Defect Landscape Engineering to Tune Skyrmion-Antiskyrmion Systems in FeGe
Jiangteng Liu Ryan Schoell Xiyue S. Zhang Hongbin Yang M. B. Venuti Hanjong Paik David A. Muller Tzu-Ming Lu Khalid Hattar Serena Eley


AIP/123-QED







Department of Electrical & Computer Engineering, University of Washington, Seattle, WA 98195


Sandia National Laboratories, Albuquerque, NM 87123


Department of Applied Physics, Cornell University, Ithaca, NY 14853


Department of Applied Physics, Cornell University, Ithaca, NY 14853


Department of Physics, Colorado School of Mines, Golden, CO 80401
 

Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials, Cornell University, Ithaca, NY 14853
School of Electrical & Computer Engineering, University of Oklahoma, Norman, OK 73019
Center for Quantum Research and Technology, University of Oklahoma, Norman, OK 73019


Department of Applied Physics, Cornell University, Ithaca, NY 14853


Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM 87123


Department of Nuclear Engineering, University of Tennessee, Knoxville, TN 37996 


Department of Electrical & Computer Engineering, University of Washington, Seattle, WA 98195
Department of Physics, Colorado School of Mines, Golden, CO 80401

[Corresponding author: ]
serename@uw.edu



§ ABSTRACT 
A promising architecture for next-generation, low energy spintronic devices uses skyrmions— nanoscale whirlpools of magnetic moments— as information carriers. Notably, schemes for racetrack memory have been proposed in which skyrmions and antiskyrmions, their antiparticle, serve as the logical bits 1 and 0. However, major challenges exist to designing skyrmion-antiskyrmion based computing. The presence of both particles in one material is often mutually exclusive such that few systems have been identified in which they coexist, and in these systems their appearance is stochastic rather than deterministic.  Here, we create a tunable skyrmion-antiskyrmion system in FeGe films through ion-irradiation and annealing, and detail the structural properties of the films under these various conditions. Specifically, we irradiate epitaxial B20-phase FeGe films with 2.8  Au^4+ ions, showing evidence that the amorphized regions preferentially host antiskyrmions at densities controlled by the irradiation fluence.  In this work, we focus on a subsequent, systematic electron diffraction study with in-situ annealing, demonstrating the ability to recrystallize controllable fractions of the material at temperatures ranging from approximately 150^∘ C to 250^∘ C, enabling further tunability of skyrmion/antiskyrmion populations. We describe the crystallization kinetics using the Johnson-Mehl-Avrami-Kolmogorov model, finding that growth of crystalline grains is consistent with diffusion-controlled one-to-two dimensional growth with a decreasing nucleation rate. The procedures developed here can be applied towards creation of skyrmion-antiskyrmion systems for energy-efficient, high-density data storage, spin wave emission produced by skyrmion-antiskyrmion pair annihilation, and more generally testbeds for research on skyrmion-antiskyrmion liquids and crystals.




Defect Landscape Engineering to Tune Skyrmion-Antiskyrmion Systems in FeGe
    Serena Eley
    September 9, 2024
==========================================================================







§ INTRODUCTION


Skyrmions are topologically protected chiral spin textures that have garnered interest as potential information carriers in low-energy spintronic devices. These textures originate from an antisymmetric exchange interaction called the Dzyaloshinskii-Moriya interaction (DMI) that can arise in magnetic materials with strong spin-orbit coupling and broken inversion symmetry. Unlike the exchange interaction that leads to ferromagnetic order (a collinear spin arrangement), the DMI can tilt magnetic moments such that the combined interactions engender whirlpool-like spin structures that behave as particles that can be controlled by applied currents.<cit.>

