Magnetic and Electronic Properties of Weyl Semimetal Co2MnGa Thin Films

Magnetic Weyl semimetals are newly discovered quantum materials with the potential for use in spintronic applications. Of particular interest is the cubic Heusler compound Co2MnGa due to its inherent magnetic and topological properties. This work presents the structural, magnetic and electronic properties of magnetron co-sputtered Co2MnGa thin films, with thicknesses ranging from 10 to 80 nm. Polarized neutron reflectometry confirmed a uniform magnetization through the films. Hard x-ray photoelectron spectroscopy revealed a high degree of spin polarization and localized (itinerant) character of the Mn d (Co d) valence electrons and accompanying magnetic moments. Further, broadband and field orientation-dependent ferromagnetic resonance measurements indicated a relation between the thickness-dependent structural and magnetic properties. The increase of the tensile strain-induced tetragonal distortion in the thinner films was reflected in an increase of the cubic anisotropy term and a decrease of the perpendicular uniaxial term. The lattice distortion led to a reduction of the Gilbert damping parameter and the thickness-dependent film quality affected the inhomogeneous linewidth broadening. These experimental findings will enrich the understanding of the electronic and magnetic properties of magnetic Weyl semimetal thin films.


Introduction
Topological materials have attracted tremendous interest in condensed matter physics due to their unique electronic band states, which give rise to novel linear and nonlinear responses [1][2][3][4][5][6][7][8][9]. Weyl semimetals constitute one class of such topological systems. They are characterized by a lack of inversion symmetry or broken time-reversal symmetry, resulting

Materials and Methods
High-quality epitaxial thin films of Co 2 MnGa were grown in a BESTEC UHV magnetron sputtering system on single crystal MgO(001) substrates and capped with 3 nm Al, which is naturally oxidized and protects the epilayer. The details of the growth are provided in [34]. The stoichiometry of the films was confirmed by energy-dispersive X-ray spectroscopy (EDXS), with an experimental uncertainty of less than 5 at. %. X-ray diffraction (XRD) and X-ray reflectivity (XRR) measurements were conducted using a PANalytical X'Pert 3 MRD diffractometer employing Cu-Kα 1 radiation (λ = 1.5406 Å). The film thicknesses were determined by using XRR measurements (not shown). Atomic force microscopy (AFM) images were collected in non-contact mode on an MFP-3D Origin + microscope from Oxford Instruments Asylum Research in replicas of the films without capping layers.
PNR measurements were conducted on the SuperADAM instrument at ILL (Grenoble, France). A fixed neutron wavelength of 5.2 Å with an incident polarization of 99.6% was used for the measurements. The neutron wavelength spread was δλ/λ ≈ 0.5%. The neutron momentum transfer was selected by changing the incident and outgoing angles to satisfy the specular reflection condition. In addition, the incident neutron polarization state was controlled by a radiofrequency spin flipper for each of the consecutive measurements. The data were collected at an applied magnetic field of 50 mT preceded by the application of a 0.7 T field. For the details of the SuperADAM polarized neutron reflectometer, see [45,46].
The HAXPES measurements were performed at beamline P22 of PETRA III (Hamburg, Germany) [47]. The photon energy was set to hν = 6000 ± 0.1 eV. The magnetic circular dichroism was measured at a fixed magnetization by changing the helicity of the photons using a phase retarder. The degree of circular polarization was about 98-99%. The thin films were magnetized in situ along the direction of the photon beam. The energy in the spectra is given with respect to the Fermi energy ε F calibrated to Au, with ε F appearing at a kinetic energy E kin of 6000.50 ± 0.2 eV. This corresponds to an overall energy resolution of about 170 meV (E/∆E ≈ 3.5 × 10 4 ). For details of the HAXPES setup and HAXPES-MCDAD experiment, see [48,49].
Magnetization measurements were performed on a Superconducting Quantum Interference Device (SQUID) vibrating sample magnetometer (MPMS 3, Quantum Design). To infer the magnetic field-dependent magnetization of the films, we subtracted the diamagnetic substrate contribution from the raw data.
