pubs.acs.org/NanoLett Letter Experimental Demonstration of a Magnetically Induced Warping Transition in a Topological Insulator Mediated by Rare-Earth Surface Dopants Beatriz Muñiz Cano, Yago Ferreiros, Pierre A. Pantaleón, Ji Dai, Massimo Tallarida, Adriana I. Figueroa, Vera Marinova, Kevin García-Díez, Aitor Mugarza, Sergio O. Valenzuela, Rodolfo Miranda, Julio Camarero, Francisco Guinea, Jose Angel Silva-Guillén, and Miguel A. Valbuena* Cite This: Nano Lett. 2023, 23, 6249−6258 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information ABSTRACT: Magnetic topological insulators constitute a novel class of materials whose topological surface states (TSSs) coexist with long-range ferromagnetic order, eventually breaking time-reversal symmetry. The subsequent bandgap opening is predicted to co-occur with a distortion of the TSS warped shape from hexagonal to trigonal. We demonstrate such a transition by means of angle- resolved photoemission spectroscopy on the magnetically rare-earth (Er and Dy) surface-doped topological insulator Bi2Se2Te. Signatures of the gap opening are also observed. Moreover, increasing the dopant coverage results in a tunable p-type doping of the TSS, thereby allowing for a gradual tuning of the Fermi level toward the magnetically induced bandgap. A theoretical model where a magnetic Zeeman out-of-plane term is introduced in the Hamiltonian governing the TSS rationalizes these experimental results. Our findings offer new strategies to control magnetic interactions with TSSs and open up viable routes for the realization of the quantum anomalous Hall effect. KEYWORDS: magnetic topological insulators, rare-earth doping, topological surface state, time-reversal symmetry breaking, angle-resolved photoemission spectroscopy, quantum anomalous Hall effect T opological insulators (TIs) define a state of matter where the strong spin−orbit interaction (SOI) induces an exotic metallic topological surface state (TSS) with relativistic, Dirac- doping,6−9 magnetic extension,10 or proximity coupling to magnetic layers,11,12 the TI becomes magnetic (MTI), and the time-reversal symmetry (TRS) can be broken, magnetically like, band dispersion with the spin locked to the momentum in inducing the opening of a bandgap at the Dirac point (DP) of an otherwise insulating material.1,2 Magnetic impurities the TSS.6,7 If this gap is tuned to the Fermi level (EF), the interaction with the TSSs is especially attractive in these QAHE can be realized as it was first experimentally observed in materials due to the emergence of novel quantum phenomena Cr- and V-doped (Bi,Sb)2Te3 thin films.13,14 Recent discov- with relevant fundamental and technological implications in eries based on the magnetic extension of TIs, as the first spintronics and quantum information processing.3 The combination of topological properties and magnetic order can lead to new quantum states of matter as the quantum Received: February 15, 2023 anomalous Hall effect (QAHE), characterized by purely spin- Revised: April 24, 2023 polarized dissipationless currents without an external magnetic Published: May 8, 2023 field.4,5 When magnetism is introduced by impurity doping with magnetic elements, either via substitutional or surface © 2023 The Authors. Published by American Chemical Society https://doi.org/10.1021/acs.nanolett.3c00587 6249 Nano Lett. 2023, 23, 6249−6258 Nano Letters pubs.acs.org/NanoLett Letter Figure 1. Pristine Bi2Se2Te crystal structure and characterization. (a) 3D quintuple layer crystal structure and (b) Brillouin zone (BZ) and projected surface BZ of Bi2Se2Te. (c) XPS spectrum (Se 3d, Te 4d, Bi 5d, and valence band) of the pristine Bi2Se2Te single crystal measured at a photon energy of hν = 100 eV and at T = 15 K. (d) ARPES bandmap of the pristine Bi2Se2Te TSS along the K direction acquired at hν = 52 eV and at T = 15 K. antiferromagnetic (AFM) TI, MnBi2Te4,15,16 have opened up anisotropy by X-ray magnetic circular dichroism (XMCD) at new perspectives for the realization of these quantized very low temperatures on close metal-packed surfaces.32 topological effects in intrinsically magnetic stoichiometric Similarly, Er or Dy single atoms can exhibit out-of-plane compounds. However, these systems heavily depend on magnetic anisotropy.33 Even more, Dy single atoms may sophisticated and complex growth methods, resulting in experience magnetization relaxation time scales as large as variations in the density of structural defects, eventually 1000 s on several nonmetallic substrates.34,35 Besides, REs leading to drastic changes in the electronic structure of the deposited on metals