Skyrmions were first observed in B20-phase cubic materials, such as MnSi,<cit.> Fe_1-xCo_xSi,<cit.> and FeGe,<cit.> due to isotropic DMI originating from the non-centrosymmetric crystal structure.  On the other hand, if the DMI is anisotropic, non-symmetric skyrmions or antiskyrmions — the antiparticles of skyrmions — can form.<cit.> Degrees of freedom within these localized magnetic textures can be indexed by parameters representing the helicity, vorticity, and topological charge Q = (1/4π)∫m(r)· [∂_xm(r)×∂_ym(r)]  dx  dy, in which m(r) is the magnetization unit-vector field.<cit.> Consequently, antiskyrmions have opposite topological charge from skyrmions, e.g. -1 for skyrmions and +1 for antiskyrmions.<cit.>  This difference in topological charge makes skyrmion-antiskyrmion systems attractive for binary data encoding in racetrack memory and logic applications. 

Skyrmion-antiskyrmion systems will also serve as fertile playgrounds for studying the dynamics of skyrmion-antiskyrmion crystals and liquids<cit.> as well as skyrmion-antiskyrmion pair annihilation, which is predicted to produce a spin wave. <cit.> Few materials have been identified in which these particles coexist,<cit.> namely in Mn_2RhSn,<cit.> Co/Ni multilayers<cit.> and our work on disordered FeGe.<cit.>  In fact, in a recent study,<cit.> we created a skyrmion-antiskyrmion system in epitaxial B20-phase FeGe films by ion beam modification, which induced amorphous regions within the crystalline matrix. Low-temperature electrical transport and magnetization studies revealed a strong topological Hall effect with a double-peak feature that served as a signature of skyrmions and antiskyrmions.  The system can be represented by the Hamiltonian<cit.>

    H_ij =     -∑_<i,j>J_ij(S_i·S_j) - ∑_<i,j>D_ij·(S_i×S_j)  
         -K∑_i(S_i^z)^2 -∑_i μ_0 BS_i^z.

Here, the first term is the symmetric component in which S_i and S_j represent neighboring spins and J_ij is the symmetric exchange constant.  The second term is the antisymmetric exchange interaction in which the DMI vector D_ij depends on local bond geometry.<cit.> The third contribution is the uniaxial anisotropy K that, along with the direction of the DMI vector D_ij, should differ in amorphous versus crystalline regions because both depend on long-range order of the lattice, which is broken during amorphization. Lastly, in the fourth term, B is the z-oriented applied magnetic field, S_i^z is the z component of S_i, and μ_0 is the magnetic moment of the magnetic atom. 

In this study, we introduce another avenue for tunability of the skyrmion-antiskyrmion system in irradiated FeGe. We first create a bath of coexisting skyrmions and antiskyrmions through ion beam modification at different fluences. Second, through in-situ annealing and selective area electron diffraction, we demonstrate the ability to systematically recrystallize the amorphized regions and study the associated recrystallization kinetics.  By analyzing the recrystallization kinetics using the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model, we describe the dynamic processes that govern the formation of crystalline regions from the amorphous matrix. This knowledge not only enhances our ability to fine-tune the defect landscape for skyrmion and antiskyrmion stabilization but also provides insights into the thermal stability and transformation pathways of these topological structures. Ultimately, a deeper understanding of these mechanisms paves the way for more effective engineering of skyrmion-antiskyrmion systems in FeGe, potentially leading to advancements in low-energy, high-density spintronic devices.





§ RESULTS AND DISCUSSION






 §.§ Growth and Ion-Beam Modification of FeGe Films


Using molecular beam epitaxy, we grew approximately 55-nm thick epitaxial films of FeGe in the B20-phase, which has space group P2_13 with eight atoms per unit cell and cubic structure, as shown in Fig. <ref>(a). To characterize the material structure, we performed x-ray diffraction (XRD), scanning transmission electron microscopy (S/TEM), and selected area electron diffraction (SAED) on the films or lamellae prepared by focused ion beam microscopy.  Details regarding the materials growth procedure, STEM characterization, and lamella preparation 
 are included the the Methods section. XRD spectra (shown in Ref. [Eley2024]) reveal a peak at 2θ =33.1 ^∘ that is consistent with the FeGe (111) B20-phase. Figure <ref>(b) displays a bright field cross-sectional STEM image of the as-grown FeGe film and the inset shows the corresponding SAED pattern. In general, SAED images show a two-dimensional (2D) slice of the reciprocal lattice, resulting in sharp spots from reflections off lattice planes.  Single crystals with little disorder produce only sharp spots, whereas defined and diffuse rings result from nanocrystalline powders and amorphous samples, respectively. Here, we see only bright diffraction spots, revealing a highly ordered crystalline structure, with no observable diffuse ring. 