Broadband FMR measurements were performed on a coplanar waveguide (CPW) in a vector network analyzer (VNA) setup. The CPW was connected to two ports of the VNA, and the complex scattering parameter S 21 was recorded by sweeping the frequency with a constant field applied perpendicular to the film plane. Consecutive measurements were performed in 0.5 mT steps. The resonance field H res and linewidth ∆H were extracted by fitting the field dependence of the complex transmission at constant frequency S 21 (H)| f to the complex Polder susceptibility, as discussed by Nembach et al. [50].
FMR measurements as a function of the external magnetic field orientation were performed on a continuous-wave Elexsys E500 spectrometer by Bruker. The measurements were conducted at X-band microwave frequencies (ω = 9.4 GHz) in a cylindrical cavity (TE 011 mode). The resonance signal was recorded in the field-derivative dP/dH of the absorbed microwave power (P) using a lock-in technique that modulated the external field at a low frequency (100 kHz). The sample orientation was manipulated by a goniometer, rotating perpendicular to H. The obtained spectra were fitted with a first-derivative Lorentzian line shape to obtain the resonance field H res . Figure 1a shows the symmetric radial ω-2θ XRD patterns of Co 2 MnGa films with different thicknesses. We observe only the 00l reflections of Co 2 MnGa, which suggest that the films grow heteroepitaxially on the MgO(001) substrates. The inset in Figure  1a portrays the asymmetric 113 superstructure reflections. From those, we determined that all of the films crystallized with L2 1 -type chemical ordering [34]. By combining the symmetric and asymmetric reflections, such as 002 and 220, respectively, from XRD measurements, we estimated the lattice parameters of our films, which are depicted in Figure 1b. The thinner films show strain-induced tetragonal distortion, whereas the thicker films are closer to the cubic bulk value (a = 5.77 Å) [33,34]. The films are under bi-axial tensile strain as expected based on the difference between the lattice parameters of the films and substrate ( √ 2a MgO = 5.956 Å).  The misfit strain (averaged through the film thickness) increases from 2.51% at 80 nm to 3.63% at 10 nm. Table 1 summarizes the structural parameters.  Figure 2 illustrates the AFM topographic images for the Co2MnGa films with different thicknesses in an area of 5 × 5 μm 2 . The films exhibit smooth surfaces, with an average RMS roughness Sq that increases from 2.56 to 5.44 Å with increasing film thickness. Simultaneously, the mean lateral surface diameter of the grains D increases with increasing film thickness. The roughness is expected to be proportional to the grain size. However, according to the results shown in Table 1, the minimum roughness is obtained for the 20 nm sample. This is not totally unexpected, as, in the initial stages (10 nm) of growth of a metallic film on an insulating substrate, island formation normally occurs. Simultaneously, the morphology is defined by kinetic mechanisms. At elevated substrate temperatures (550 °C), accelerated recrystallization and grain growth result from rapid surface diffusion coupled with mobile dislocations and grain boundaries. Further, the improved crystallinity inferred from rocking curve measurements [34] indicates that the overall film quality increases with increasing film thickness. Similar behavior can also be observed in other thin films [51,52]. Table 1 summarizes the values of Sq and D. The misfit strain (averaged through the film thickness) increases from 2.51% at 80 nm to 3.63% at 10 nm. Table 1 summarizes the structural parameters. Table 1. Structural parameters of Co 2 MnGa films with different thicknesses t. Lattice parameters perpendicular to the film plane c and in the plane a with an error of ±0.001 Å. Misfit strain f, root-mean-square (RMS) roughness S q and mean lateral surface diameter D of the grains.  Figure 2 illustrates the AFM topographic images for the Co 2 MnGa films with different thicknesses in an area of 5 × 5 µm 2 . The films exhibit smooth surfaces, with an average RMS roughness S q that increases from 2.56 to 5.44 Å with increasing film thickness. Simultaneously, the mean lateral surface diameter of the grains D increases with increasing film thickness. The roughness is expected to be proportional to the grain size. However, according to the results shown in Table 1, the minimum roughness is obtained for the 20 nm sample. This is not totally unexpected, as, in the initial stages (10 nm) of growth of a metallic film on an insulating substrate, island formation normally occurs. Simultaneously, the morphology is defined by kinetic mechanisms. At elevated substrate temperatures (550 • C), accelerated recrystallization and grain growth result from rapid surface diffusion coupled with mobile dislocations and grain boundaries. Further, the improved crystallinity inferred from rocking curve measurements [34] indicates that the overall film quality increases with increasing film thickness. Similar behavior can also be observed in other thin films [51,52]. Table 1 summarizes the values of S q and D.

