Fe dopants and surface adatoms versus nontrivial topology of single-crystalline Bi₂Se₃

Results of the electronic transport characteristics of bulk doped crystal at low temperature and high magnetic field are presented in figure 1. Longitudinal, ρ_xx, and Hall, ρ_xy, resistivities probed at 300 mK versus external magnetic field are shown in figure 1(a). Negative Hall resistivity proves that the charge carriers are electrons, which is the same as for pristine samples of Bi₂Se₃ [28]. Shubnikov–de Haas quantum oscillations are easily discerned from ρ_xx as well as QHE plateau from ρ_xy which proves that Landau-levels pass through the Fermi level with increasing magnetic field. Pure oscillations were extracted from the field dependence of longitudinal conductivity by subtraction of polynomial background. The resulting Δρ_xx, plotted in Δρ_xxB³ vs 1/B parameterization reveal single frequency oscillations. Fourier transform analysis (inset in figure 1(b)) provides the characteristic frequency of quantum oscillations of approx. 230 T. A detailed quantitative analysis of these results will be published elsewhere [29].

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Figure 2 shows the results of EXAFS experiment performed on pristine and Fe bulk doped Bi₂Se₃ crystals. Respective Bi L₃ and Se K-edge spectra of the two samples are identical within experimental accuracy, both, in the near edge structure (figure 2(a)) and in the extended range (figure 2(b)). Edge shape and edge energy position are similar to that observed in Se and Bi pure metals [30, 31]. Local atomic structure around both ions has been derived from EXAFS oscillations. Fits were performed using reduced parameterization involving hexagonal unit cell parameters (a, c), atomic positions and Debye–Waller factors. At first, structural parameters were refined independently for each edge. Secondly, both edges were fitted simultaneously, using common parameterization (supplemental material, figure S2). Structural parameters derived from such local probe are in very good agreement with crystal lattice obtained from x-ray diffraction data. See supplemental materials for more details.

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Fe K-edge spectrum of Bi₂Se₃:Fe crystal (figure 2(a)) reveals the edge position slightly shifted from that of metal, being close to that observed in FeSe and in thin films of Fe-doped Bi₂Se₃ [32]. However, it does not reveal a pronounced pre-edge structure due to the dipole transition between the 1s initial state and the Fe 3d–Se 4p hybrid orbital, which is considered a fingerprint of FeSe alloy formation [33]. Thus, Fe bulk dopants in the studied crystal are predominantly diluted impurities. Comparison of EXAFS oscillations extracted from Fe spectra to those of Bi and Se provides first approximation of the crystal sites in the case of substitutional doping. As shown in figure 2(b) major features observed in Fe spectrum are common to those of Bi spectrum, which suggests that significant amount of Fe ions substitute Bi sites. Nevertheless, there is a clear admixture of additional oscillations in Fe K-edge spectrum. Since the additional spectral features are not common with Se spectrum, these are attributed to Fe dopants residing in interstitial sites. Detailed analysis of the Fe distribution derived from Fe K-edge EXAFS is presented in chapter 4.

Field and temperature dependencies of bulk magnetization of Bi₂Se₃:Fe monocrystal, obtained with a SQUID magnetometer, are shown in figure 3. At 300 K, M(B) is almost linear and negative, due to low Fe content and the dominating diamagnetic susceptibility of Bi₂Se₃ host. The magnetization at 2 K is clearly anisotropic. When probed along the c-axis (out-of-plane), M(B) is positive at low field and becomes negative at B > 1 T. Such dependence can be attributed to a weak ferro- or paramagnetic component that adds up to the diamagnetic, linear M(B) background that is almost the same as at 300 K. For the direction within a – b plane, M(B) is positive in the entire field range, and the paramagnetic contribution is several times larger than in the case of c-axis. Nevertheless, the magnetization in a – b plane at 2 K and 5 T, reaches only 0.017 μ_B per Fe ion if the Fe content x = 0.017 is used for calculation. Moreover, M(B) does not reveal any traces of saturation at high field, nor a remanence (and hysteresis) at low field, which were reported for crystals with higher Fe concentration, i.e. Bi_1.96Fe_0.04Se₃ [34] and Bi_1.84Fe_0.16Se₃ [35] respectively.