We subsequently irradiated cleaved 6 × 6 cuts of the films with 2.8 MeV Au^4+ ions using a 6 MV High Voltage Engineering (HVE) EN Tandem Van de Graaff Accelerator at the Sandia National Laboratories Ion Beam Lab.  To test the effects of various defect levels, each film was irradiated with a fluence of 10^13 and 10^14 , inducing 10^-1 and 1 displacement per atom (dpa), respectively, as determined by the Stopping and Range of Ions in Matter (SRIM) simulations, shown in  Fig. <ref>(a). The SRIM results predict that the irradiation process should introduce a homogeneous distribution of defects throughout the film depth, without implanting Au-ions into the FeGe. Further details of the ion beam modification process and corresponding SRIM simulations are included in the Methods section.

To identify phases as well as determine the effects of irradiation on the crystalline structure, chemical composition throughout the film depth, and crystalline orientation, we performed STEM imaging, electron energy loss spectroscopy (EELS), and SAED. The low magnification cross-sectional STEM image in Fig. <ref>(b) shows a top-layer carbon coating (applied for microscopy), FeGe layer, and Si (111) substrate. In addition to these three layers, the EELS results in Fig. <ref>(c) show a surface oxide, the thin FeSi seed layer that was formed on the substrate to mediate growth of epitaxial B20-phase FeGe, no detectable Au concentration within the measurement resolution (consistent with simulations that indicate Au was not implanted in the FeGe). In the high-resolution annular bright-field STEM image in Fig. <ref>(d) of a film irradiated at 10^13   we also see irradiation-induced amorphous regions within the crystalline matrix, highlighted using red and purple false color overlays, respectively. The presence of amorphous regions is also revealed in the SAED pattern, in which a distinct diffuse ring is notable that did not exist in the SAED image of the pristine sample [Fig. <ref>(b) inset].



 §.§ In-situ recrystallization of Irradiated FeGe


The next goal was to develop an annealing procedure to tune the density and sizes of the amorphized versus crystalline regions in the irradiated FeGe films, which would subsequently enable tunability of the relative skyrmion and antiskyrmion populations. To actively monitor the crystalline orientation, we performed SAED with in-situ annealing on plan view lamellae of films irradiated at 10^13  and 10^14 , as well as a pristine lamella, for reference.  The electron beam was incident on the FeGe (111) lattice plane and the annealing process followed the stepwise heating profile depicted in Fig. <ref>. Further details describing the experimental setup are included in the Methods section and SAED data for the pristine film is presented in the Supplementary Materials. 




Figure <ref>(a-h) presents the raw SAED patterns of the sample irradiated at 10^13   with each panel showing results at a fixed location while heating at the indicated temperature. We see that as the temperature rises, the number of diffraction spots noticeably increases while the intensity of the diffuse ring diminishes, a trend suggestive of heating-induced recrystallization of the amorphous regions. To approximate the relative fraction of crystalline regions and the effect of each heating stage on this fraction, we separate the raw data into amorphous and crystalline components, and then integrate to convert the 2D diffraction data into one-dimensional (1D) profiles of normalized intensity. Finally, the intensity data is plotted against the reciprocal space parameter g = 1/d, where d is the spacing between crystalline reflection planes. Refer to the Supplementary Material for more details on our signal separation procedure.