PNR
To determine the magnetic depth profile of an 80-nm-thick Co2MnGa film, we performed PNR measurements. Figure 3a shows the intensity of the specular reflection for two incident neutron polarizations: R + (spin up, along the applied field) and R -(spin down) as a function of the momentum transfer perpendicular to the film surface (Qz). The data exhibit well-defined oscillations that are resolved up to ~0.14 Å -1 . Reflectivity measurements for the two neutron polarizations enabled us to separate the contributions from the nuclear (ρn) and magnetic (ρm) scattering length density (SLD) profiles. To extract the SLD profiles, we fitted the experimental data with a model that included the Al capping layer and magnetic Co2MnGa layer on top of the MgO substrate using the GenX software [53]. To achieve the most accurate refinement of the magnetic profile, the nuclear SLD values for the MgO substrate and Co2MnGa layer were fixed to the values calculated based on the lattice constants. Thus, the fitted parameters included the thicknesses of the Co2MnGa and capping layers, roughness of each interface and magnetization of the Co2MnGa layer. The applied model resulted in good agreement with the experimental data, as demonstrated by the fitting curves in Figure 3a.  Figure 3b presents the corresponding SLD profiles. The interface between the substrate and Co2MnGa layer is relatively sharp (the roughness is less than the measurement

PNR
To determine the magnetic depth profile of an 80-nm-thick Co 2 MnGa film, we performed PNR measurements. Figure 3a shows the intensity of the specular reflection for two incident neutron polarizations: R + (spin up, along the applied field) and R − (spin down) as a function of the momentum transfer perpendicular to the film surface (Q z ). The data exhibit well-defined oscillations that are resolved up to~0.14 Å −1 . Reflectivity measurements for the two neutron polarizations enabled us to separate the contributions from the nuclear (ρ n ) and magnetic (ρ m ) scattering length density (SLD) profiles. To extract the SLD profiles, we fitted the experimental data with a model that included the Al capping layer and magnetic Co 2 MnGa layer on top of the MgO substrate using the GenX software [53]. To achieve the most accurate refinement of the magnetic profile, the nuclear SLD values for the MgO substrate and Co 2 MnGa layer were fixed to the values calculated based on the lattice constants. Thus, the fitted parameters included the thicknesses of the Co 2 MnGa and capping layers, roughness of each interface and magnetization of the Co 2 MnGa layer. The applied model resulted in good agreement with the experimental data, as demonstrated by the fitting curves in Figure 3a.

PNR
To determine the magnetic depth profile of an 80-nm-thick Co2MnGa film, we performed PNR measurements. Figure 3a shows the intensity of the specular reflection for two incident neutron polarizations: R + (spin up, along the applied field) and R -(spin down) as a function of the momentum transfer perpendicular to the film surface (Qz). The data exhibit well-defined oscillations that are resolved up to ~0.14 Å -1 . Reflectivity measurements for the two neutron polarizations enabled us to separate the contributions from the nuclear (ρn) and magnetic (ρm) scattering length density (SLD) profiles. To extract the SLD profiles, we fitted the experimental data with a model that included the Al capping layer and magnetic Co2MnGa layer on top of the MgO substrate using the GenX software [53]. To achieve the most accurate refinement of the magnetic profile, the nuclear SLD values for the MgO substrate and Co2MnGa layer were fixed to the values calculated based on the lattice constants. Thus, the fitted parameters included the thicknesses of the Co2MnGa and capping layers, roughness of each interface and magnetization of the Co2MnGa layer. The applied model resulted in good agreement with the experimental data, as demonstrated by the fitting curves in Figure 3a.  Figure 3b presents the corresponding SLD profiles. The interface between the substrate and Co2MnGa layer is relatively sharp (the roughness is less than the measurement  Figure 3b presents the corresponding SLD profiles. The interface between the substrate and Co 2 MnGa layer is relatively sharp (the roughness is less than the measurement sensitivity). The Co 2 MnGa layer has a refined thickness of 80.3 nm and exhibits a roughness of 1.7 nm at the interface with the capping layer. The SLD of the 1.1-nm-thick capping layer is slightly higher than the theoretical SLD of Al (~0.21 × 10 −5 Å −2 ), which indicates the presence of an oxide layer (Al 2 O 3 has a higher SLD) at the film surface. As shown by the good quality of the fit, the model that assumes a uniform magnetization within the Co 2 MnGa layer well reproduces the experimental data. The magnetization calculated from the magnetic SLD [54] is 827 ± 49 kA/m. Figure 4 depicts the polarization-dependent core-level spectra near the Co and Mn 2p excitations for a 40-nm-thick Co 2 MnGa film. Note that the spectra were taken from remanently magnetized samples; hence, the magnetic moment may be lower than the saturation moment. The dichroism is quantified by an asymmetry defined as:

HAXPES
where I + and I − are the intensities for opposite helicities, I + − I − = I CD is the dichroism, I 0 = I + + I − is the sum of the intensities and I bg is the background intensity.