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The temperature dependence of magnetization measured at 0.5 T is shown in figure 3(b), and demonstrates that the magnetic anisotropy of Bi₂Se₃:Fe persists also at higher temperatures (see, however, the discussion below). The data measured at 0.01 T show exactly the same features in the range 2–30 K, but due to better estimations of different corrections, 0.5 T data were used for further analysis. The in-plane magnetization (DC susceptibility) follows the Curie–Weiss law χ(T) = χ₀ + C /(T −θ_CW) with θ_CW = −9.7(5) K and the Curie constant, C, that corresponds to an effective paramagnetic moment p_eff ≈ 2.1(1) μ_B per Fe ion. A deviation from the fitted curve is visible below 10 K in figure 3(b). Such anomaly may be caused by an antiferromagnetic ordering of magnetic moments, but also by another process, like spin-crossover in Fe²⁺ ions from S = 2 to S = 0 state, or AF exchange interaction between pairs of Fe moments. The magnetization along c-axis is significantly smaller in the whole temperature range. The attempt to fit the Curie–Weiss law leads to effective moment below 0.8 μ_B and θ_CW around −5.8 K, however the quick saturation of the positive component of M(B) at 2 K for the c-axis contradicts this low value and suggests that this paramagnetic component originates from a fraction of Fe moments.

XAS and XMCD bare results are presented in figure 4. The geometry of the experiment, which was performed at normal, φ = 90°, and near grazing incidence, φ = 20°, with respect to a – b plane is shown in the figure 4(a). Fe L₃-edge XAS spectra of Fe adatoms on pristine Bi₂Se₃ (figures 4(d) and (e)) consist of a strong maximum at approx. 709 eV and a weak shoulder centered at approx. 712 eV in agreement with the spectra of Fe adatoms deposited on Bi₂Se₃ [9] and Bi₂Te₃ [36, 37]. There is only a very week angular dependence between grazing and normal incidence in XAS, which is manifested by a slight change of the spectral intensity. However, a strong angular dependence is observed in XMCD. The intensity of the dichroism is approx. two times stronger at grazing incidence, which is in line with the observed in-plane anisotropy of Fe adatoms on Bi₂Se₃ [9], but opposite to that of Fe adatoms deposited on Bi₂Te₃ [37].

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XAS spectra collected from Fe atoms embedded in the few nm-thick surface volume of Bi₂Se₃:Fe show a significantly different shape with respect to adatoms. Fe L-edge XAS spectra for Bi₂Se₃:Fe are much more complicated forming a two-peak structure (figures 4(b) and (c)). The first peak resembles the one in Fe/Bi₂Se₃ and thus will mainly be attributed to Fe residing on the surface or, in this case, in VdW gap. Since basically only the surface QL has a peculiar electronic structure [38] and the penetration depth of soft x-rays in our material does not exceed 7 nm (i.e. probes ca 10 QL), we infer that the electronic structure of Fe ions within VdW gap is close to those on the surface or XAS cannot see the subtle differences. Peak around 711 eV is strongly enhanced with respect to the spectra of adatoms and it shows a significant angular dependence. A similar behavior was ascribed to surface oxidation [39]. However, such behavior was confirmed in three independent measurements—two at former ID08 beamline of ESRF and one at PEEM/XAS beamline of Solaris (at room temperature)—all performed on different in-situ cleaved crystals. Thus we attribute this feature to the presence of Fe³⁺ ions localized in distorted octahedral crystal field of Se anions, namely Fe ions in Bi substitutional sites. Fe L₃-edge XMCD signal probed on Bi₂Se₃:Fe is slightly weaker than that of adatoms. It does not show any significant angular dependence. However, when it is normalized to XAS, it is stronger at normal incidence. It is due to intensity evolution of the dominant peak at higher energy, which is more pronounced with x-ray quanta nearly parallel to a – b plane. As such, the out-of-plane easy magnetization direction is expected. Such scenario is analyzed in details in chapter 4.

We have used nuclear inelastic and resonant scattering of gamma radiation to check what factors define the vibrations of individual adatoms on the surface of TI, in particular to see how topologically protected surface electrons in Bi₂Se₃ affect these vibrations, in comparison to those on non-TI material, Bi₂S₃. Although the latter crystal exhibits different crystal structure than Bi₂Se₃, it is also layered structure with alternating blocks of Bi–S polyhedral units stacked perpendicular to the short b-axis, leading again to the easy cleavage in (010) plane. The cleavage plane is rectangular, in contrast to hexagonal in Bi₂Se₃ case, as revealed by LEED (supplemental material, figure S3). Both materials also differ electronically: while Bi₂Se₃ is a topological insulator with a bulk band gap of 0.3 eV, Bi₂S₃ has rather large gap of 1.3 eV. Finally, due to structure defects, well described in the literature, and ensuing Fermi energy position not in a bulk gap, both materials are metallic. However, since surface metallicity is of different kind (spin-momentum confinement on Bi₂Se₃ surface), the difference in lattice vibration of Fe individual adatoms deposited on those surfaces is expected. NRS signal for Fe/Bi₂Se₃ is presented in figure 5; comparison with metallic Fe assures that the surface layer was not magnetically ordered. Since exactly the same preparation conditions were applied for Bi₂S₃, the same was assumed for Bi₂S₃, although, due to rougher surface, the direct measurements for Bi₂S₃ were not possible.