Figures <ref>(i) and <ref>(j) display the resulting separated 1D profiles for the amorphous and crystalline components, respectively. For the amorphous component [Fig. <ref>(i)], the diffuse ring at 1/d = 4.9 nm^-1 matches expected values for amorphous FeGe, as reported in previous studies,<cit.> and the peak intensity decreases with increasing temperature. On the other hand, Fig. <ref>(j) illustrates an increase in the number and intensity of diffraction peaks associated with the crystalline component as the temperature rises. To identify phases associated with these peaks, we used the Materials Project database<cit.> of calculated and experimental diffraction pattern data for the Fe-Ge and Fe-Ge-O systems, and subsequently found that these peaks correspond to the B20-phase of FeGe as well as to the cubic Fe_3Ge-Fm3m phase. More information regarding the phase identification process is discussed in the Supplementary Materials. 



We repeated the in-situ annealing and SAED process on the sample irradiated at the higher fluence of 10^14 , observing similar recrystallization behavior, as shown in Fig. <ref>. It is important to note that the peak intensities in the SAED patterns are influenced by the image contrast during data acquisition. Though this was not adjusted during the annealing process, it did differ between runs for each sample such that peak intensities should not be compared  between the different samples. As expected, the width and relative intensity of the diffuse ring (compared to the diffraction spots) is significantly stronger than observed in the sample irradiated at a lower fluence. This can be attributed to the higher irradiation dose inducing larger amorphous regions. Additionally, the greater number of diffraction spots suggests that the recrystallized grains possess more grain boundaries with varying orientations. 


We again separate the amorphous and crystalline components into 1D profiles of intensity versus g, shown in Figs. <ref>(i) and <ref>(j), respectively. Similar to the other irradiated film, Fig. <ref>(i) reveals that the intensity of the amorphous component decreases with temperature, but we also see that the diffuse ring persists over a wider range of temperatures. This indicates that the initial higher density of amorphous regions in sample irradiated at 10^14   results in increased stability of the amorphous phase during annealing.
Regarding the crystalline component, shown in Fig. <ref>(j), we again see an increase in the number and intensity of diffraction peaks with temperature. In this case, the identifiable phase is primarily B20 FeGe. However, additional unidentified phases are observed at temperatures between 100-180^∘C at a 1/d of 4.9 nm^-1 and 5.5 nm^-1, which may originate from lattice strain, oxides, or various other defects such as twin boundaries and stacking faults.<cit.> 



 §.§ Recrystallization Kinetics of Irradiated FeGe


To determine the evolution of the effective crystalline volume fraction with temperature and time, we characterize the recrystallization kinetics using the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model.<cit.> This model provides an estimate of the local Avrami exponent n, which can be used to extract information about nucleation and grain growth<cit.> — the nucleation rate at different stages of crystallization (increase or decrease), the growth mechanism (interface or diffusion controlled), and the dimensionality of the grain growth in the system (3D-bulk materials, 2D-thin film, 1D-nanotube). The classic JMAK model assumes that the phase transformation occurs under isothermal conditions and that the time t evolution of the effective crystalline volume fraction X can be expressed as<cit.>


    X(t) = 1 - exp[-k(t-t_0)^n],
 where k is the kinetic coefficient, which is constant under a fixed temperature, and t_0 is induction time (the duration between when sample heating initiates and the onset of crystallization).<cit.> Consequently, the local Avrami exponent depends on the crystalline volume fraction as follows: <cit.>


    n(X)    =   dln[-ln(1-X)]/dln(t-t_0) .



Because our stepwise heating profile alternates between isothermal steps and temperature ramps, we also consider the extended JMAK model applicable for non-isothermal conditions. In this model, the crystalline volume fraction depends on the Avrami exponent, time, and temperatures as<cit.>


    X_extended(t) = 1 - exp{ -[ ∫_t_0^t k(T)   dt ]^n }.