remanently magnetized samples; hence, the magnetic moment may be lower than the saturation moment. The dichroism is quantified by an asymmetry defined as: where and are the intensities for opposite helicities, − = is the dichroism, = + is the sum of the intensities and is the background intensity. Figure 4a shows the polarization-dependent spectra and dichroism in the energy region of the Co 2p states. The Co 2p state exhibits a spin-orbit splitting of ΔSO = 15 eV into the 2p1/2 and 2p3/2 sub-states, slightly larger than that of Co2MnSi [49]. The dichroism exhibits a sign change (+ − − +) across the energy range of the 2p excitation, which is typical for Zeeman-type level ordering in the single-electron model [55]. A pronounced satellite is observed at about 4.3 eV below the 2p3/2 state but is not detectable at the 2p1/2 state. Further, the 2p3/2 excitation exhibits a splitting of about 100 meV. The asymmetry (Equation (1)) varies between +23% and -6% across 2p3/2 and between -6% and +5% across 2p1/2. Both the polarization-dependent spectra and dichroism indicate that the lines of the multiplet extend over the entire spectral range. In particular, the dichroism does not vanish between the two main parts of the spin-orbit doublet. Comparison with calculated spectra [49] revealed a jj-type coupling in accordance with multiplet calculations [56]. The Zeeman-type splitting observed at both lines is caused by the exchange interaction. The dichroism at the Co 2p states is close to that observed for exchange-biased CoFe or Co2FeAl films [57].   Figure 4a shows the polarization-dependent spectra and dichroism in the energy region of the Co 2p states. The Co 2p state exhibits a spin-orbit splitting of ∆ SO = 15 eV into the 2p 1/2 and 2p 3/2 sub-states, slightly larger than that of Co 2 MnSi [49]. The dichroism exhibits a sign change (+ − −+) across the energy range of the 2p excitation, which is typical for Zeeman-type level ordering in the single-electron model [55]. A pronounced satellite is observed at about 4.3 eV below the 2p 3/2 state but is not detectable at the 2p 1/2 state. Further, the 2p 3/2 excitation exhibits a splitting of about 100 meV. The asymmetry (Equation (1)) varies between +23% and -6% across 2p 3/2 and between -6% and +5% across 2p 1/2 . Both the polarization-dependent spectra and dichroism indicate that the lines of the multiplet extend over the entire spectral range. In particular, the dichroism does not vanish between the two main parts of the spin-orbit doublet. Comparison with calculated spectra [49] revealed a jj-type coupling in accordance with multiplet calculations [56]. The Zeeman-type splitting observed at both lines is caused by the exchange interaction. The dichroism at the Co 2p states is close to that observed for exchange-biased CoFe or Co 2 FeAl films [57].
The polarization-dependent 2p spectra of Mn in Figure 4b exhibit a more complicated structure. Splittings of ∆ 1/2 ≈ 1 eV and ∆ 3/2 ≈ 1.3 eV occur at the 2p 1/2 and 2p 3/2 excitations, respectively. The total intensity I 0 (not shown) does not reveal spin-orbit splitting due to the additional splitting of both lines, 2p 1/2 and 2p 3/2 . The mean splitting between the doublet-type structure amounts to about ∆ = 11 eV, similar to that in Co 2 MnSi [49].