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The bare results of NIS measurements are shown in figure 6. Data processing to extract partial phonon DOS g(E) from inelastic scattering data was done following the procedure described in [40, 41]; we estimate that due to subtraction difficulties of the elastic central part, g(E) are reliable for E > 3.5 meV.

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Experimental evidence on topological character of Fe-doped Bi₂Se₃ crystals was gathered using the studies of magnetic field influence on electrical conductivity. First of all, as it was mentioned in section 3.1, we observe quantum oscillations in ρ_xx and QHE plateau in ρ_xy. Positions of the minima in Δρ_xx (longitudinal conductance after subtracting polynomial background), figure 1(b), are related to Landau level indices N and positions of the maxima in Δρ_xx are related to N + 1/2. The Landau fan diagram i.e. Landau level index N vs 1/B is shown on figure 7. The linear fitting to the data with the slope fixed to frequency of oscillations (obtained from Fourier analysis) gives the intercept equal to −0.452, so its absolute value is close to 0.5. According to [1], the phase of the SdH oscillations is proportional to the Berry phase. If phase of oscillations is 0.5 the Berry phase is π. Thus we interpret our results as an evidence of non-trivial topology of our sample [1, 42] (although some authors claim that the intercept may also depend on other factors [43]).

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Besides the phase of the oscillations, also their frequency contains useful information. Based on the Onsager relation, SdH oscillations frequency depends on Fermi wave vector which is linked to surface carrier density [44]. In our case, frequency of 230 T (see figure 1(b)) is higher than frequencies for pristine samples (106–190 T) depending on sample quality and the method of sample preparation [28, 42, 45, 46]. This means that Fe doping increases surface carrier density, possibly due to Fe intercalation in the van der Waals gap (as supported by EXAFS results presented below). Similar effect was observed in Fe-doped single crystal of Bi₂Se₃ [47] and was also explained by ionized iron atoms that occupy interstitial positions in the crystal lattice adding up to the concentration of conduction electrons.

The results of magnetotransport measurements, together with their comparison to the literature data, are shown in table 1.

So although surface topology is not affected by magnetic dopants, this material cannot be considered as magnetic topological insulator since the net magnetic response is weak (as shown in figure 3). On the other hand, a significant XMCD signal is found (see figures 4(d) and (e) and the discussion below). All these indicate variety in doping character, which are checked by quantitative analysis of Fe K-edge EXAFS oscillations.

Since our EXAFS results exclude any bulk intergrowth of FeSe_x phases, observed e.g. in [49], four sites in Bi₂Se₃ occupied by Fe were considered following the observation of [32]. These were: octahedral (Oh vdW) and tetrahedral (Td vdW) interstitial site positions in van der Waals gap between two Se layers, octahedral interstitial site within quintuple layer (Oh QL) and substitutional Bi site (see figure 8(a)). Fits of EXAFS results were performed simultaneously in the k-space range 3.0 ÷ 12.2  Å⁻¹ and R-space range 1.75 ÷ 5.5 Å⁻¹. Thus, at least four coordination shells around Fe were covered as well as trifold multiple scattering paths. The free parameters of the fit were unit cell parameters, indices of Bi and Se2 sites as well as Debye–Waller factors. None of the fits performed assuming only one doping site was satisfactory (figures 8(b)–(e)). Therefore further analysis was performed by fitting two-site occupation of Fe atoms testing all possible combinations. Such a procedure resulted in a very good match of the model and the experiment for only one combination of Fe sites (figure 8(f)): distribution of Fe atoms between Bi substitutional sites (approx. 20%) and O_h interstitial sites in the van der Waals gap (approx. 80%). Unit cell parameters drawn from this fit are shown in table S1 of the supplemental materials.