For a constant heating rate where dT/dt ≡β, the term ∫^t_t_0 k(T)  dt can be rewritten as ∫^T_T_0 k(T)/β dT such that  ∫^T_T_0 k(T)dT = k'(T-T_0).<cit.> Hence, the temperature dependence of the crystalline volume fraction becomes


    X_extended(T)    =    1 - exp{- [k'(T-T_0)/β]^n }


for k'(T) = k'_0exp(E_a/RT), k'_0 is a constant, E_a is activation energy, T_0 is the onset temperature for crystallization, and R is the gas constant. Rearranging terms and taking the logarithm of both sides of the equation, we see that the local Avrmai constant under non-isothermal conditions can be expressed as<cit.>


    n_extended(X)    =   [RT^2/RT^2+E_a(T-T_0)] dln[-ln(1-X)]/dln[(T-T_0)/β].


Based on Eqs. (<ref>) and (<ref>), we calculated the local Avrami exponent using both the classic and extended JMAK model to describe the nucleation and growth mechanism of our irradiated FeGe samples. To apply these models, the effective crystalline volume fraction X must first be obtained. Having separated the diffraction data into amorphous and crystalline components, we can apply a classic Rietveld-based metric called the Degree of Crystallinity (DOC) to extract the crystalline volume fraction,<cit.>. Here, DOC is simply defined as the area-under-the-curve of the diffraction intensity for the crystalline component I_cryst(g) normalized by the area-under-the-curve for the total diffraction intensity — the sum of I_cryst(g) and the intensity of the amorphous component, I_amorph(g): 


    DOC = ∫I_crystdg/∫I_crystdg + ∫I_amorphdg






Figure <ref>(a) compares the temperature dependence of the effective crystalline volume fraction for the as-grown and irradiated films, obtained using Eq. (<ref>), and the diffraction data is shown in Figs <ref>(i,j) and <ref>(i,j). First, notice that the effective crystalline fraction for the pristine sample is around 0.92 pre-annealing and falls to around 0.82 by the end of the annealing sequence, whereas an X of around 1 would ideally be expected for a perfectly crystalline film. We attribute this reduced extracted crystallinity to artefacts — the broadening of the diffraction spots and the presence of Kikuchi lines, highlighted in Supplementary Materials Fig. S1. Likely owing to slight movements of the sample, the Kikuchi lines shift, causing an inconsistent broadening of the diffraction spots at different temperatures. Extensive diffraction data collected on the pristine sample is included in the Supplementary Materials.

Before the recrystallization process starts, we see that the sample irradiated at 10^14  exhibits a crystallized volume fraction of approximately 0.22, while the film irradiated with the lower fluence has a significantly higher initial crystallized volume fraction of approximately 0.6. This disparity is consistent with our more qualitative observations from microscopy and diffraction studies, all showing that the higher ion dose leads to more amorphous regions, resulting in a lower crystallized volume fraction. We also see from Fig. <ref>(a) that after annealing at a maximum temperature of 250^∘C, X is nearly equivalent for the film irradiated at 10^13  and the as-grown film. However, the crystallized volume fraction for the sample irradiated at 10^14  reaches a lower value compared to the lower-dosed sample. This suggests that either longer annealing times are required or there are defects that have larger activation energies which require higher temperatures to eliminate. 


Figure <ref>(a) also reveals a distinct difference in the temperature at which X(T) upturns in each sample, showing that recrystallization in the sample irradiated at 10^14  occurs at a higher temperature compared to the one irradiated at 10^13 .  This shift suggests that the higher density of the amorphous phase leads to greater phase stability and thus requires a higher activation energy for recrystallization. To validate this explanation, further experiments are needed, for example, differential scanning calorimetry to calculate the activation energy using the Kissinger method.<cit.>

Next, from our crystallized volume fraction data, we can apply the JMAK model to determine the Avrami exponent and then extract information regarding the nucleation rate and mechanism from these values.  As shown in Fig. <ref>, our heating profile is stepwise, therefore, neither completely isothermal nor non-isothermal. Consequently, we apply both the classic and extended JMAK models, Eq. (<ref>) and (<ref>), respectively. For the extended model, which considers non-isothermal conditions, we approximate the temperature sweep as linear, for β = 2^∘C/min, and use an activation energy of E_a = 0.1011 × 10^-19 J/atom for FeGe, based on Ref. [FeGeActivationE].





