The antiferromagnetic insulator α-Fe2O3 (hematite), widely used in spintronics and magnonics, features a spin-reorientation transition (Morin transition) at 263 K. Thin films, however, often lack this Morin transition, limiting their potential applications. Here, we investigate the impact of different growth conditions on the magnetic anisotropy in α-Fe2O3 films to tune the Morin transition temperature. To this end, we compare the structural, magnetic, and magnon-based spin transport properties of α-Fe2O3 films with different thicknesses grown by pulsed laser deposition in molecular and atomic oxygen atmospheres. We observe a finite Morin transition for those grown by atomic-oxygen-assisted deposition, interestingly even down to 19 nm thickness, where we find a Morin transition at 125 K. In easy-plane antiferromagnets, the nature and time-evolution of the elementary excitations of the spin system are captured by the orientation and precession of the magnon pseudospin around its equilibrium pseudofield, manifesting itself in the magnon Hanle effect. We characterize this effect in these α-Fe2O3 films via all-electrical magnon transport measurements. The films grown with atomic oxygen show a markedly different magnon spin signal from those grown in molecular oxygen atmospheres. Most importantly, the maximum magnon Hanle signal is significantly enhanced, and the Hanle peak is shifted to lower magnetic field values for films grown with atomic oxygen, suggesting changes in the magnetic anisotropy due to an increased oxygen content in these films. Our findings provide new insights into the possibility to fine-tune the magnetic anisotropy in α-Fe2O3 and thereby to engineer the magnon Hanle effect.
Magnetic anisotropy has a major impact on the behavior of magnetically ordered systems and, thus, on their magnonic modes. Therefore, the possibility of tuning the magnetic anisotropy is of great importance in the field of magnonics. The latter utilizes the quantized spin excitations of magnetically ordered systems, i.e., magnons, and offers a variety of interesting opportunities such as information processing with bosons and magnon-based computing approaches.1–3 Antiferromagnets are particularly appealing for magnonic logic devices due to their very fast magnetization dynamics in the THz regime and their robustness against external magnetic fields.4–8 Antiferromagnetic magnons are represented by two modes with opposite precession chiralities of the Néel order vector and thus opposite pseudospin.9,10 In the case of easy-plane antiferromagnets, linearly polarized spin waves with zero effective spin, which can be viewed as an equal superposition of basis states with opposite chirality, form the appropriate eigenmodes of the spin system.11–15 The manipulation and read-out of information encoded into antiferromagnetic magnons is demanding due to the vanishing stray fields of antiferromagnets. However, it has been demonstrated that this can be achieved by all-electrical magnon transport.16–21 There, the electrical injection and detection of magnonic spin transport are realized via two heavy-metal electrodes adjacent to the antiferromagnetic insulator by making use of the spin Hall and inverse spin Hall effect.22–26 In such experiments, the magnon Hanle effect, the analog of the electron Hanle effect, has been demonstrated in the easy-plane antiferromagnetic insulator α-Fe2O3. This has been achieved by a coherent control of the magnon pseudospin and long-distance magnon-based spin propagation in α-Fe2O3.24
Bulk hematite (α-Fe2O3) is an antiferromagnetic insulator (AFI) below the Néel temperature TN = 953 K and exhibits a spin-reorientation transition at the Morin transition temperature of TM = 263 K.27 In the temperature range TM < T < TN, the magnetic moments are parallel to the magnetically easy α-Fe2O3 (0001)-plane as described by a uniaxial magnetic anisotropy along the -trigonal hard axis. In addition, a finite spin canting is induced by the Dzyaloshinskii–Moriya interaction (DMI) resulting in a net magnetization of 2.5 kA m−1 in the (0001) easy plane at room temperature.27,28 For T < TM, the uniaxial magnetic anisotropy reverses sign, leading to a reorientation of the magnetic Fe3+-moments along the -axis representing now the magnetically easy axis.27,29 In this easy-axis antiferromagnetic configuration, the spin canting is absent and the net magnetization vanishes. However, this Morin transition is often suppressed in α-Fe2O3 thin films as it is very sensitive to growth-induced changes in magnetic anisotropy such as strain and oxygen deficiency in the α-Fe2O3 layers.30–33 Since this is a widely encountered problem, we here determine optimal growth conditions for α-Fe2O3 films in order to change the magnetic anisotropy and, thus, shift the Morin transition to finite temperatures.