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Similar conclusions on two-site occupancy were drawn in [50], where the same crystal as we used, grown in the same laboratory, was measured by scanning tunneling spectroscopy (STS). Two different shapes of Fe-related structural defects were reported, with 10% and 90% abundance of Fe positions. STS of the latter resembles the shape of Fe adatoms deposited on Bi₂Se₃ surface [9]. Thus it is attributed to interstitial position within VdW gap. Moreover, the discussion in [50] suggests that the valence state of Fe may depend on the actual site the atom occupies. Fe position in volume doped Bi₂Se₃ was also investigated in [51]: STM/STS and atomic force microscopy (AFM) experiments on Fe-doped Bi₂Se₃ single crystal reveal features resulting from two Fe dopant positions, interstitial and Bi-substitutional ones, as in our studies.

Summarizing, our analysis shows that Fe atoms in Bi₂Se₃:Fe act both as substitutional dopants replacing Bi, like usually described in the literature, but also, to the larger extent locate in octahedral interstitial positions in the van der Waals gap, the former suggesting strong bonds with Se atoms. This result can rationalize our XAS spectrum, probed at three angles, in particular the evolution of the higher energy peak, 711.2 eV, (figures 4(b) and (c)) which is, as the discussion below shows, ascribed to Fe³⁺ ionic state of certain fraction of dopants imbedded in the bulk.

At first, this higher energy peak of XAS and resulting XMCD was fitted with Brillouin-like functions (see the inset in figure 9(a)) following the procedure described in [52] and assuming temperature of the sample of 10 K. It showed that magnetic anisotropy is negligible for the site responsible for the peak, while the magnetic moment is approx. 2.5(±0.5)  μ_B i.e. the value typical for bulk Fe. Then, using the values obtained from the first fit (i.e. keeping magnetic moment and anisotropy energy of one site fixed) another fit with two sites contributing to the entire width of 2p_3/2 multiplet (from 705 to 720 eV) was performed using the same approach (figure 9(a)). It showed an out-of-plane anisotropy of the other magnetic site, which contributes mainly to the lower energy peak of XAS.

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The out-of-plane and magnetically isotropic sites contribute to the net paramagnetic moment of near surface Fe dopants as 70 (±20)% and 30 (±20)%, respectively. The anisotropy energy and the moment of the out-of-plane site is 4 (±3) meV and 4.5 (±0.8) μ_B, respectively. Assuming that the two sites revealed by EXAFS and XMCD magnetization fits correspond to each other, the most likely attribution is that Fe atoms in the Bi substitutional sites are responsible for the 711.2 eV peak and have paramagnetic moment close to that of a bulk Fe of negligible anisotropy. Then Fe atoms in O_h interstitial in the van der Waals gap (responsible for the ca 709 eV peak) in the surface region (few QLs) possess magnetic moment of 4.5 μ_B, characteristic of single-like atom with an out-of-plane anisotropy. As shown below (and also in [9]), the anisotropy in this case is opposite to that observed for Fe adatoms, but similar to that of Co adatoms on Bi₂Se₃ [53].

The out-of-plane anisotropy and a relatively large magnetic moment of Fe dopants settled in the van der Waals gap (i.e. also on the sample's surface) should break the time reversal symmetry and thus influence the topology. This is not the case as we observe by electronic transport and ensuing Berry phase of π (figure 7), which means that the magnetism of Bi₂Se₃:Fe is weak. Such a weak magnetism is revealed by our bulk studies with SQUID magnetometer (figure 3) where only a paramagnetic signal (with the effective moment of p_eff = 2.1 μ_B drawn from temperature dependence of susceptibility), strongly diminishing with temperature and with weak AF interactions was found in a – b plane, while diamagnetic signal was measured along c direction. Qualitatively similar anisotropy in Bi_1.84Fe_0.16Se₃ was observed in [35].

The Bi₂Se₃ host is reported [54] to be an isotropic diamagnet with temperature-independent susceptibility χ = −3.0 × 10⁻⁷ emu g⁻¹. The susceptibilities measured for our sample at 300 K were −1.47 × 10⁻⁷ emu g⁻¹ and −2.89 × 10⁻⁷ emu g⁻¹ in a – b plane and along c axis, respectively. Assuming Fe concentration of 0.017, the estimated paramagnetic susceptibility is 0.44 × 10⁻⁷ emu g⁻¹, the value lower than diamagnetic susceptibility of the host. Curie–Weiss law fits well to the experimental data (see figure 3) in temperature range below 150 K (where paramagnetic signal dominates) therefore we expect that at 300 K the influence of the crystal field on Fe is small and magnetocrystalline anisotropy is negligible.