Figures <ref>(b, c) show the calculated local Avrami exponents n(X) plotted against the crystallized volume fraction X, for the film irradiated at 10^13  and 10^14 , respectively.  To now resolve the nucleation rate and growth mechanism, we consider that the local Avrami exponent n(X) can be described using the equation n = a + bc.<cit.>  Here, a ≥ 0 provides information on the relative nucleation rate, where a < 1, a = 0, and a > 1 for a decreasing, constant, or increasing nucleation rate with time, respectively. The term b relates to the growth mechanism, for which b = 1 indicates interface-controlled growth and b = 0.5 signifies diffuse-controlled growth. Lastly, the term c indicates the growth dimension, therefore can only be 1, 2, or 3.

Based on our data, the possible indices a, b, and c are not unique. We discuss the possibilities here, which are also summarized in Table <ref>. It has been previously reported that crystallization of Fe-Ge films is diffusion controlled,<cit.> therefore we assume b = 0.5. Consequently, under this assumption, the lower limit for n(X) is 0.5, calculated from minimum values for c=1 and a=0. Therefore, for the film irradiated at 10^13 , our n(X) data that can be applied to the model lies within the range 0.64 < X < 0.85, highlighted in grey shading in Fig. <ref>(b). According to the classic JMAK model, the n value initially increases to approximately 1.2 before rapidly decreasing to below 1 with increasing temperature and X. Similarly, n(X) calculated from the extended JMAK model exhibits comparable behavior, increasing initially, though it peaks at a lower value of 1.0 before decreasing. We then use the average Avrami exponent n — 0.9 and 0.8 for the JMAK and extended JMAK models, respectively — to determine the indices. For an increasing nucleation rate (a > 1) to exist, n(X) must be greater than 1.5 even for the lowest possible c = 1, again considering b=0.5. Under the constraint of n < 1.0 and the assumption of b = 0.5, c can only be 1 and a < 1. Therefore, both models conclude that grain growth in the film irradiated at 10^13  is diffusion-controlled, one-dimensional growth with a decreasing nucleation rate.


We now consider the film irradiated at 10^14 , examining our n(X) data within the range of 0.27 < X < 0.65, which is highlighted in grey shading in Fig. <ref>(c). This applicable range was determined using a lower limit of n(X) = 0.5. We see that the recrystallization behavior follows a similar pattern to that in the lower-dose film: the nucleation rate decreases since n(X) mostly remains below 1.5. However, the peak n values are higher, reaching 1.6 and 1.34 for the extended and classic JMAK models, respectively. In this case, the n for JMAK is 1.1, and for extend JMAK is 1.0. Accordingly, 1.0 < n <  1.1, a < 1, and b = 0.5 indicate that the grain growth is dominated by diffusion-controlled one-to-two dimensional growth with a decreasing nucleation rate.  





The difference between n(X) for the classic and extended JMAK models reaches a maximum of approximately 16% in both samples, with all terms remaining within a range that yields the same conclusions regarding nucleation. Both models indicate our irradiated FeGe film experienced a decrease in nucleation rate at all times. This is consistent with the non-zero crystallized volume fraction at the start of annealing because these unaffected crystalline regions can act as nuclei. Notably, the higher dimensional growth observed in the film irradiated at 10^14  compared to the one irradiated at 10^13  aligns with the experimental conditions: the higher density of amorphous regions in the former leads to less restricted growth directions.

