.5 ps. The Co/Pt multilayer which has slightly higher demagnetization rate, stays demagnetized as the electron temperature reaches its Currie temperature before getting switched ~ 3 ps due to enough angular-momentum transfer from the CoGd sublattice as shown in Fig. 1(a). We rule out the possibility of Co/Pt swithcing triggered by non-local spin current generated from CoGd as Co/Pt switched for both ferromagnetic and anti-ferromagnetic coupling. We performed analytical calculation to simulate the time-resolved dynamics as shown in Fig. 1(b) using an extended microscopic three temperature model (M3TM) proposed by Beans et al5. Considering inter-sublattice, intra-sublattice and indirect RKKY exchange scatterings, we explain the magnetization reversal dynamics of different magnetic components of ferromagnetically and antiferromagnetically coupled as well as decoupled ferromagnet-ferrimagnet heterostructures. We demonstrate that irrespective of the nature of RKKY coupling, ultrafast switching of the Co/Pt multilayers can be achieved, and its switching time strongly depends on the RKKY interaction strength. This work experimentally as well as theoretically establishes the mechanism of all-optical switching in such magnetic heterostructures.

![](https://assets.underline.io/uploads/markdown_image/1/image/17766eb2037f4c3871163c64928d3c26.jpg)

(a) Experimental and (b) theoretical time-resolved magnetization dynamics of a ferromagnetically ([Co/Pt]3/Co/Pt 1 nm/CoGd/cap) coupled stacks.

RKKY exchange coupling mediated ultrafast all-optical switching of a ferromagnet

Single pulse all-optical switching (SP-AOS) using 40 fs light pulses was discovered in films of the amorphous rare earth-transition metal (RE-TM) alloy a-Gd(FeCo)3 [1]. The switching takes less than 5 ps and relies on the different demagnetisation times of the Gd and Fe,Co subnetworks. Replacing Gd by another RE was expected to yield more materials that exhibit ultrafast switching, but it did not happened. Indeed, amorphous RE-TM alloys other than Gd(FeCo)3 have only been switched transiently by a single pulse [2] or slowly using many polarised pulses [3]. Here, we report stable SP-AOS in amorphous Dy-Co and Tb-Co films with perpendicular anisotropy. Room-temperature coercivity is 30-50 mT, and compensation temperatures Tcomp are below 300 K. The example of a-DyCo3 is shown in Fig 1. The behavior is surprising. A single 200 fs pulse creates a non-uniform 40 µm dark spot on a uniformly-magnetized light film. Domain structure on a scale of ~ 3 µm is observed. After two pulses, the darker domains switch back, and the multidomain state will toggle for a few more pulses before leaving the sample in a nonuniform mid-gray state. Images are obtained on a strip of material irradiated with 1-5 pulses, using an off-site Kerr microscope. Other samples show a variety of behavior. The switching of a-TbCo4 shown in Fig. 2 is also granular, but the lighter and darker spots are aggregated into lighter and darker rings with unequal numbers of small dark and light domains. The contrast between rings again disappears after a few pulses, but the small domains persist. This is quite unlike the uniform toggling of large domains, comparable in size to the laser spot, that are seen in SP-AOS of ferrimagnetic a-Gd(FeCo)3 and crystalline Mn2RuxGa. The key difference is probably the random uniaxial anisotropy for the non S-state rare ions and temperature-dependence, which governs that of the coercivity. The influence of stray dipolar fields on a µm scale and possible of radial heat waves in the substrate will be considered in the context of ultra-fast SP-AOS in these a-RE-TM materials.

![](https://assets.underline.io/uploads/markdown_image/1/image/d2f69edc767f147428037a22f4910d14.jpg)

SP-AOS in a 10 nm a-DyCo3 alloy film with perpendicular magnetization. Scale bar 40 μm.

![](https://assets.underline.io/uploads/markdown_image/1/image/952962fa921f2d2bdfcf19a77cdb0149.jpg)

SP-AOS in 20 nm a-TbCo4 with perpendicular magnetic anisotropy.