We subtracted the estimated paramagnetic susceptibility (0.44 × 10⁻⁷ emu g⁻¹) value from experimental susceptibilities thus estimating the anisotropic diamagnetic susceptibility of Bi₂Se₃ as −1.9 × 10⁻⁷ emu g⁻¹ and −3.3 × 10⁻⁷ emu g⁻¹ in a – b plane and in c direction, respectively, comparable to the diamagnetic susceptibility of the sample holder (subtracted). Even if some paramagnetic anisotropy of Fe atoms exists, this shows that Bi₂Se₃ is probably an anisotropic diamagnet, similar to Bi₂Te₃ [34, 54].

The situation at low temperature, 2 K, is different. If a diamagnetic signal of −0.004 μ_B for Bi₂Se₃ formula at 5 T and at 2 K is assumed (as estimated from the moment for Bi₂Te₃ in [54] and their diamagnetic susceptibilities for Bi₂Se₃ and Bi₂Te₃) then our mean Fe saturation moment of 1.3 μ_B/Fe atom (estimated from the effective moment using g = 2) gives the saturation moment of Bi₂Se₃:Fe equal to 0.15 emu g⁻¹. This value is much higher than the observed 0.024 emu g⁻¹ (figure 3(a)). This suggests that Fe magnetic moments may order antiferromagnetically at 10 K, where the clear anomaly in χ(T) is observed (figure 3(b)), or part of Fe atoms switch to a low spin state.

Such AF order may also roughly rationalize the Fe anisotropy visible at 2 K. Since the majority of Fe atoms reside in QL gap as our EXAFS results show, the anisotropic surrounding can force AF-coupled Fe moments pointing along c direction. The collection of such coupled pairs would present a higher magnetic in-plane than out-of-plane signal. At temperature higher than 10 K the moments decouple, but the small out-of-plane anisotropy may still exist at sufficiently low temperatures, what is qualitatively in accord with our XMCD results (where an out-of-plane anisotropy was found). It should be noted, however, that Fe atoms probed by this surface sensitive technique are different, because of proximity of the surface symmetry and a possible influence of 'topological^' electrons (what is visible, e.g. by their large moment of 4.5 μ_B/Fe atom).

Several studies of Fe-doped Bi₂Se₃ have already been performed and the variety of results show that magnetic state of Bi₂Se₃:Fe is not well understood. For example, antiferromagnetic interactions observed in Curie–Weiss dependence were theoretically predicted [55] along with effective moment per Fe atom of 5 μ_B, which is substantially higher than the p_eff value observed in our experiment. Also Kulatov in their [56] DFT studies found antiferromagnetic order in Fe-doped Bi₂Se₃. In their calculations, Zhang et al showed [55] that Fe ions should locate in cation site substitutional positions, as assumed while growing single crystals. In line with this, another group [57] found a homogeneous magnetism that cannot be attributed to magnetic impurities. In their experimental studies of Bi_2−xFe_xSe₃ (for x = 0.1–0.3), a coexistence of two complicated magnetic structures were found, one below 10 K (i.e. where the anomaly in our results is seen—figure 3(b)) and the other up to 250 K. Magnetic ordering at 40 K was also reported in Bi₂Se₃ nanowire doped with two times more Fe than in our case (x = 0.05) homogeneously distributed in a whole sample [12]. Also in single crystalline Bi_1.96Fe_0.04Se₃ a higher and almost saturated moment (0.01 μ_B/f.u. in 5 T when normalized to our concentration of Fe) was found [54]. Finally, the antiferromagnetic correlations were theoretically predicted by the interaction of native Se vacancies with Fe dopants that turn to ferromagnetic ones when the number of Se-vacancies around Fe increases [58]. This result suggests that although the crystal is structurally homogenous, its magnetic response is site dependent and can easily be changed. In general, magnetic state in Fe-doped Bi₂Se₃ is not unambiguously defined and may be unstable due to concentration fluctuations of Fe.