can be efficiently coupled via itinerant s TSSs (opening or not of an intrinsic magnetic gap at the DP) and p electrons of the metal to achieve ferromagnetism with or affecting its magnetic properties (formation or not of Curie temperatures as high as 80 K.36,37 RE bulk substitutional antiferromagnetic order).17 Similar discrepancies have been doping with Eu,38,39 Gd,40 Dy,31 or Ho41,42 on Bi2Te3 thin found because of inhomogeneities of the spatial distribution of films has been achieved. Even though the TSSs are preserved bulk magnetic dopants.18,19 despite RE large magnetic moments, all films remained Surface doping offers an alternative to separate the two essentially paramagnetic or weak AFM. Regarding the bandgap aforementioned critical processes, namely, growth and doping, opening, massive Dirac fermions have only been observed for a limiting the dopant’s presence to where the TSSs are most given concentration of Dy-doped Bi2Te3 thin films,41 sensitive to their effects and maximizing the magnetic attributed to inhomogeneous and short-range ferromagnetic anisotropy by the lower coordination symmetry.20 Exper- patches.3,43 Magnetic proximity effects have also been explored imental attempts at magnetically doped TI surfaces also on EuS layers on TI thin films with neither significant induced indicate that achieving control on the magnetic ground state magnetism nor an enhancement of the Eu magnetic moment at and anisotropy is challenging due to the existence of multiple the interface.44 adsorption sites, strong surface relaxations, and significant Recently, the magnetic order in MTIs, particularly in the doping of the bulk states from defects or inhomogeneities.21−24 newly discovered MnBi2Te4 family,45 has been theoretically Although gaplike features have been interpreted as magneti- predicted not only to open a gap at the DP but also to lower cally induced, numerous factors such as momentum and the Dirac cone’s warping symmetry from hexagonal to trigonal, energy spatial fluctuations near the DP25 or surface chemical alongside an induction of a gap opening at the DP.46−49 modifications26−28 may contribute to the observation of a gap. Notably, this trigonal warping at the magnetically ordered Furthermore, the DP can be buried into the bulk band phase is sensitive to the direction of a net surface magnetic projections, making the possible gap opening undetectable by moment, providing an effective approach for the detection of techniques such as angle-resolved photoemission spectroscopy magnetic ordering effects on the TSSs when the gap cannot be (ARPES). These ambiguities show the necessity to go beyond unequivocally resolved and/or related to the TRS breaking by the present state-of-the-art in the development of these doping out-of-plane magnetic moments. However, an experimental strategies. observation of these phenomena is still lacking. An alternative route to this problem is to surface dope TIs Herein, by means of ARPES, we report the effects on the with magnetic rare-earths (REs) whose larger size can prevent TSS of the prototypical three-dimensional (3D) TI, Bi2Se2Te, the occurrence of substitutional sites at the surface, reducing doped with RE impurities (Er and Dy). As expected, the the multiplicity of adsorption configurations29 and enhancing pristine surface features hexagonal warped TSSs which, as the the magnetic anisotropy. Likewise, RE large magnetic mo- RE atoms are deposited even for small coverages, exhibit the ments, originating from the unpaired 4f electrons,30 can predicted transition from hexagonal to trigonal, providing the maximize the magnetically induced gap hosting the spin- first experimental evidence of such magnetically induced polarized currents7 and also allow a lower doping concen- warping modification. In addition, with the systematic doping, tration,31 which could eventually lead to a robust QAHE at signatures of a bandgap opening at the DP are found, whereas higher temperatures.3 In particular, Er clusters have been the chemical potential is gradually modified, resulting in a shown to exhibit hysteresis and out-of-plane magnetic controllable p-type doping. This allows us to tune the DP 6250 https://doi.org/10.1021/acs.nanolett.3c00587 Nano Lett. 2023, 23, 6249−6258 Nano Letters pubs.acs.org/NanoLett Letter Figure 2. XPS characterization of Er-doped Bi2Se2Te acquired with a photon energy of hν = 100 eV and at T = 15 K. (a) Comparison of the XPS spectra of pristine (red line) and 0.3 monolayer (ML) Er/Bi2Se2Te (blue line). A second component of the Bi 5d peak is developed after Er deposition (green arrows). Right: zoom-in on