Single pulse all-optical magnetic switching in amorphous DyCox and TbCox

The ability to control and tune magnetic dissipation is a key concept of emergent spintronic technologies. Magnon-magnon processes constitute a major dissipation channel in nanomagnets [1-3], redefine their response to spin-torques [4], and hold promise for manipulating magnetic states on the quantum level. Controlling these processes [5,6], while being imperative for many spintronic applications [4], has remained difficult to achieve. We identify two avenues to realize this goal: by breaking the symmetry of the static magnetic state or by breaking the symmetry of the magnon modes. Here we focus on the latter approach due its particular technological relevance. As a vehicle for our study, we employ magnetic tunnel junction nanopillars that consist of a free layer and a synthetic antiferromagnet (SAF) [7]. In the normal state of the SAF, its stray field is small at the position of the free layer – the fields from the two constituent layers of the SAF largely cancel out [8]. However, once we trigger SAF’s spin-flop transition, their spins become canted and generate a stray field which is nonuniform at nanoscale – a prerequisite for breaking the symmetry of free layer’s magnons. By controllably switching the SAF between its normal and spin-flop states, we achieve to toggle three-magnon processes in the free layer. We tune the magnon interaction by at least one order of magnitude and thus engineer two distinct dissipative states. Our results open up an avenue for manipulating magnon processes by external stimuli at nanoscale, tuning the nonlinear response in magnetic neuromorphic networks, and controlling large excitation regimes in spin-torque devices. They furthermore show promise for engineering coherent magnon coupling in hybrid quantum information systems. This work was supported by the National Science Foundation through Grant No. ECCS-1810541.

Controlling Magnon Interaction by a Nanoscale Switch

Ferromagnetic [Pt/Co]n multilayers that are composed of n stacked [Pt/Co] bilayers have been widely investigated over the past decades, mainly due to the easy tunability of various magnetic properties such as the potentially strong perpendicular magnetic anisotropy (PMA). More recently, it has been demonstrated that the addition of heavy metals (HM) such as Ir or W can lead to the presence of sizeable chiral exchange interactions in [Pt/Co/HM]n systems [1]. As a consequence, topological spin textures (e.g., skyrmions) are commonly reported in these material systems even at room temperature, thus making them promising candidates for future spintronics applications [2]. In the present work, we use additional manganese layers to break the spatial inversion symmetry of conventional [Pt/Co]n stacks and thereby, in combination with spin-orbit interaction, introduce chiral exchange interactions. The investigated [Pt/Co/Mn]n samples were fabricated by magnetron sputtering. Structural characterization of the multilayer stacks was done by performing X-ray reflectometry (XRR) measurements, while magnetic hysteresis curves were acquired in a vibrating sample magnetometer (VSM). In addition, real-time imaging of magnetic domains as a function of the external magnetic field was conducted using a home-built magneto-optical Kerr effect (MOKE) microscope. Our results indicate a complex and sensitive dependence of various magnetic energy terms on the individual layer thicknesses, number of multilayer repetitions as well as on deposition parameters. This is particularly reflected in the shape of hysteresis loops or the types of spin textures seen in our magneto-optical imaging experiments. For instance, we discuss that the presence of defects leads to a very slow dynamics of dendritic-type domain groth in some of the investigated multilayers. Finally, we also elaborate on various approaches towards the possible observation of magnetic skyrmions in [Pt/Co/Mn]n multilayers. This work is supported by the Deutsche Forschungsgemeinschaft (DFG) through the research fellowship LO 2584/1-1 and the NSF through the University of Illinois at Urbana-Champaign Materials Research Science and Engineering Center under Grant No. DMR-1720633. .