However not only a homogenous magnetic structure of Bi_2−xFe_xSe₃, but also magnetic impurities were considered to explain its magnetic properties. For example, Huiwen [49] suggested that the weak magnetic signals in Bi₂Se₃ doped with Fe are extrinsic rather than caused by either Fe replacing Bi or intercalation. Instead, the possibility of inclusions of nanocrystals of Fe_ySe_z to the parent phase was demonstrated for x = 0.075 and higher Fe concentrations. They may be ferrimagnetically and/or antiferromagnetically ordered, with varying magnetic moment depending on the exact Fe to Se ratio. The creation of some additional phase was confirmed by the direct observation of two phases Bi₂Se₃ and Fe₇Se₈ in the nominally Bi_2−xFe_xSe₃ compound with no indication of Fe incorporation into Bi₂Se₃ lattice [49]. Similar conclusions on Fe_ySe_z nanoclusters-based extrinsic magnetism in Bi_1.84−xFe_0.16Ca_xSe₃ were reported in [35].

In our experiments no assumption of spurious phases needed to fit EXAFS spectra and the reasonable attribution of two Fe sites to magnetic moments was proposed. Thus, we conclude that our observations point to the intrinsic properties of Bi₂Se₃:Fe. However further effort is needed to better characterize magnetism in low Fe-doped Bi₂Se₃ and explain possible antiferromagnetic ordering realized in such magnetically diluted system. Despite the origin of magnetism of Bi₂Se₃:Fe, our and most of other results on low Fe-doped Bi₂Se₃ suggest that Fe ions do not affect topological properties of this compound, as do Mn dopants [59].

Location and magnetic properties of bulk and near surface Fe dopants in Bi_2−xFe_xSe₃ are summarized in table 2.

Table 2. Comparison of the probed/assumed Fe location, saturation magnetic moment and anisotropy of Fe in Bi_2−xFe_xSe₃.

x	Fe locationa	Saturation magnetic moment [μB/Fe]	${E}_{\mathrm{a}}$b[meV]	Source
N/A	Intc	0	—	[47]
0.04	Int	0.5	—	[54]
0.333	Bith	4.5–5.00	—	[60]
0.002	Bisurf/intsurf	—	—	[61]
0.2–0.3	Bi	0.34 ± 0.07	<0	[57]
0.083	Bith	4.73–4.99	>0	[55, 62]
0.083	Bith	3.07–3.42	—	[58]
0.083	Bith	3.702 (μs)	—	[56]
		0.0596 (μl)
0.05	Binw	—	—	[12]
0.083	Bith,surf	3.482 (μs)	+6	[63, 64]
		0.144 (μl)
0.02	Bisurf	2.5 ± 0.5	∼0	This work
	intsurf	4.5 ± 0.8	−4 ± 3
	Bi/int	1.3	>0

^aBi–Bi substitution; int–interstitial/intercalated. ^bE_a > 0 indicates easy magnetization within a-b-plane, while E_a < 0 indicates easy magnetization direction parallel to c-axis. ^cLow spin Fe^{2+ th}theory. ^surfnear surface. ^nwnanowires.

The influence of Fe adatoms on Bi₂Se₃ surface have been reported by others e.g. [7–9, 33]. Thus, we have collected only a specific set of experimental data using XMCD and NIS. The former were probed for the sake of comparison to that of bulk dopants. The latter, to our best knowledge made for the first time, are expected to provide an answer to the question on whether magnetic adatoms reveal vibrational states of the host crystal (strong bond) or vibrate independently (weak bond).

Magnetic state of the surface Fe adatoms were drawn from XAS spectra characterized by one strong absorption peak shown in figures 4(c) and (d). We have fitted the resulting XMCD signal to the Brillouin-like function, see figure 9(b). Similar to Bi₂Se₃:Fe, two components were considered, in line with STM observations of two sites of adatoms [65]. Paramagnetic Fe moment of 3.5 (±1.0) μ_B is similar for Fe atoms occupying both sites: exhibiting in-plane easy magnetization direction (85%, E_a = 3 (±1) meV) and a weak out-of-plane anisotropy (15%, E_a = 0.5 (±0.5) meV). We attribute the first group to the surface Fe adatoms with their 3d states interacting with, possibly, host surface electronic states characterized by linear dispersion relation. This is in rough agreement with more 2D Fe environment of the surface atoms resulting in an enhanced magnetic moment [66]. We also suggest that the second group of Fe atoms exhibiting weaker out-of-plane anisotropy are those that migrated from the surface and behaving like single Fe atoms for which the enhanced magnetic moment is expected as well. It is quite reasonable to assume that Fe atoms migrated into either quintuple layer, or even replaced Bi atoms, as it was with Bi₂Se₃:Fe. This means that the electronic state of the second group is representative for Fe in QL, but also, to a lesser extent, for Fe in Bi sites.

