Journal of Science: Advanced Materials and Devices 8 (2023) 100608 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Control of magnetic vortex states in FeGa microdisks: Experiments and micromagnetics Gajanan Pradhan a, b, *, Alessandro Magni a, Federica Celegato a, Marco Coisson a, Gabriele Barrera a, Lenka Mikulickova   c, Jon Ander Arregi d, Ladislav Celko d , ch Uhlír , Paola Rizzi , Paola Tiberto Vojte d b a a Advanced Materials and Life Science Divisions, Istituto Nazionale di Ricerca Metrologica (INRIM), Strada delle Cacce, 91, Turin, 10135, Italy b Chemistry Department and NIS, University of Turin, Via Pietro Giuria, 7, Turin, 10125, Italy c Thin Film Technological Service s.r.o., Novodvorska, 994-138, Prague, 14200, Czech Republic d Central European Institute of Technology (CEITEC), Brno University of Technology, Purkynova, 123, Brno, 61200, Czech Republic a r t i c l e i n f o a b s t r a c t Article history: Magnetic vortices have been an interesting element in the past decades due to their flux-closure domain Received 21 February 2023 structures which can be stabilized at ground states in soft ferromagnetic microstructures. In this work, Received in revised form vortex states are shown to be nucleated and stabilized in Fe80Ga20 and Fe70Ga30 disks, which can be an 2 July 2023 upcoming candidate for applications in strain-induced electric field control of magnetic states owing to Accepted 8 July 2023 Available online 14 July 2023 the high magnetostriction of the alloy. The magnetization reversal in the disks occurs by the formation of a vortex, double vortex or S-domain state. Micromagnetic simulations have been performed using the FeGa material parameters and the simulated magnetic states are in good agreement with the experi- Keywords: Magnetic vortex mental results. The studies performed here can be essential for the use of FeGa alloy in low-power Magneto-optic Kerr effect electronics. Magnetic force microscope © 2023 Vietnam National University, Hanoi. Published by Elsevier B.V. This is an open access article Micromagnetic simulations under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction component (polarity, p). The clockwise (CW) and counter- clockwise (CCW) rotations correspond to c ¼ 1 and þ1, respec- Magnetic vortex states have been studied quite extensively in tively. The polarization can point up (p ¼ þ1) or down (p ¼ 1). The the past two decades due to its potential to be used in memory combination of c and p will result in four different states. The first applications and microwave oscillators [1e8]. These states have report on lifting the degeneracy of these states was given by Im topologically stable spin configurations which are suitable to be et al. where the authors demonstrated both experimentally and formed in confined small-scale ferromagnetic structures like with micromagnetic simulations that the two groups, cp ¼ þ1 and squares or disks [9]. The suitable materials for stabilizing a vortex cp ¼ 1 can have different probabilities in formation [11]. This are the ones with a soft magnetic behavior, where a good balance symmetry breaking is explained by the presence of intrinsic between exchange and dipolar energies exists. The stabilization of a DzyaloshinskiieMoriya interaction (DMI) having broken inversion single vortex state depends largely on the size of the magnetic symmetry or due to other surface related defects. The shape of a element. An experimental phase diagram in the diameter and magnetic element like a rectangle or an ellipse can also favor thickness of disks was studied by Cowburn et al. [10]. Single domain different vortex states [12e15]. states are preferred for small disks below the vortex regime and Magnetization reversal mechanisms have been studied in cir- multi domain states are stabilized for larger sizes. The vortices are cular disks at micron and nano scale with various materials like defined by two fundamental quantities, i.e., the character of in- NiFe [16e18], Co [19e21], FePd [22] etc. The disks stabilizing a plane spin rotations (circularity, c) and the out-of-plane vortex state at remanence have a typical hysteresis behavior. The nucleation occurs at a field value lower than the saturation field, termed as the nucleation field and the vortex gets annihilated * Corresponding author. Advanced Materials and Life Science Divisions, Istituto before the saturation field intensity along the opposite direction. Nazionale di Ricerca Metrologica (INRiM), Torino, 10135, Italy. E-mail addresses: gajananpradhan2@gmail.com, g.pradhan@inrim.it The spin direction along a vortex core was observed by Wacho- (G. Pradhan). wiak et al. using spin-polarized scanning tunneling microscope Peer review under responsibility of Vietnam National University, Hanoi. (STM) and the change of out-of-plane and in-plane magnetization https://doi.org/10.1016/j.jsamd.2023.100608 2468-2179/© 2023 Vietnam National University, Hanoi. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/). G. Pradhan, A. Magni, F. Celegato et al. Journal of Science: Advanced Materials and Devices 8 (2023) 100608 along a vortex core was calculated [23e25]. The major quest of was exploited to fill the holes with FeGa alloys. Fe80Ga20 and vortex states for non-volatile storage applications is the switching Fe70Ga30 targets were used for deposition. Fe70Ga30 disks were of vortex polarity or circularity (i.e. writing) by external pertur- fabricated using RF sputtering at room temperature. The base bations. The first observation of vortex core switching by AC pressure of the chamber was 107 mbar and the deposition electric current through a vortex state was performed by Van et al. pressure was kept at 1.2  102 mbar. For the preparation of [26,27]. Vortex core switching by rotating magnetic field with Fe80Ga20 disks, triode sputtering was used. The base pressure was inducing spin polarized currents and by frequency dependent 3.9  106 mbar. The deposition rate was kept at 1.33 Å/s. The perpendicular magnetic fields have also been performed [28,29]. resist around the disks, and the metallic deposits on top of it are The circularity has been switched using magnetic force micro- then removed by acetone washing and subsequent cleaning, scope (MFM) tips [30], by nanosecond field pulses [31] and by leaving the desired disk arrays. electric fields [32,33]. The chirality determination (i.e. reading) has been done by several electrical techniques like anisotropy 2.2. Structural characterization methods magnetoresistance (AMR) [34e36], and planar Hall effect (PHE) [37]. Imaging techniques like MFM [14,38], Magneto-Optic Kerr Scanning electron microscope equipped with an energy effect (MOKE), X-ray photoemission electron microscopy (XPEEM) dispersive detector (SEM-EDS) was used to observe the [18], scanning electron microscope with polarization analyzer morphology of the FeGa disks. In order to verify the composition of (SEMPA) [39] and magnetic transmission soft X-ray microscopy FeGa in the disk arrays, additional FeGa thin films were prepared on (MTXM) [11,31,40,41] have also been employed for circularity and bare substrates with the same deposition conditions as for the polarity determination. patterned ones. The composition of the films as recorded by EDS Vortex states have also been realized in FeGa microstructures was found to be 69.4 %at Fe and 30.6 %at Ga, similar to the Fe70Ga30 fabricated on piezoelectric substrates, enabling voltage-induced target. Similar values were observed with the concentration control of magnetization via magnetoelastic coupling to the sub- determined by ICP-OES i.e. 69.39 %at Fe and 30.61 %at Ga [46]. strate [42,43]. FeGa is a good candidate for microstructures to be Similarly, the composition of a Fe80Ga20 thin film were near to 81.3 used in various applications due to its high magnetostriction, %at Fe and 18.7 %at Ga, as recorded by EDS. magnetic softness and ductility [44e46]. However, an in-depth investigation of magnetization reversal and possible domain con- 2.3. Magnetic characterization methods figurations in FeGa microstructures is less performed. In this work, Fe80Ga20 and Fe70Ga30 disks with different dimensions are fabri- Magnetization reversal was studied by means of a magneto- cated. These compositions possess the peak magnetostriction optic Kerr effect (MOKE) microscope by Evico magnetics and us- constants (w.r.t at% Ga) which makes them susceptible to magnetic ing an oil immersion lens with a magnification of 100. The state changes under external strain. It has been reported that disks magnetic domains in the disks were recorded at different in-plane with