 




§ CONCLUSIONS


In conclusion, we developed a method of creating a tunable skyrmion-antiskyrmion system in B20-phase FeGe through ion beam modification and annealing, which is of high interest because few systems exist in which skyrmions and antiskyrmions coexist. First, in a previous study, <cit.> we showed that ion beam modification of epitaxial FeGe films through irradiation with 2.8 MeV Au^4+-ions at difference fluences induces varying densities of amorphized regions. From extensive Hall effect studies, we observed a topological Hall effect evidencing skyrmions in the as-grown film and a double-peak feature in the Hall effect data that is consistent with the presence of skyrmions and antiskyrmions in the ion-beam-modified films. Given that skyrmion formation is favorable in the crystalline regions and antiskyrmion formation in the amorphous regions, the relative populations of each quasiparticle appears dependent on the volume fractions of crystalline and amorphous regions.

In this study, we added another degree of tunability to the system by developing an annealing process that progressively recrystallizes the ion-beam-modified films.  By monitoring the heating-induced changes in the crystalline structure through in-situ SAED, we determined that as the temperature increases, the crystalline volume fraction is first constant, then sharply increases, before plateauing. We also found that the temperature at which the crystalline volume fraction sharply increases depends on initial structural conditions and that the mostly amorphized FeGe from high fluence irradiation does not fully recrystallize at the temperatures up to 250^∘C within the duration of our annealing process (104 minutes total, 3 minutes at 250^∘C). Lastly, by applying both JMAK models, we found that the nucleation rate in both samples decreases during recrystallization, which suggests the formation of larger grains with fewer grain boundaries. This reduction in grain boundary defects may affect the formation and motion of skyrmions and antiskyrmions in the system, in this case reducing skyrmion-defect interactions. 

Furthermore, the higher dimensional growth observed in the sample irradiated with a 10^14  fluence implies a more complex, diverse defect landscape that skyrmions and antiskyrmions must navigate. More generally, the process we developed can be applied to creating skyrmion-antiskyrmion systems in FeGe for technological applications such as racetrack memory<cit.> and logic<cit.> or for fundamental research on phenomena such as spin wave emission by skyrmion-antiskyrmion pair annihilation <cit.> as well as skyrmion-antiskyrmion liquids and crystals. <cit.>




§ METHODS




 §.§ Film Growth


Our FeGe films on Si (111) substrates were prepared at the Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM) at Cornell University, applying a process similar to that detailed in Ref.  PhysRevMaterials.2.074404 for growth of Mn_xFe_1-xGe films. Using molecular beam epitaxy in a Veeco GEN10 system (2 × 10^-9 torr base pressure), an FeSi seed layer was first formed by depositing a monolayer of Fe onto a 7 × 7 reconstructed Si (111) surface then flash annealing at 500C. Fe and Ge sources were then co-deposited from 40 cc effusion cells at a rate of 0.5 Å/s and substrate temperature of 200C. This resulted in B20-phase, epitaxial FeGe films that were fairly uniform over 1.5 inch substrates.




 §.§ Ion Beam Modification


The FeGe films were irradiated in a 6 MV HVE EN Tandem Van de Graaff Accelerator at the Ion Beam Lab at Sandia National Laboratories. Prior to the irradiation process, the beam energy and fluences were chosen based on estimations of resulting atomic displacements from Stopping Range of Ion in Matter (SRIM) simulations.<cit.> The SRIM simulation considered the densities,  displacement energies, lattice energies, and surface energies indicated in Table <ref>. FeGe films cleaved into 6 x 6mm fragments were adhered onto a Si backing plate with double sided carbon tape and mounted into the tandem end station which was pumped to a base pressure of at least 1e-6torr. Ion irradiation was performed using 2.8 MeV Au^4+ ions with an ion beam current of 100nA, equivalent to an ion flux of 1.56e11ions/cm^2.