The notion of Fe atoms migrating from the surface to the first van der Waals gap is in accord with our XMCD observation for Bi₂Se₃:Fe. These Fe atoms, strongly influenced by the surface, have a weak out-of-plane anisotropy and relatively high moment, both similar to the ones that constitute 70% of the atoms seen by XMCD in Bi₂Se₃:Fe. Similar conclusions were drawn in [33], where XAFS measured on 0.3 ML Fe deposited on single crystalline Bi₂Se₃ at temperature close to our experiment revealed that many of Fe atoms migrated into the substrate substituting Bi atoms. Location and magnetic properties of Fe atoms deposited on Bi₂Se₃ are summarized in table 3.

Summarizing, surface sensitive XMCD showed anisotropic paramagnetic response for Fe on top of Bi₂Se₃, or between QL, but more isotropic one for Fe migrating into volume of Bi₂Se₃. Thus, the results of our observation suggest that Fe adatoms on or close to the surface behave as in nearly 2D symmetry or as individual entities (large magnetic moment due to low dimensionality of Fe, not mutually interacting, but linked to the environment (anisotropy).

In order to further check the Fe–Fe and Fe–host link, we have tested vibrational states of Fe adatoms using NIS. This is not only important as a mean to check the cohesive energy of Fe adatoms, especially in view of the idea to control quantum transport in TI via magnetic doping, but can, in principle, provide the information of the underlying topological nature of surface electronic states. Indeed, the surface electronic states of TI, due to their special properties, their spin confinement to momentum and the lack of backscattering, might react with the Fe adatoms in different way than do 'normal' electron states as those on top of non TI material, in particular insulating one. As reported, [6, 17, 67], these different interactions can e.g. give rise to the topologically enhanced magnetism, but may also affect the Feynman–Hellman forces that define vibration spectrum of adatoms, resulting in strong electron–phonon interactions [18]. These forces are both of ionic and itinerant-electron origin and the fact that the number of itinerant electrons are different in TI and non-TI matter, despite a small number of those in TI, may lead to different elastic properties. Also, the electron–electron interactions affect vibration spectrum [68] and those interactions, again taking into account spin-momentum confinement, may be different.

The phonon DOS curves of 0.5 ML Fe on Bi₂Se₃ and on non-TI material, Bi₂S₃, drawn from the NIS data in figure 6, are presented in figure 10. It is clear, bearing in mind poor statistics, especially in Bi₂S₃, that DOS calculated from the experimental data are practically the same for both samples. Apparently, either Fe adatoms, in amount used here, do not differentiate between the surface they sit on, or the differences caused by these surfaces are too subtle to be discerned. Consequently, only DOS calculated for Bi₂Se₃, as a representative for 0.5 ML Fe on QL, will be further discussed.

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We have compared our experimental DOS for Fe/Bi₂Se₃ (i.e. also for Fe/Bi₂S₃) with the phononic density of states of those systems that can be relevant to our case. First, we have compared our results with the vibrations of the surface iron layer of 20 ML thick Fe single crystalline film [73]. We have found that both NIS curves coincide well in the higher energy part of spectra provided some small shift to lower energies of this Fe surface DOS is done (figure S4 of supplemental material). In both cases: the '2.5D' symmetry of Fe atoms on the surface of Fe thin film, and 2D symmetry of Fe atoms forming monolayer patches on Bi₂Se₃, are lower with respect to the 3D symmetry of Fe atoms in the bulk. Therefore the similarity in vibration spectra in both cases could be expected. However this is very improbable that nominally 0.5 ML Fe deposited in our experiment really created monolayer Fe patches, in particular on two different surfaces (Bi₂Se₃ and Bi₂S₃, with different surface structure) and most likely (although this needs to be experimentally verified) Fe does not grow layer-by-layer, i.e. not only monolayer but also double- and three-layer Fe patches could be formed. Although our XAS/XMCD data from figure 4(b) does not indicate cluster formation, the higher amount of Fe deposited (0.5 ML instead of 0.1 ML grown for XMCD experiment) and the higher sample temperature at which Fe atoms were deposited and NIS measurements were performed, may promote 3D growth.

Therefore, we have also compared our results with phononic DOS of a few MLs of ⁵⁷Fe grown on W (110) substrate [69]. Such a structure is more relevant to our experimental conditions and, additionally, modeled substrate-layer mismatch present in both systems that can also, apart from symmetry, affect 0.5 ML Fe/Bi₂Se₃ vibrations. As shown in figure 11, the vibrations of 3 ML Fe/W nicely reproduce our results at higher energies. Note also that 3 ML Fe/W DOS contains a small portion of 1 and 2 ML Fe vibrations spectra (as seen from a characteristic shoulder, a reminiscence of the peaks at 13–14 meV in 1 and 2 ML Fe/W DOS, see figure 11). Such 1 or 2 ML Fe patches are very probable also in our case, which makes DOS of 3ML Fe/W from [69] even more realistic in simulating the vibrations of our Fe structure formed on Bi₂Se₃.