In atoms, multiplet splitting occurs due to the interaction of the nl −1 core hole with the polarized open valence shell. The core hole (here 2p 5 ) in a solid is expected to interact with the polarized d states of the valence band. The localized valence d states, however, are screened by delocalized electrons; therefore, quantification is not easily possible. The multiplet theory can be used to explain the observed splittings in the spectra [49,[58][59][60], assuming that the atomic character of the valence electrons is partially retained in the solid. Comparison indicated that the two parts of the multiplet could be assigned to the 5 P and 7 P states with the dipole allowed transitions 2p 5 3d 5 ( 5,7 P j + (s, d) ( 6 P 7/2,5/2,3/2 ). The dichroic asymmetry across the 2p 3/2 -type part varies between +47% and −24% and does not vanish between the 2p 3/2 and 2p 1/2 lines. Thus, the splitting is not of Zeeman type, where no additional states would appear between the main lines of the spin-orbit doublet similar to the Co 2p state. Hence, the core hole created by the emission of a Mn 2p electron interacts strongly with the valence band. The multiplet structure and magnetic dichroism of the Mn 2p states of Co 2 MnGa are very similar to those of Co 2 MnSi [49], indicating the similarity of the electronic structures, in particular, half-metallic character with very high spin polarization. Figure 5 depicts the IP and out-of-plane (OOP) magnetization hysteresis loops at 300 K for the Co 2 MnGa films of various thicknesses. All films show magnetization hysteresis loops characteristic for soft ferromagnetic materials with high magnetization and small coercivity. Magnetic saturation (M s ) is reached easily along the IP direction, which is the easy magnetic axis, while the hard magnetic axis is normal to the film plane along the OOP direction. Between 80 and 20 nm the M s is similar, while for the thinner film of 10 nm we observe the highest M s . This enhanced M s can be attributed to the strain-induced changes of the electronic structure.

Broadband FMR
We performed broadband FMR measurements of the Co 2 MnGa films at 300 K with H applied perpendicular to the film plane. This configuration ensured minimization of the two-magnon scattering contribution to the extrinsic broadening of the linewidth [61]. Figure 6a-d presents H res of the FMR mode as a function of the excitation frequency for the Co 2 MnGa films. Notably, for the 80-nm-thick film (Figure 6d), H res of another mode in addition to the uniform FMR mode was extracted at lower fields. Aside from possible film non-uniformities, the origin of this mode could be a perpendicular standing spin wave (PSSW) with a nonzero wave vector q = np/t (integer order of mode n, with n = 0 as the uniform mode) pointing perpendicular to the film plane. Here, the absence of additional higher order modes may be related to a very weak excitation, resulting in an intensity below the detection limit and preventing us from attributing this mode to a PSSW with certainty. the two-magnon scattering contribution to the extrinsic broadening of the linewidth [61]. Figure 6a-d presents Hres of the FMR mode as a function of the excitation frequency for the Co2MnGa films. Notably, for the 80-nm-thick film (Figure 6d), Hres of another mode in addition to the uniform FMR mode was extracted at lower fields. Aside from possible film non-uniformities, the origin of this mode could be a perpendicular standing spin wave (PSSW) with a nonzero wave vector = / (integer order of mode n, with n = 0 as the uniform mode) pointing perpendicular to the film plane. Here, the absence of additional higher order modes may be related to a very weak excitation, resulting in an intensity below the detection limit and preventing us from attributing this mode to a PSSW with certainty. To determine the effective magnetization Meff, g-factor and exchange stiffness A, a simplified resonance condition was evaluated. For parallel M and H (applied perpendicular to the film surface), this gives: with the gyromagnetic ratio = ℏ . The exchange stiffness was only extracted for the 80nm-thick film, assuming that the second mode originated from a PSSW. Here, A = 16.8 pJ/m is comparable to the exchange stiffness in other Co-based Heusler compounds (4.8-31.5 pJ/m) [62][63][64]. Table 2 summarizes Meff and g for all of the investigated Co2MnGa films. As the thickness increases, Meff drastically decreases. Further, a noticeable uniaxial magnetic anisotropy perpendicular to the film plane, attributed to the growth-induced lattice strain, can be inferred from the increased size of Meff compared to Ms. Table 2. Magnetic parameters of the Co2MnGa films extracted from linear fits to the resonance fields and linewidths (Figure 6), including saturation magnetizations from the hysteresis curves (cf. Figure 5).