the Er 4f states and the Bi2Se2Te valence band energy range. Multipeak fit of XPS data for (b) the pristine sample and (c) the 0.3 ML Er-doped sample. A second component (orange) is related to the Er−Bi interaction, as its area is proportional to the Er coverage (see SM, Figures S1 and S3). energy closer to the EF, thus fulfilling the prerequisites for the the expected Curie temperature of Er and Dy clusters,53 so a realization of the QAHE. When the Hamiltonian governing the magnetic ordering of the RE surface dopants can be expected. TSS considers a net magnetic moment, with an exchange field The Bi2Se2Te quintuple layer (QL) three-dimensional (3D) coupling of ≈0.1 eV, the experimental observations are crystal structure and the Brillouin zone (BZ) and its projected rationalized. surface Brillouin zone (SBZ) are sketched in Figure 1(a),(b), Ternary Bi2Se2Te single crystals50 were grown by a modified respectively. As previously commented, Bi2Se2Te bulk single Bridgman method in a standard crystal growth system and crystals were mechanically exfoliated in situ at 15 K to characterized by X-ray powder diffraction and Raman spec- minimize the induced density of defects. The high sample troscopy (see Supporting Information (SM), section I), quality is derived, apart from the aforementioned LEED showing high crystal quality and crystalline long-range order. patterns in SM, from the XPS spectrum (Figure 1(c)), showing The crystals were exfoliated in situ at T = 15 K (base highly intense and narrow peaks with no signs of oxidation, temperature), and the surface quality and crystal structure were contamination, or large disorder28 for the Se 3d, Te 4d, and Bi further verified by low energy electron diffraction (LEED) at 5d core levels. The very well-defined spin−orbit doublets as base temperature before and after RE deposition. The obtained compared to isostructural TI films grown by molecular beam LEED patterns do not show any evidence of surface epitaxy prove the surface quality after in situ exfoliation.54−56 reconstructions originating from the RE dopants (see SM, Figure S14 in section VIII). X-ray photoemission spectroscopy The pristine Bi2Se2Te TSS ARPES bandmap along the K (XPS) and ARPES measurements were performed on the in direction is shown in Figure 1(d). The DP is located 440 meV situ exfoliated single crystals with a MBS hemispherical below the EF, outside the bulk projection bandgap, and the analyzer at the LOREA beamline51,52 in ALBA Synchrotron, Fermi velocity is vF ∼ (7.1 ± 0.2) × 105 m/s, estimated from with linear horizontal polarization and photon energies of hν = 1/ℏ(∂E/∂k),57 consistent with previous works.57,58 100 and 52 eV, respectively. Er and Dy were sublimated with Figure 2(a) displays XPS spectra, showing the main effects an e-beam evaporator. The deposition rates and coverages on the core levels and the valence band (VB) states induced by were calibrated with a quartz crystal microbalance and Er deposition, as compared to the pristine sample. The Se 3d, correlated with the attenuation of the XPS Bi 5d core level Te 4d, and Bi 5d core levels are attenuated (SM, Figure S3 in (see Figure S1 in SM, section II). XPS and ARPES section III). No extra components are detected at higher measurements were also performed at T = 15 K, well below binding energies (left side of the peaks), consistent with the 6251 https://doi.org/10.1021/acs.nanolett.3c00587 Nano Lett. 2023, 23, 6249−6258 Nano Letters pubs.acs.org/NanoLett Letter Figure 3. Experimental observation by ARPES of the magnetically induced hexagonal to trigonal TSS warping transition upon Er deposition. (a)− (c) Fermi surfaces and constant energy maps at 100 and 200 meV below the Fermi level (EF) for pristine Bi2Se2Te, showing the hexagonal warping of the topological surface state (TSS). (d)−(f) Same as in (a)−(c) for 0.3 monolayer (ML) Er/Bi2Se2Te, showing the induced trigonal warping of the TSS. TSS bandmaps along the K direction (red and blue dashed lines in (a) and (d)) for (g) pristine and (h) 0.3 ML Er/Bi2Se2Te, acquired with a photon energy hν = 52 eV and at T = 15 K. Momentum distribution curves (MDCs) extracted at the EF are shown on the top of each bandmap. The induction of a trigonal warping in the TSS is also evidenced by the Fermi wavevector kF and Fermi velocity vF asymmetry around the point for the Er-doped system in (h). absence of surface oxidation or contamination. Additionally, no atoms at the van der Waals gap between QLs.59 As a result, a further disorder is introduced since no widening of the peak significant macroscopic concentration of Bi atoms about 1−5% line shapes is