smaller diameter ~300 nm tend to stabilize single domain magnetic field intensities and the corresponding magnetic hyster- structures at remanence due to high shape anisotropy [47]. In esis loops were reconstructed based on the change in image contrast, disks with larger diameter ~10 mm stabilize multi-domain contrast. Magnetic force microscope (MFM) by Bruker Multimode V structures due to larger dipolar coupling [43]. Hence, we have Nanoscope 8, was used under the application of an in-plane mag- chosen the diameter of the disks in the range of 1e2.8 mm, to netic field (intensity up to 60 mT), to analyze the magnetic generate a balance of shape anisotropy energy and magnetic configuration (out-of-plane stray magnetic fields) within individual dipolar energy where possible vortex states can be stabilized. disks with higher spatial resolution. The magnetic tips used in our Magnetic domain images were recorded at various applied mag- measurements were MESP-HR10 (resonant frequency of 89 kHz netic field values, revealing the spin textures forming at each stage with Co/Cr reflective coating and coercive field of ~ 95 mT). The of the hysteresis curve. Micromagnetic simulations have been height of the tip was kept at 101 nm to obtain the best quality performed to understand the experimental results and precisely images. define the evolution of spin textures during reversal. To achieve implementation of nanostructures in memory applications, a better 2.4. Simulation techniques understanding of vortex formation and control has to be gained. This work shows the stabilization of vortex states through Micromagnetic simulations were performed to understand the magnetization reversal mechanism in FeGa disks with different domain configuration and the magnetic hysteresis of individual sizes and compositions. FeGa disks using mumax3 [48]. The geometrical parameters ob- tained by atomic force microscopy (AFM) were incorporated 2. Experimental (Supplementary Fig. S1). The saturation magnetization (MS) values of the Fe80Ga20 and Fe70Ga30 alloys were determined to be 1030 kA/ 2.1. Fabrication method m and 820 kA/m, respectively, by measuring the magnetic moment of the continuous thin films using alternating gradient field FeGa disk arrays were fabricated by means of direct write laser magnetometer (AGFM). Local variations in magnetic anisotropy lithography on SiO2/Si substrates followed by sputtering. The were considered using a built-in 2D Voronoi tessellation function. substrates had a thermally oxidized SiO2 layer with thickness of The first order magneto-crystalline anisotropy constant (Kc1) was 500 nm. Focused laser spot was exposed on selected regions of the considered to be 60 kJ/m3 with a 10 percent average magnitude resist-coated substrate and which was further placed inside a variation between the grains. The exchange constant (A) was taken developer and ultrasonification was performed to remove the as 14 pJ/m [49]. The damping constant (a) and the cell size were areas exposed. Circular holes having center-to-center distance of kept at 0.007 and 6  6  6 nm3. Periodic boundary conditions were approximately 3 mm were prepared as an array of 33  33 ele- considered with 3 repetitions of disks along x and y directions. The ments. The size of the holes depends on the power of the laser distance between the disks was maintained at 3 mm, matching the used, which decides the final diameter of the disks. Increase in experimental design and considering the magnetostatic in- power of laser influences greater reflections from the substrate, teractions between the disks. The simulations were performed resulting in an increase of net exposed area. Further, sputtering under an in-plane magnetic field with intensity up to 500 mT. 2 G. Pradhan, A. Magni, F. Celegato et al. Journal of Science: Advanced Materials and Devices 8 (2023) 100608 3. Results and discussion field was applied with decreasing magnitude to obtain a demag- netized state (shown in Supplementary Fig. S4). The chirality of the Fig. 1(a) represents the magnetic hysteresis curve (M e H) of vortex states in magnetic disks can also be affected due to sym- Fe80Ga20 disk array recorded with application of in-plane magnetic metry breaking causing intrinsic DzyaloshinskiieMoriya interac- field using longitudinal MOKE. The