t (nm)
Ms (kA/m)  To determine the effective magnetization M eff , g-factor and exchange stiffness A, a simplified resonance condition was evaluated. For parallel M and H (applied perpendicular to the film surface), this gives: with the gyromagnetic ratio γ = gµ B . The exchange stiffness was only extracted for the 80-nm-thick film, assuming that the second mode originated from a PSSW. Here, A = 16.8 pJ/m is comparable to the exchange stiffness in other Co-based Heusler compounds (4.8-31.5 pJ/m) [62][63][64]. Table 2 summarizes M eff and g for all of the investigated Co 2 MnGa films. As the thickness increases, M eff drastically decreases. Further, a noticeable uniaxial magnetic anisotropy perpendicular to the film plane, attributed to the growthinduced lattice strain, can be inferred from the increased size of M eff compared to M s . Table 2. Magnetic parameters of the Co 2 MnGa films extracted from linear fits to the resonance fields and linewidths (Figure 6), including saturation magnetizations from the hysteresis curves (cf. Figure 5).  Figure 6e-h presents ∆H as a function of the excitation frequency for the Co 2 MnGa films. Notably, the data for the 10-nm-thick film show significant scattering, attributed to a less accurate fit of the FMR mode due to the low signal intensity. ∆H characterizes the relaxation of the magnetization due to extrinsic frequency-independent contributions (inhomogeneous linewidth broadening ∆H 0 ) as well as intrinsic contributions linearly pro-portional to the resonance frequency (Gilbert damping parameter α). These contributions can be determined from the frequency dependence of ∆H as: The α values summarized in Table 2 agree well with previously reported values for Co 2 MnGa films (α ≈ 2 × 10 −3 ) [42,43]. In that context, the low α values in conjunction with the previously inferred high degree of spin polarization agree well with the correlation of those properties established by Liu et al. [65]. Further, α slightly increases with thickness. This thickness dependence likely originates in the lattice distortion affecting the spin polarization [66]. In contrast, ∆H 0 decreases with increasing film thickness, which indicates increased inhomogeneities in the thinner films and lower crystalline quality [34]. Figure 7 shows the H orientation dependencies of H res in the (001) plane (IP) and (110) plane (IP to OOP). Note that, for the 80-nm-thick film, we only considered the main mode. In the (001) plane (Figure 7a-d), H res has a four-fold H orientation dependence, which can be explained by the cubic symmetry of the Heusler structure. Here, the easy axes lie along the [110] and equivalent directions. In the (110) plane (Figure 7e-h), the H orientation dependence of H res agrees with the magnetization measurements (cf. Figure 5), with the magnetic hard axis along the (001) axis (OOP). From the Hres simulation results (Figure 7, solid lines) obtained using Equations (4) and (5), the anisotropy constants at 300 K were derived, using Ms and g (entering via = ℏ ) in Table 2. The simulations well reproduced both rotation planes, and Table 3 summarizes the corresponding anisotropy constants. The magnetic anisotropies of the Co 2 MnGa films can be determined from the dependence of the FMR resonance condition on the direction of the applied magnetic field H with respect to the growth orientation of the crystallographic axes (inset in Figure 7h). For that purpose, the total free energy density (F tot ) was employed. Here, we describe F tot of the Co 2 MnGa films using the Zeeman energy, the shape anisotropy, a uniaxial anisotropy term perpendicular to the film plane and a cubic anisotropy term:

X-Band FMR
(Θ, Φ) and (θ, φ) correspond to the angles of the magnetization and applied magnetic field defined in relation to the sample, respectively. K u, [001] and K c are the perpendicular uniaxial and cubic anisotropy constants, respectively. The resonance condition can, in turn, be derived from F tot for arbitrary orientations of the external magnetic field with respect to the sample as [67]: with the derivatives evaluated for the equilibrium direction of the magnetization. In addition, for the simulation of the resonance condition in the presented coordinate system, φ was fixed at 90 • for rotation in the film plane, whereas θ was fixed at 90 • for rotation out of the film plane.