The easy-plane phase gives rise to the magnon Hanle effect in α-Fe2O3 described by the precessional motion of antiferromagnetic magnon pseudospin around its equilibrium pseudofield.9,10 In the easy-axis phase, instead, one expects the magnon Hanle effect to disappear. This conjecture, however, is difficult to prove since the films with small thickness are desirable in all-electrical magnon transport experiments to discern the magnon Hanle signature from the finite spin signal stemming from low energy magnons.34 However, in thin α-Fe2O3 films with a thickness below 100 nm, the Morin transition is usually suppressed as size-related effects change the delicate balance between magnetic-dipolar and uniaxial anisotropy contributions, which determines the Morin transition temperature.35,36 Therefore, the identification of growth conditions for α-Fe2O3 thin films, which show a Morin transition, is key for confirming the conjecture that an easy plane anisotropy is required for the presence of the magnon Hanle effect.
In this article, we investigate the crystallographic, magnetic, and magnon transport properties of epitaxial α-Fe2O3 films with thickness values ranging from 15 to 124 nm. These films have been grown by pulsed laser deposition using two different growth atmospheres: (i) pure molecular oxygen and (ii) molecular oxygen with additional atomic oxygen. We observe a finite Morin transition temperature TM in α-Fe2O3 films fabricated by atomic-oxygen-assisted deposition, while a Morin transition is absent in α-Fe2O3 films grown in the molecular oxygen atmosphere. This suggests a modification of the magnetic anisotropy in α-Fe2O3 by changing the oxygen content. In all-electrical magnon transport measurements, the atomic-oxygen assisted growth of α-Fe2O3 yields a modification of the antiferromagnetic magnon pseudospin dynamics. Within the scope of the magnon Hanle effect, this manifests itself in an enhanced magnon spin signal amplitude and a shift of the Hanle peak toward smaller magnetic field magnitudes.
II. SAMPLE FABRICATION AND CHARACTERIZATION
Epitaxial α-Fe2O3 films are grown via pulsed laser deposition on (0001)-oriented, single crystalline sapphire (Al2O3) substrates. The growth process is carried out in an atmosphere of molecular oxygen with a partial pressure of 25 µbar, while the substrate temperature is kept at 320 °C. The laser fluence at the polycrystalline α-Fe2O3 target is 2.5 J cm−2, and the pulse repetition rate is set to 2 Hz.37 To reduce the formation of oxygen vacancies, we fabricated a second set of α-Fe2O3 films utilizing an atomic oxygen RF source (AOS) at a power of 400 W, where we add atomic oxygen to the deposition atmosphere while all other deposition parameters are kept constant. In the following, we differentiate between no AOS (NAOS)-Fe2O3 films (no AOS used during deposition) and AOS-Fe2O3 films (AOS used during deposition). The thicknesses of the α-Fe2O3 films discussed in this article range from 15 to 124 nm to investigate the differences between NAOS- and AOS-Fe2O3 for both thin and thick films. Hereby, we consider α-Fe2O3 films as thin (thick) if the film thickness tm is comparable to (or much larger than) the thermal magnon wavelength lth, which is typically much smaller than the magnon spin decay length. The thin and thick film limits and their influence on the magnon Hanle signal have been studied in detail in our previous work.34 The thickness values of the discussed α-Fe2O3 films are summarized in Table I.
|Atomic oxygen source used .||Thin α-Fe2O3 (nm) .||Thick α-Fe2O3 (nm) .|
|Atomic oxygen source used .||Thin α-Fe2O3 (nm) .||Thick α-Fe2O3 (nm) .|
2θ-ω x-ray scan.
All-electrical diffusive magnon transport.
2θ-ω x-ray scan and reciprocal space map (see the supplementary material).