applied magnetic field was tion (DMI) [11]. However, in our case, the surface related defects varied in the range of ±20 mT. The loop corresponds to variation in and slight shape deformation during the fabrication process are intensity of polarized Kerr signal obtained from a 4  4 disk array resulting in irregular circularity of vortex [39]. with a diameter of 2.3 mm and thickness of 24 nm. The saturation The magnetic configurations of the Fe80Ga20 disks were also field value is recorded to be 12.14 mT. The normalized remanent recorded with MFM due to its ability to detect stray magnetic sig- magnetization recorded is low with a value of 0.11. The loop ob- nals at higher resolution (tens of nm). Fig. 2(a)e(c) represent MFM tained from a larger disk array is shown in Supplementary Fig. S2, images of the 3  3 disk array with diameter of 2.3 mm which is a where a smoother and averaged contribution of magnetic contrast portion of the larger array that was recorded with MOKE. The im- is achieved. The opening of the loop, i.e., the vertical distance of the ages were recorded by applying a constant in-plane magnetic field two loop branches at any given applied field, seems increased when and scanning the tip over the sample surface for stray magnetic saturation is approached. In nanostructures, this behavior is typical signals. Fig. 2(a) and (c) represents the single domain states to the nucleation of a vortex state below saturation level and its recorded beyond saturation field values of þ50 mT and 50 mT, stabilization at remanence. The domain textures in these disks respectively. In Fig. 2(a), the contrast changes from bright to dark were recorded using a Kerr microscope at different magnetic field (left to right) which indicates a single domain state pointing along intensities as shown in Fig. 1(b)e(g). They correspond to the the þx direction. Similarly, a single domain state pointing along respective points marked in the hysteresis loop. The single domain the x direction is seen in Fig. 2(c) where the dark to bright (left to state pointing along the þx direction is shown by the dark contrast right) contrast change is observed. At remanence, a flux closure in the disks, represented in Fig. 1(b). The bright contrast in the disks domain pattern is observed representing a vortex-like magnetic (Fig. 1(g)) refers to a saturated single domain state aligned along state as shown in Fig. 2(b). The dark lines represent domain walls the x direction. When the field is decreased from 20 mT to 6.1 mT, with a vortex core at the center [33,50]. A different color scale was slight bright contrast is observed at the bottom of the disks which used to better visualize the vortex core and the domain walls marks the rotation of spins. The bright contrast increases at the forming during magnetization rotation (Supplementary Fig. S5). remanent state, and forms a spin rotation representing a vortex- The domain structures were also recorded as a function of field like state (Fig. 1(d)). The domain contrast is evidenced as a curl- for Fe80Ga20 disks with a lower diameter of 1.4 mm, represented by ing of magnetization in a CW pattern. The simultaneous acquisition Fig. 2(d)e(f). Single domain states were observed at saturation field of the Kerr contrast for longitudinal and transverse components values of þ50 mT (magnetization along þx direction) and 50 mT was obtained for visualization of magnetization orientation as (magnetization along x direction). The domain states recorded at shown in Supplementary Fig. S3. The dark contrast further de- remanence (Fig. 2(e)) are similar to the states observed in Fig. 2(b). creases as the field value is increased in the x direction (Fig. 1(e)) Slight perturbations in the intensity of domains were detected and almost annihilates as the negative saturation field is during the scanning of the tip. This can be a result of the lower stray approached as observed in Fig. 1(f). The CW rotation of magneti- field of the domain walls observed for the soft FeGa alloy as zation is observed for a majority of disks during the positive to compared to hard ferromagnets, as reported in literature [32]. negative field reversal. However, for some disks of the array Similar magnetic disks were also fabricated for the Fe70Ga30 (Supplementary Fig. S2), a CCW rotation is also