Tuning the Magnetic Properties of Ferromagnetic [Pt/Co/Mn]n Multilayers

The recent reports on magnetodynamic properties of soft magnetic thin films attain the lowest damping factor [1-3]. The damping is required for spin-wave propagation and spin manipulation investigation where the reduced spin-wave dissipation leads to a larger decay length. The low damping thin films are important for microwave applications [4], spin transfer switching devices, and other application in magnon spintronics. In order to achieve the lowest damping, the FeGaB has chosen with Al2O3 in this study. Ta(10nm)/FeGaB(15nm)/Al2O3(3nm)/Ta(3nm) thin film were deposited on Si/SiO2(190nm) substrate by sputtering and was annealed at 300oC for 3 hours in the Ar gas. The static magnetization results inform that saturation and remanent magnetization has increased for annealed thin film shown in Fig.1 (a). After annealing, the dipolar field influence has reduced, the magnetic moment fluctuation has not observed. Fig. 1 (b) shows the annealed films have monotonously increased. The dynamics properties are studied with temperature variation with 100 K to 300 K and exciting frequency from 2 to 20 GHz. Fig.2 (a) illustrates the absorption spectrum of both films at 100K, the spectrum has shifted to lower fields for annealed films. The unannealed thin film have existed the small hump at higher magnetic films before resonance peak, which may be impurities and surface defects of the thin film. But, the hump has disappeared for annealed films in Fig. 2 (b). The absorption spectrum provides linewidth and resonance fields (Hr) for excitation frequency. The linewidth –frequency plot provides damping factor and inhomogeneous linewidth [5]. The damping factor of both films are decreasing with decreasing temperature as Fig.2 (c). Fig.2 (d) shows the annealed film has larger effective magnetization value than that of unannealed thin film.

![](https://assets.underline.io/uploads/markdown_image/1/image/456a20cfd7f6097c2f6a3fe240b5f535.jpg)

Fig.1 (a) Normalized M-H loop for unannealed and annealed thin films at 300K. Insets shows M-H loop at different temperatures; (b) Coercive fields (Hc) versus temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/f9b3d8de83b131c23c6946adfb17f683.jpg)

Fig.2 (a) Absorption spectrum of both thin films at 100K, (b) absorption of annealed thin film at 20GHz with different temperatures, (c) damping factor (α) versus temperature, (d) effective magnetization versus temperature.

Temperature dependence static and dynamic properties of soft magnetic thin film FeGaB/Al2O3 for microwave applications

Magnetization dynamics in laterally confined nanodots have potential applications in spin-torque nano oscillators,1 magnetic logic and sensors2. The ground state of nanodot shows vortex at remanence and it exhibits rich spin dynamics spectra3. With the application of magnetic field, the vortex and saturated magnetization states are observed at low and high field regions respectively4. In our present work, we have studied the magnetization dynamics in high aspect ratio single and trilayer nanodots. Circular Permalloy (Py) nanodots (diameter = 120nm) are fabricated over a large area using deep ultraviolet lithography technique. The structures consist of single layer nanodots with thicknesses (L) 20 and 50 nm and a trilayer with two Py layers separated by a non-magnetic layer: Py(20)/Pd(10)/Py(50). Numbers within the brackets are in nm. The dynamic properties are characterized using the ferromagnetic resonance (FMR) technique. The simulated hysteresis loops are shown in Fig. 1(a). The FMR absorptions show rich spectra as a function of magnetic field and thickness. For instance, we discuss the experimental results at an excitation frequency of 10 GHz as shown in Fig. 1(b). We observed two modes for L = 20 nm nanodots at resonance fields 130 and 220 mT and a single mode appears at 210 mT for L = 50 nm nanodots. We performed micromagnetic simulations to understand the experimental results. The simulated mode profiles reveal that the high intense mode corresponds to the center mode (CM) and the low intense mode corresponds to the edge mode (EM) arising due to the inhomogeneous effective field. The CM is found to be sensitive to the thickness of the nanodot. On the other hand, in the FMR spectra of Py(20)/Pd(2)/Py(50), two resonant modes appear at 200 mT and 250 mT. These two center modes arise due to the in-phase and out-of-phase precession of spins in magneto-dynamically coupled layers. These results can be useful for nanoscale magnonic applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/2e01f4ef86e02401510bbe909771a373.jpg)

Fig 1: (a) Simulated hysteresis loops for single and trilayer nanodot arrays. The remanent states are shown in the inset. (b) Experimental FMR spectra of single and trilayer nanodot arrays.

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