We analyze the structural properties of our α-Fe2O3 films by high-resolution x-ray diffraction (HR-XRD) measurements. The corresponding 2θ-ω scans around the α-Fe2O3 (0006) film and Al2O3 (0006) substrate reflections are shown in Figs. 1(a) and 1(b) for thin and thick α-Fe2O3 films, respectively. Thereby, we observe no secondary crystalline phases. Finite thickness fringes around the α-Fe2O3 (0006) reflections indicate coherent growth and, thus, a good crystalline quality of the α-Fe2O3 films.38 Moreover, the (0006) reflections of the AOS-Fe2O3 films (black lines) are slightly shifted toward smaller 2θ-values with respect to the ones of the NAOS-Fe2O3 films (blue lines). This indicates an increase in the out-of-plane lattice constant c when adding atomic oxygen to the fabrication process and, thus, reducing the oxygen deficiency in α-Fe2O3. Reciprocal space maps (RSMs) around the asymmetric α-Fe2O3 () and Al2O3 () reflections also confirm a slight reduction in c for AOS-Fe2O3 films, while the in-plane lattice constant a remains nearly constant (see the supplementary material). It should be mentioned that the changes in c are small and within the range of the measurement uncertainty. The extracted lattice parameters indicate a nearly relaxed growth of α-Fe2O3 on the Al2O3 substrates for all samples investigated. We obtain comparable values of the small but finite epitaxial in-plane strain ɛip for NAOS- and AOS-Fe2O3 films suggesting that the value of ɛip is independent of the growth method. Furthermore, we do not observe any indication of an additional, strained α-Fe2O3 layer near the film-substrate interface due to clamping effects as stated in a recent publication.39 A detailed discussion of the RSMs and the extracted lattice constants is given in the supplementary material.
To identify possible magnetic phase transitions in our α-Fe2O3 films, we performed superconducting quantum interference device (SQUID) magnetometry. After cooling the samples down to 10 K in zero field, we measured the magnetization M as a function of temperature T at a fixed magnetic field of μ0H = 100 mT applied in the film plane. The corresponding results are shown in Figs. 1(c) and 1(d), where a temperature-independent background signal was subtracted beforehand. This background signal is a linear function of μ0H, which mainly stems from the diamagnetic Al2O3 substrate but also from an increased sublattice canting in α-Fe2O3 with increasing μ0H.38 The NAOS-Fe2O3 films exhibit no phase transitions over the whole temperature range from 300 K down to 10 K and, thus, remain in the magnetically (0001)-easy plane phase with a finite net magnetization induced by DMI. Generally, the shift of the Morin transition toward lower temperatures or its complete absence in α-Fe2O3 films can be attributed to strain-induced changes of the magnetic anisotropy.30–32 However, as discussed above, all investigated α-Fe2O3 films are nearly relaxed and, therefore, exhibit only small in-plane strain values (see the supplementary material). At low temperatures, some of the α-Fe2O3 films show a small increase in M [cf. Fig. 1(c)], which is most probably caused by paramagnetic moments within the Al2O3 substrate.
The AOS-Fe2O3 films, instead, reveal Morin transition temperatures of TM ≈ 205 K and TM ≈ 125 K for thick and thin films, respectively, which are found to decrease with increasing applied magnetic field [see inset of Fig. 1(d)]. As the small in-plane strain is comparable for NAOS- and AOS-Fe2O3 films, the absence (appearance) of the Morin transition in NAOS (AOS)-Fe2O3 can not be explained by strain-induced effects on the magnetic anisotropy. The atomic-oxygen-assisted deposition could rather lead to a reduction of oxygen vacancies and, therefore, to a change in the magnetic anisotropy in AOS-Fe2O3 films compared to the possibly more oxygen deficient NAOS-Fe2O3 films. We note that an oxygen deficiency in the α-Fe2O3 films results in a partial reduction of Fe3+ to Fe2+ ions and, thus, is expected to change the magnetic anisotropy and TM.33 However, the Morin transition temperature of the AOS-Fe2O3 films is still smaller than in bulk crystals, which has also been recently reported for α-Fe2O3 thin films.31,35 In addition, a second Morin transition at , indicated by the small kink in the M(T) curve, can be observed for the thick AOS-Fe2O3 film [see Fig. 1(d)]. This low temperature Morin transition coincides with the single Morin transition in the thin AOS-Fe2O3 film and suggests the existence of a second α-Fe2O3 phase in the sample with a different magnetic anisotropy. The detailed origin of the different magnetic anisotropies remains unknown. However, we can speculate that it is related to an increased defect density (e.g., oxygen vacancies) at the film-substrate interface, which affects the magnetic properties of our α-Fe2O3 films.40
Although we expect a drop of M to zero for T < TM in the easy-axis phase, we observe a surprisingly large magnetization for T < 125 K for the AOS-Fe2O3 films. Since we do not find any indications from HR-XRD for the presence of other iron oxide phases such as ferrimagnetic γ-Fe2O3 (maghemite) or Fe3O4 (magnetite) that could contribute to the finite magnetization of the samples, we suggest that the spin-reorientation at TM is incomplete and leads to co-existing easy-plane and easy-axis phases in our AOS-Fe2O3 films below the respective Morin transitions. Notably, the net magnetization is larger in thin than in thick films, which can be induced by changes in the DMI, the exchange coupling, or the magnetic anisotropy in α-Fe2O3. This observation is interesting and demonstrates that the impact of film thickness on the magnetic properties of the α-Fe2O3 films has to be taken into account and needs detailed consideration. In total, our SQUID magnetometry measurements suggest a more complex spin structure of our α-Fe2O3 films, proving that an extensive study of the Morin transition can be a powerful tool to investigate the magnetic anisotropy in hematite films.