observed. During alloy composition to understand the variation of domain structures the negative to positive field cycle, CCW vortex patterns becomes forming during magnetization reversal as a function of alloy the majority. In both the cycles, the nucleation of vortex core is composition. The diameter and thickness of the disks were nearly observed from the bottom of the disks which stabilizes CW and 2.2 mm and 24 nm. The magnetic hysteresis curve and the domain CCW in the first and the second cycle, respectively. An equal structures forming during the reversal, are shown in Fig. 3(a)e(g). probability of CW and CCW vortices was also achieved when an AC The normalized remanent magnetization is recorded to be 0.83 and Fig. 1. Magnetic hysteresis curve measured using longitudinal MOKE for a Fe80Ga20 disk array of 4  4 elements is shown in (a). The diameter and the thickness of the disks are 2.3 mm and 24 nm, respectively. The magnetic domain images are shown in (b)e(g) representing the points marked in the hysteresis loop. The scale bar and the field direction are shown in (b) and are the same for all the domain textures. 3 G. Pradhan, A. Magni, F. Celegato et al. Journal of Science: Advanced Materials and Devices 8 (2023) 100608 Fig. 2. Magnetic domain textures of the Fe80Ga20 disks of diameter 2.3 mm and 1.4 mm measured using MFM. (a), (b) and (c) represents the 2.3 mm disks with in-plane magnetic field of þ50 mT (positive saturation), 0 mT (remanence) and 50 mT (negative saturation), respectively. (d), (e) and (f) represents the 1.4 mm disks at þ50 mT, 0 mT and 50 mT, respectively. a coercive field to be 6.1 mT. The saturation field value is measured rotation of magnetization and the dark-white suggest a CW rota- to be 26.1 mT. Fig. 3(b)e(g) represent the domain images as marked tion. These states may symbolize the stabilization of a double to the respective field intensities in the hysteresis curve. The single vortex state as also reported in literature for Permalloy [51]. The domain states at negative saturation field is represented by the dark contrast increases and appears in all the disks as the field is disks with bright contrast as shown in Fig. 3(b). Near remanence, increased to 7.6 mT and small bright contrasts are only left at the slight dark contrast is observed at disk edges due to the rotation of top and bottom portions in some disks (Fig. 3(e)). It can also be spins (Fig. 3(c)). With further increase in field, near 4.6 mT, a bright- observed that there is a single vortex nucleation in some of the dark-bright contrast is observed in some of the disks as marked by disks (green circles), which can be attributed to the shape defor- the yellow circles in Fig. 3(d). The longitudinal and transverse mity and uneven sizes of the disks. As the positive saturation field is magnetization components were acquired simultaneously to un- approached, the spins align along the þx direction with very derstand the possible domain configuration (Supplementary minimal bright contrast in Fig. 3(f). A completely positive saturated Fig. S3). The bright-dark contrast at the top suggest a CCW state is observed in Fig. 3(g). Fig. 3. Magnetic hysteresis curve measured using longitudinal MOKE for a Fe70Ga30 disk array of 4  4 elements is shown in (a). The diameter and the thickness of the disks are 2.2 mm and 24 nm, respectively. The magnetic domain images are shown in (b)e(g) representing the points marked in the hysteresis loop. The yellow and green circles represent the disks stabilizing a double vortex and single vortex state, respectively. The scale bar and the field direction are shown in (b) and are the same for all the domain textures. 