 §.§ Scanning Transmission Electron Microscopy and Focus Ion Beam Milling


Lamellae were prepared using a Thermo Fisher Helios G496 UX-focused ion beam (FIB) at PARADIM. Plan-view lamellae were used for SAED and cross-sectional lamellae was fabricated for STEM and EELS measurements. Initially, a protective overlayer
stack of 20 - 30 nm of carbon and 0.8–1 μm of Pt was deposited on the sample surface. Subsequently, a Ga-ion beam was used to carve out the thinned lamellae, which is then attached to a needle using a sputtered Pt paste to facilitate transfer onto a TEM grid. Both the cross-section and plan-view lamellae went through successive milling on both sides down to a thickness of 200 - 500 nm using a 30 keV Ga-ion beam. Lastly, the lamellae were milled at 5 keV until the Pt layer thickness fell below 20 nm. Throughout the plan-view FIB thinning process, the film surface and substrate underwent milling at a 2-3^∘ angle with respect to the ab-plane, ensuring a continuous gradient across different regions. The STEM images depicted in Fig. <ref>(b) and Fig. <ref>(d) as well as the EELS data in Fig. <ref>(c) were captured using a Thermo-Fisher Scientific Spectra 300 STEM in the PARADIM facility.  



 §.§ Selective Area Electron Diffraction


The SAED data captured during the in-situ annealing process were collected using a 300 kV Titan Transmission Electron Microscope at Sandia National Laboratories (SNL). The sample was sandwiched onto a single-tilt Gatan heating holder using a screw. Then, after the chamber was pumped down to 1.5×10^-9 torr, the sample was heated from 50^∘C to 250^∘C using the stepwise profile depicted in Fig. <ref>. This heating process alternated between a temperature ramp of 5^∘C/min for 2 minutes and then a 3-minute hold. At each holding step, the temperature was allowed to stabilize for one minute, after which the following data was collected over a period of two minutes: a bright-field (BF) TEM image of the entire sample at a magnification of 3800X, a diffraction pattern using the selected area aperture with sample distance of 480 mm with an area of 0.35 μ m^2, and a BF TEM image of where the SAED data was taken, both at 8100X. The exposure time for all the images was 1 s and, throughout the imaging process, the SAED location remained fixed and microscope voltage was maintained at 300 kV.



§ SUPPLEMENTARY MATERIALS


See Supplementary Materials for selected area electron diffraction results on the as-grown FeGe film as well as further details regarding our SAED data analysis process.






§ AUTHOR DECLARATIONS




 §.§ Conflict of Interest

The authors have no conflicts to disclose.



 §.§ Authors' contributions

S.E. conceived and designed the experiment, with input from D.M., K.H., and T.L. M.B.V. conducted the SRIM simulations and coordinated sample preparation, irradiation, and microscopy based on Hall effect studies.

H. P. grew the FeGe films.

X.Z. and H.Y. prepared the FIB samples. X.Z. collected and analyzed EELS and STEM images with advice from D.M. H.Y. also collected TEM images, and conducted room-temperature SAED measurements of the pristine film, with advice from D.M. 

R.S. and K.H. collected the TEM and diffraction data under various temperatures. J.L. analyzed, interpreted, and modeled the diffraction data. 

S.E. and J.L. wrote the manuscript. 

S.E. and T.L. assisted with general data analysis and interpretation.

All authors commented on the manuscript.


This material is based upon work supported by the National Science Foundation under grants DMR-1905909 and DMR-2330562 at the Colorado School of Mines and University of Washington. 

This work also made use of synthesis and microscopy facilities at the Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM), which are supported by the National Science Foundation under Cooperative Agreement No. DMR-2039380.

Part of this work was performed at the Center for Integrated Nanotechnologies, a DOE Office of Science User Facility, and Sandia National Laboratories, managed and operated by NTESS, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration. The views expressed in the article do not necessarily represent the views of the U.S. DOE or the United States Government.




§ DATA AVAILABILITY STATEMENT


The data that support the findings of this study are available on Mendeley Data (doi.org/10.17632/xd8s497nsz.2) as a zip file. This includes .csv files containing the data used in figures, microscopy images (.tif files), python code used for the analysis, and an Origin file (.opju) containing all figures and data spreadsheets, which can be opened using Origin Viewer, a free application that permits viewing and copying of data contained in Origin project files.