III. ALL-ELECTRICAL MAGNON TRANSPORT
In the following, we study the impact of different magnetic anisotropies induced by different oxygen atmospheres during the deposition of α-Fe2O3 films on their magnon transport properties. For our experiments, two 500 nm wide and 5 nm thick Pt strip electrodes with different center-to-center distances d [see Fig. 2(a)] are patterned on the top of the α-Fe2O3 films via a lift-off process using electron-beam lithography and sputter deposition. We apply a DC charge current Iinj = 500 µA to one Pt electrode injecting a spin current into the α-Fe2O3 film via the spin Hall effect (SHE).22–25 The hereby excited diffusive pseudospin magnon current is electrically detected in the second electrode as a voltage signal Vdet via the inverse SHE (iSHE).23,26 We use the current reversal technique to extract the voltage signal originating from the SHE excited magnons.17,41 For fabrication and measurement details we refer to the supplementary material. The electrically induced magnon spin signal depends on the orientation of the Néel vector n with respect to the spin polarization s of the injected spin current. The Néel vector is defined by the sublattice magnetizations M1 and M2 with corresponding saturation magnetizations M1 and M2 resulting in n = (M1/M1 − M2/M2)/2. To orient the net magnetization Mnet = M1 + M2 and, thus, n ⊥ Mnet, we apply a magnetic field H in the film plane. We find to be maximum (zero) for n‖s (n ⊥ s), which is the case for H at φ = 270° (180°) [see the coordinate system in Fig. 2(a)].
The corresponding results of the thin and thick AOS-Fe2O3 films are shown in Figs. 2(d) and 2(e). Clearly, the maximum value of is larger than for the NAOS-Fe2O3 counterparts shown in (b) and (c). Since the injector–detector distances of the respective NAOS- and AOS-Fe2O3 samples are comparable, the increased for AOS-Fe2O3 cannot be explained by a decrease in d. Fits to Eq. (1) [see Figs. 2(b) and 2(d)] reveal a larger magnon spin decay length for the device with d = 750 nm on AOS-Fe2O3 than for the NAOS-Fe2O3 (d = 700 nm) sample. For the devices with d = 1000 nm, the extracted fit parameters suggest that the increased for AOS-Fe2O3 originates from an increased factor js0/χ. As the measured spin Hall magnetoresistance (SMR) at the injector of all α-Fe2O3 samples is in the same order of magnitude (see the supplementary material), the larger for AOS-Fe2O3 cannot be attributed to an enhanced spin current transparency of the α-Fe2O3/Pt interfaces, as it would also affect js0. Instead, the prefactor χ is reduced, which describes a change in the magnon density of states possibly due to a change in the magnetic anisotropy of α-Fe2O3. Thus, a larger lm as well as a smaller χ can explain the larger magnon Hanle peak signal for AOS-Fe2O3 films. In addition to the increase in , we observe a narrowing of the magnon Hanle peaks for the thin AOS-Fe2O3 film compared to the corresponding NAOS-Fe2O3 film [cf. Figs. 2(b) and 2(d)]. As the injector–detector distances of the respective NAOS- and AOS-Fe2O3 samples are comparable with each other, the fits to Eq. (1) suggest an increase in the fit parameter c2 describing the magnetic field dependent contribution to the pseudofield ω = −c1 + c2H and, thus, a change in the frequency of the pseudospin precession around its equilibrium pseudofield (see the supplementary material for details on the fitting procedure and extracted fit parameters).10
To further investigate the differences in between devices on NAOS-Fe2O3 and AOS-Fe2O3 films, we measure at different temperatures ranging from 100 to 300 K. The results are given in Fig. 3, where we focus on datasets for devices with fixed injector–detector distances for each α-Fe2O3 film. With increasing T, μ0Hc clearly shifts to higher magnetic fields as the magnetic anisotropy in α-Fe2O3 is temperature dependent.29,43,44 Moreover, at μ0Hc first increases with increasing T due to an increased amount of thermally occupied magnon states.17,18 In (b) and (c), however, the maximum of decreases again for T > 250 K as a result of an increase in magnon scattering processes.30 For the thin AOS-Fe2O3 film shown in Fig. 3(c), no significant changes in across the Morin transition temperature TM = 125 K can be observed due to the low TM, which further decreases for μ0H > 0. In the case of devices on thick films, distinct differences in between devices on NAOS-Fe2O3 [Fig. 3(b)] and on AOS-Fe2O3 films [Fig. 3(d)] appear at T ≤ 150 K. For μ0H < 4 T, the plateau in originating from the contribution of low-energy magnons disappears in AOS-Fe2O3 and a peak-like behavior becomes visible instead [see Fig. 3(d)]. From the linear fit to TM(μ0H) in the inset in Fig. 1(d), we can conclude that at 150 K and at 100 K, the AOS-Fe2O3 film is partially in the easy-axis phase for magnetic fields up to 3 and 6 T, respectively. The peak-like behavior of is, therefore, in agreement with measurements in easy-axis α-Fe2O3, where it is attributed to a spin reorientation induced by the DMI.45
We extract the compensation field μ0Hc and the electrically induced magnon spin signal amplitude at μ0Hc from the magnon Hanle curves recorded at different temperatures 100 K ≤ T ≤ 300 K and present both as functions of T in Figs. 4(a)–4(d). The compensation field exhibits the expected T2 dependence for thin (a) as well as for thick α-Fe2O3 films (b).29 Compared to the NAOS-Fe2O3 films (blue symbols), the respective compensation fields of the AOS-Fe2O3 films (black symbols) are reduced over the whole temperature range but converge at higher temperatures. The thick AOS-Fe2O3 film [black in Fig. 4(b)] exhibits the Morin transition at sufficiently large temperatures, below which the magnon Hanle effect simply vanishes. Correspondingly, μ0Hc and can not be extracted for thick AOS-Fe2O3 at temperatures below 170 K. At 100 K ≤ T ≤ 300 K, the amplitude shown in Figs. 4(c) and 4(d) is larger for AOS-Fe2O3 films than for NAOS-Fe2O3 films despite the slightly larger injector–detector distances for the AOS-Fe2O3 films. In addition, in (c), the maximum of of AOS-Fe2O3 is shifted to a lower T and in (d) to a higher T compared to the NAOS-Fe2O3 films. Thus, the influence of magnon scattering at higher T strongly depends on the individual α-Fe2O3 film. Additional data for different d are provided in the supplementary material and confirm the observed behavior at μ0Hc.
To investigate differences between NAOS- and AOS-Fe2O3 films in terms of the magnon spin decay length lm, we extract lm from the fits to Eq. (1) depicted in Figs. 2(b) and 2(d) and in Figs. 3(a) and 3(c) for the thin α-Fe2O3 films. For the thick α-Fe2O3 films, it is not possible to adequately fit . Therefore, we determine the magnon spin decay length of thick α-Fe2O3 by a different fitting procedure as described in the supplementary material. In Figs. 4(e) and 4(f), lm is plotted as a function of T for thin and thick α-Fe2O3, respectively. Hereby, in (e), we average over all investigated two-terminal devices with d ranging from 450 to 1300 nm depending on the respective thin film. In (f), lm is determined at a magnetic field magnitude of 2 T, at which exhibits a plateau above the Morin transition and a maximum below the Morin transition for thick α-Fe2O3. For thin as well as for thick α-Fe2O3 films, lm first increases with decreasing T due to a reduction of magnon scattering processes. At lower T down to 100 K, lm seems to saturate. In (e), the magnon spin decay length of NAOS-Fe2O3 is slightly reduced compared to the one of AOS-Fe2O3. However, taking into account the given uncertainties, lm is approximately the same for NAOS- and AOS-Fe2O3 films. In (f), the magnon spin decay length of both α-Fe2O3 films is nearly the same for temperatures above 200 K. For T ≤ 200 K, the magnon spin decay length of the NAOS-Fe2O3 film is slightly smaller than for the AOS-Fe2O3 film. As we expect a partial reduction of Fe3+ to Fe2+ ions in oxygen deficient α-Fe2O3 films, the NAOS-Fe2O3 films could exhibit a higher density of Fe2+ ions than the AOS-Fe2O3 films, where the atomic-oxygen assisted deposition should enhance the oxygen content. Therefore, increased magnon scattering at Fe2+ ions could reduce the magnon spin decay length in NAOS-Fe2O3. All in all, the magnon spin decay length of the four investigated α-Fe2O3 samples is in the same order of magnitude but sightly larger for AOS-Fe2O3. Hence, a change in the magnetic anisotropy affecting the effective susceptibility χ of the AOS-Fe2O3 films and the magnon spin decay length lm in AOS-Fe2O3 is possibly causing the increase in the amplitude of the magnon Hanle peak.