4 G. Pradhan, A. Magni, F. Celegato et al. Journal of Science: Advanced Materials and Devices 8 (2023) 100608 The domain states in the Fe70Ga30 disks having a diameter of The magnetic hysteresis curves were extracted from MOKE 1.8 mm and a thickness of 18 nm were recorded with MFM. A measurements for two separate Fe70Ga30 disks individually from a 2  2 array was chosen from the larger array of 33  33 array. At larger array (shown in Supplementary Fig. S7) where a vortex state a field value of þ60 mT (positive saturation), single domain states and a double vortex state were observed during reversal, as shown with bright-dark contrast (left-right) pointing along the þx di- in Fig. 5(a) and (b), respectively. The evolution of magnetic domain rection are observed (Fig. 4(a)). Similarly, domains pointing along in the disks is observed along both the branches of the hysteresis the x direction are observed at 60 mT with opposite contrast curve. In disk 1, dark contrast is observed at the bottom of the disk (dark-bright) as observed in Fig. 4(c). At the positive remanent as the coercive field is approached (Fig. 5(a)2) which mark the state, shown in Fig. 4(b), a multidomain state is observed. The nucleation of a vortex state. The dark contrast increases in Fig. 5(a) central bright region is surrounded by darker regions (having 2e5(a)5 gradually, indicating the rotation of magnetic moments antiparallel configurations) which can resemble to the stabiliza- along þx direction and the vortex core moving up. On the other side tion of a double vortex state. Similar states observed under MFM of the branch (Fig. 5(a)7e5(a)10), bright contrast is observed to be in 1 mm diameter Co disks were reported previously by Prejbeanu formed in a similar pattern representing a vortex with opposite et al. [20]. circularity as compared to the vortex formed in the first branch. For Fig. 4. Magnetic domain textures of Fe70Ga30 disks with diameter of 1.8 mm with in-plane applied field of þ60 mT (positive saturation), 0 mT (remanence) and 60 mT (negative saturation) is shown by (a), (b) and (c), respectively. Fig. 5. (a) and (b) represent the magnetic hysteresis curve of two individual disks chosen from a larger array of Fe70Ga30 disks with diameter of 2.3 mm. (a)1e(a)10 and (b)1e(b)10 represent the domain structures formed in disk 1 and disk 2, respectively, during magnetization reversal as marked in the corresponding hysteresis curves. 5 G. Pradhan, A. Magni, F. Celegato et al. Journal of Science: Advanced Materials and Devices 8 (2023) 100608 disk 2, as shown in Fig. 5(b)3e5(b)5, the formation of a double with an enlarged view. Fig. 6(f) demonstrates the simulated hys- vortex state is evident from the bright-dark-bright contrast. A teresis of another Fe70Ga30 disk with same thickness and a higher change in the slope of the hysteresis is marked after the formation diameter of 1.8 mm. The domain configuration near coercivity is a of a double vortex state. This is due to the requirement of more double vortex state as represented in Fig. 6(g). The x-component of Zeeman energy to annihilate the stable structure and reach to a the state shown in Fig. 6(h), is similar to the bright-dark-bright saturated state. Similar state is also recorded on the other branch of state as observed in MOKE. The comparison of Fig. 6(a) and (f) the hysteresis where is dark-bright-dark pattern is observed in shows that the hysteresis of a disk stabilizing a double vortex state Fig. 5(b)8e5(b)10. is more squared with higher coercive field than that of a single In order to understand the exact spin textures of the domain vortex state. This characteristic of disks stabilizing different states states observed experimentally, micromagnetic simulations were are also observed experimentally, as shown in Fig. 5(a) and (b). The performed using the optimal material parameters. Fig. 6(a) shows plots of micromagnetic energies as a function of field, that are the simulated magnetic hysteresis curve of a circular Fe70Ga30 disk considered in the simulations are shown in Supplementary Fig. S9. with a diameter of 1.4 mm and thickness of 24 nm. The observed The magnetization reversal and domain structures were simu- hysteresis behavior corresponds to nucleation and stabilization of a lated for different diameters and thicknesses of the disk to deter- vortex-type state similar to the behavior observed experimentally mine the possible stable states. This was performed to overcome in Fig. 5(a). The spin configuration of the disk near the coercive field the experimental limitations and constraints for such wide range of is shown in Fig. 6(b) where a typical vortex state is observed. The parameters. A 2D plot of magnetization configurations forming color wheel represents the direction of the magnetic moments, during the magnetic reversal for the Fe80Ga20 and Fe70Ga30 disks where red and sky blue points along þx and x directions, are shown in Fig. 7(a) and (b), respectively. The formation of S- respectively. The x-component of the magnetization is shown with domain states (red squares) are limited to 18 nm thickness of the black and white scale(þx and x) in Fig. 6(c) where the contrast is Fe80Ga20 disks whereas the range expands to 30 nm in the Fe70Ga30 similar to the state observed experimentally in MOKE (Fig. 6(d)). ones. In the S-domain state, the moments in the central part of the The circularity of the vortex state is CCW. The vortex core moves up disk start curling along the direction of applied field forming a S- and annihilates at the top of the disk at saturation as more mag- shaped spin configuration. Single vortex states (yellow circles) are netic moments start curling along the þx direction. The in- observed for lower diameters of the disks due to less dipolar en- homogeneity in the contrast of the disks is due to the dispersion of ergies. The range of diameters, where a single vortex state can be anisotropy and the grain sizes across the simulated area. The vari- stabilized in higher for the Fe70Ga30 disks. For relatively higher ation in anisotropy and grain distribution is represented by Fig. 6(e) diameters and thickness of the disks, double vortex states (blue Fig. 6. Simulated magnetic hysteresis curves of Fe70Ga30 disks with diameter of 1.4 mm and 1.8 mm are shown in (a) and (f), respectively. In the 1.4 mm disk, single vortex state is observed near coercive field, represented by (b). The corresponding x-component of the magnetization (c) looks similar to the experimental observed state (d). In the 1.8 mm disk, double vortex state is observed near coercive field (g). The corresponding x-component of the magnetization (h) looks similar to (i). The distribution of grains having an anisotropy, shape and size variation is shown by (e). 6 G. Pradhan, A. Magni, F. Celegato et al. Journal of Science: Advanced Materials and Devices 8 (2023) 100608 Fig. 7. Phase diagrams representing the different domain configurations forming during magnetization reversal in disks of different thicknesses and diameters. (a) and (b) correspond to the Fe80Ga20 and Fe70Ga30 compositions, respectively. The buckling, S-domain, vortex, double vortex and multiple vortex states are represented by green diamonds, red squares, yellow circles, blue stars and pink triangles, respectively. The physical representations of the spin configurations are shown on the right. stars) are observed. Multiple vortex which are meta-stable states Acknowledgments (pink triangle) are also observed for higher thickness of 30 nm for most range of the diameter in Fe80Ga20 disks. The actual repre- This work has received funding from the European Union's sentations of the simulated states obtained here are shown in Horizon 2020 research and innovation programme under the Marie Supplementary Fig. S10. The buckling states (green diamonds) are Skłodowska-Curie grant agreement No 861145. The experimental observed in every dimension where the magnetization starts to work has been partially performed at NanoFacility Piemonte, an reverse. In a comparison of magnetic state of Fe80Ga20 and Fe70Ga30 INRIM laboratory supported by Compagnia di San Paolo. Czech- disks with same dimensions, it can be observed that complex spin NanoLab project LM2018110 funded by MEYS CR is gratefully textures are preferentially more stable in the Fe80Ga20 ones. This is acknowledged for the financial support of the measurements at due to higher MS value which tends to generate more demagnet- CEITEC Nano Research Infrastructure. The authors also thank izing energy. The points marked on the phase diagrams represent Adriano Di Pietro for technical help in simulations. the lowest energy state during magnetization reversal at the particular dimension. The magnetic states forming during the Appendix A. Supplementary data reversal are dependent on the thickness, the diameter and the composition of the FeGa disks. Hence, the shape anisotropy and the Supplementary data to this article can be found online at saturation magnetization play a major role in the formation of flux https://doi.org/10.1016/j.jsamd.2023.100608. closure domain structures like single vortex or double vortex states. References 4. Conclusion [1] J.M. Kosterlitz, D.J. 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