From the H res simulation results (Figure 7, solid lines) obtained using Equations (4) and (5), the anisotropy constants at 300 K were derived, using M s and g (entering via γ = gµ B ) in Table 2. The simulations well reproduced both rotation planes, and Table 3 summarizes the corresponding anisotropy constants. Table 3. Anisotropy constants of the Co 2 MnGa films determined from simulations of the magnetic field orientation-dependent resonance fields (Figure 7). Based on the previous M eff results (cf. Table 2), the Co 2 MnGa films indeed show a uniaxial contribution to the effective anisotropy perpendicular to the film plane according to: with the effective perpendicular uniaxial anisotropy constant K u,eff . The uniaxial term (K u,[001] ) originates from the aforementioned tensile strain-induced tetragonal distortion (cf. Table 1), adding to the effects of the shape anisotropy and, in turn, increasing the effective anisotropy. Table 3 demonstrates that this behavior is the most pronounced in the 10-nm-thick film and decreases with increasing thickness, in agreement with the thickness dependence of the tetragonal distortion along the [001] axis. This behavior is also reflected in the cubic anisotropies K c determined from the IP H orientation dependence of H res . Specifically, K c decreases with increasing thickness. For the IP H orientation dependence, the absence of a uniaxial contribution supports the observation by Pechan et al. [44] that the strain is isotropic in the film plane.

Summary and Conclusions
In this work, we studied the magnetic and electronic properties of L2 1 -ordered Co 2 MnGa thin films, particularly as functions of the film-thickness-dependent structural and morphological properties. We observed a uniform magnetization throughout the entire film thickness and determined the itinerant and localized characters of the Co d and Mn d valence electrons and accompanying magnetic moments, respectively. Further, by comparing the Mn 2p spectra of Co 2 MnGa with those of Co 2 MnSi [49], a very high degree of spin polarization could be inferred. The combination of high-spin polarization with low Gilbert damping makes the L2 1 -Co 2 MnGa films very interesting for potential spin-orbit-torque and spin-transfer-torque devices [68]. In terms of thickness dependence, we made three main observations. First, as the film thickness decreases, a tensile strain, related to a lattice mismatch between the film and substrate, leads to tetragonal distortion of the Co 2 MnGa lattice. Similar tetragonal distortion has been observed in other cubic films, using buffer layer and adding small amounts of a third element [69,70]. This tetragonal distortion likely affects the spin polarization [66] and, in turn, leads to the reduction of the Gilbert damping parameter α (from 2.1 × 10 −3 to 1.1 × 10 −3 ) in thinner films. This demonstrates the possibility of further reducing the Gilbert damping parameter via the film thickness or lattice matched film growth. Second, the crystalline quality increases with increasing thickness [34], resulting in decreased inhomogeneous linewidth broadening (from 14.4 to 5.8 mT). This observation emphasizes the importance of controlling the thickness-dependent film quality in the development of potential materials for device-based applications. Third, the increasing tetragonal lattice distortion with decreasing thickness also results in decreasing uniaxial anisotropy (from −59 to −95 kA/m 3 ) perpendicular to the film plane and increasing cubic anisotropy (from 1.9 to 7 kA/m 3 ) in the film plane. These features demonstrate that not only the substrate [44] but also the film thickness enables the tuning of the magnetic anisotropies of Co 2 MnGa films, in particular at the thin film limit. Lastly, a potential perpendicular standing spin wave mode was observed in the 80-nm-thick film and enabled quantification of the exchange stiffness (A = 16.8 pJ/m). The ability to manipulate the intrinsic magnetic properties with strain-induced epitaxial engineering represents an important springboard for exploiting thin films of Co 2 MnGa in topological spintronic applications. This work enriches the knowledge on the electronic and magnetic properties of Co 2 MnGa films, which are promising in the development of magnetic storage and non-volatile memory technology.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.