We fabricated α-Fe2O3 films of different thicknesses without (NAOS-Fe2O3) as well as with the addition of atomic oxygen during the deposition process (AOS-Fe2O3). We study the Morin transition in our samples, which is sensitive to the magnetic anisotropy in α-Fe2O3. The NAOS-Fe2O3 films exhibit no Morin transition down to 10 K, while the AOS-Fe2O3 films clearly show a Morin transition at around TM = 125 K for the 19 nm thin film and at around 205 K for the 89 nm thick film. This proves that we are able to tune the magnetic anisotropy and thus the Morin transition in thin as well as in thick α-Fe2O3 films using an atomic oxygen source. Furthermore, the thick AOS-Fe2O3 film reveals an additional Morin transition at 125 K, which indicates the existence of a second α-Fe2O3 phase in the investigated sample with a different magnetic anisotropy.
We conducted all-electrical magnon transport measurements above and below TM and studied the magnon Hanle effect in our α-Fe2O3 films. Adding atomic oxygen during the growth process leads to two distinct changes: (i) an increase in the electrically induced magnon spin signal amplitude at the compensation field μ0Hc and (ii) a reduction of μ0Hc. The increase in originates from an increase in the magnon spin decay length lm or a decrease of the effective susceptibility χ describing a change in the magnon density of states. In addition, at μ0Hc the easy-plane anisotropy of α-Fe2O3 is compensated by the externally applied magnetic field. Therefore, the reduction of μ0Hc is consistent with the increase of TM as for AOS-Fe2O3 the strength of the easy-plane anisotropy is reduced compared to the strength of the easy-axis anisotropy.
In summary, our results show that a variation of the oxygen content during the deposition process as well as a variation of the film thickness alters the magnetic anisotropy of α-Fe2O3. Our results provide a pathway toward a finite TM in hematite films with thicknesses below 100 nm and a new perspective on the role of magnetic anisotropy in the magnon Hanle effect.
Additional XRD data, details on the fabrication and measurement methods, and all-electrical magnon transport data are provided in the supplementary material. This includes reciprocal space mappings and calculated lattice constants as well as explanations of the fitting procedures, extracted fit parameters, and further temperature dependent data.
We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy–Grant No. EXC-2111-390814868, and the Spanish Ministry for Science and Innovation–AEI Grant No. CEX2018-000805-M (through the “Maria de Maeztu” Program for Units of Excellence in R&D). This research is part of the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus.
Conflict of Interest
The authors have no conflicts to disclose.
M. Scheufele: Data curation (lead); Formal analysis (equal); Writing – original draft (lead). J. Gückelhorn: Data curation (equal); Formal analysis (supporting); Investigation (lead); Writing – review & editing (supporting). M. Opel: Formal analysis (equal); Writing – review & editing (equal). A. Kamra: Formal analysis (supporting); Writing – review & editing (supporting). H. Huebl: Writing – review & editing (supporting). R. Gross: Funding acquisition (equal); Project administration (equal); Writing – review & editing (supporting). S. Geprägs: Conceptualization (equal); Data curation (supporting); Formal analysis (equal); Investigation (supporting); Project administration (equal); Supervision (lead); Writing – review & editing (equal). M. Althammer: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Supervision (supporting); Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request.