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We have thus an experimental confirmation of our hunch that majority of adatoms deposited on the surface of Bi₂Se₃ (and Bi₂S₃) form ca 3 ML high clusters. This explains a main part of DOS in the range 15–35 meV.

Apart from higher energy dynamics, our experiment revealed the existence of low energy vibrations, with the shape estimated by subtraction of our experimental DOS obtained for 0.5 ML Fe/Bi₂Se₃ and 3 ML Fe/W DOS from [69]. The product of subtraction shows a characteristic dome-like peak at ca 10 meV, presented in figure 12 (blue bold triangles). This dome-like low energy vibration spectrum may come either from isolated Fe adatoms on top of QL, or Fe atoms that migrated into the structure of QL. It may characterize individual Fe atom dynamics or, in case these atoms are strongly bound with the surroundings, mainly the vibration spectrum of the host crystal.

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The problem of adatoms migration was addressed in [74] and, according to these studies, the temperature of our experiment is sufficiently low to assure that Fe remains on top of the surface. However, our results from XMCD suggested that Fe adatoms might migrate into the body of QL layer, the effect possibly enhanced by the higher temperature of NIS experiment. Similar conclusion may be drawn from [33] where it was observed at 160 K that Fe atoms went into the first QL substituting bismuth atoms. Apparently, some movement of Fe atoms to the bulk and their ensuing vibrations cannot be excluded.

We may also expect that some isolated atoms may reside on QL surface and contribute to the observed Fe vibrations. There are conflicting reports on how the Fe adatoms behave on the TI surfaces, i.e. to what extent they behave as individual atoms, with their electronic states possibly modified by host surface states, or they form well defined surface patches which interact weakly with the substrate. Although it was well established that there are two Fe surface positions, either of comparable surface energies [9] or considerably differing energetically (75.8 meV) [67], 'infrequent hopping events of a single Fe atom' [9] between these two positions were observed, even at 0.3 K. Hopping at such a low T would suggest a very limited Fe–host interactions i.e. Fe acted as free atoms, with only their outer s electrons transferred into host surface, imposing some force on Fe atoms that can be observed by Fe atom vibrations. Also in [8], where Fe atoms were deposited at RT, 3d spectra of individual Fe atoms are atomic like, what is also seen from relatively large orbital momentum, a few times larger than in bcc iron (although the spectra widen with increasing Fe coverage, possibly indicating increasing Fe-atom substrate coupling). In such case, our low-energy part of DOS would describe rather weakly linked Fe atoms, the feature possibly irrelevant to the host properties.

On the other hand, the same authors [9] report a strong Fe-d orbitals hybridization with electronic states from the surrounding crystal and influenced by its crystal fields, which leads to an in-plane magnetic easy axis. At higher Fe coverages (>0.1 ML), atomic multiplet features disappear due to the formation of Fe clusters of variable size [9]. In this scenario, Fe adatoms behave as electron donors [74] rather strongly interacting with the host material. Iron atoms strongly bound to the Bi₂Se₃ surface was found also in [75] studies. In such case Fe vibrations might reflect QL vibrations.

Since neither vibration of individual Fe atoms on Bi₂Se₃ nor on Bi₂S₃ were reported in literature, we have compared our spectra only with vibration DOS of Sb₂Te₃ (experiment: NIS [72]), surface layer of Bi₂Te₃ (calculated [70]) and bulk Bi₂Se₃ (calculated [71]), see figure 12. The additional comparison with bulk Bi₂Se₃ [76] and Bi₂S₃ [77] (both measured by Raman spectroscopy) are presented in figure 3S of the supplementary information. In all the results the characteristic peak structure, 5–8 meV, 12–13 meV and 15–18 meV is present and this structure is roughly reproduced in our results for ⁵⁷Fe/Bi₂Se₃. Therefore and also taking into account a good agreement of our DOS at higher energies with 3 ML Fe/W vibrations, we conclude that our 0.5 ML ⁵⁷Fe layer reproduces vibrations of both the host material, possibly its first QL, and ca 3 ML thick clusters of iron.