detected, also evidenced by the very sharp, well ML17,59 cannot be excluded at the outermost surface. Besides, resolved multipeak structure of highly localized and, in it has also been shown that when REs (i.e., Dy) are introduced principle, weakly interacting (nondispersive) Er 4f states at E as substitutional dopants on Bi2Te3 thin films they tend to − EF = 5−12 eV (magnified in the inset in Figure 2(a)). The occupy Bi substitutional sites on Bi layers,60 highlighting that multipeak fit of the XPS spectra in Figures 2(b),(c) was used RE dopants are prone to ionic or covalent bonding with Bi. for the estimation of the Er coverage. ARPES VB maps This effect is also reflected in an energy shift as the Er content acquired at this energy region are included in the SM, Figure increases (see SM, Figure S1 in section II). A similar behavior S2 in section III. has been observed for other metal−TI interfaces in the same Bi Remarkably, a second Bi 5d component is developed at 5d state.55 The same Bi 5d second component also appears in lower binding energies (green arrows in Figure 2(a) and Dy-doped Bi2Se2Te (SM, Figure S5 in section IV). orange curve in Figure 2(c)). These feature intensity that The Fermi surface (FS) and constant energy (CE) maps for linearly increases with the Er coverage (SM, Figures S1 and pristine and 0.3 monolayer (ML) Er/Bi2Se2Te are shown in S3), demonstrating its relationship with a superficial Bi−Er Figure 3. Pristine Bi2Se2Te TSS exhibits the hexagonal warped bond and revealing a degree of interaction at the RE−TI FS and the circular-like shaped lower energy CE maps interface. Based on a simple electronegativity analysis, we expected for rhombohedral 3D TIs (Figures 3(a)−(c)). The attribute the change in the line shape of Bi 5d to the charge warping strength is consistent with the literature, being similar transfer produced by the deposition of Er. The partial charge to most warped TSSs, as in Bi2Te3,61,62 and higher than in given by Er is then shared with the more oxidized species isostructural Bi2Te2Se63 or Bi2Se3,64 whose warping effects are (Bi3+), although the substrate is Se-terminated. However, smoother or even negligible. When depositing Er, the FS and intrinsic native point defects naturally occur in binary or CE maps drastically change. Upon the 0.3 Er ML, the TSS ternary tetradymite TIs as vacancies, antisites, or interstitial warping symmetry evolves from hexagonal to trigonal (Figures 6252 https://doi.org/10.1021/acs.nanolett.3c00587 Nano Lett. 2023, 23, 6249−6258 Nano Letters pubs.acs.org/NanoLett Letter Figure 4. Theoretical modeling of the TSS band structure and the warping transition. Band structure of the surface state of a topological insulator and the evolution of the constant energy (CE) maps (red lines) as a function of the Fermi energy for the (a) pristine system, with vF = 7.1 × 105 m/ s and λ = 250 eV·Å3, and (b) the system with magnetic impurities, with Δ = 0.12 eV. The transition from a hexagonal to a trigonal warping, as well as the induction of a gap, is observed. The small panels display CE maps at three different energies relative to the Dirac point, corresponding to the energies of the experimental ones. 3(d)−(f)), clearly away from the DP and closer to EF. Similar carrying the fitting parameter Δ. The Δ value is then changed modifications in the Dirac cone warping, from hexagonal to until the theoretical CE maps match the experimental ones trigonal, have been predicted below the magnetic ordering (Figures 3(d)−(f)), finally obtaining an optimized corre- temperature in the family of MnBi2nTe3n+1 MTIs.47 spondence with Δ = 0.12 eV (see SM, Figure S7 in section V, To give some insight into the warping transition of the TSS, for more details). The theoretical results are shown in Figure 4. the description of an undoped TI using the model developed Note that the EF (with respect to the DP) is modified by the by Fu61 can be applied, in which the low energy dispersion of introduction of the RE dopants (Figures 3(g),(h)), so the the system is described by the following Hamiltonian values of the energies for the theoretical CE maps have been accordingly changed. Also and as a direct consequence of the H = vF(k x y k y x) + (k+3 + k 3) z warping transition, asymmetric kF values are found as a 2 (1) consequence of the different theoretically obtained vF of 9.8 × with k± = kx ± iky. The last term is only invariant under 3-fold 105 m/s and 8.2 × 105 m/s, respectively, for the flat and corner rotation and responsible for the hexagonal warping.46,47,61 The sides of the trigonal TSS (see SM, Figure S8 in section VI, for 3D band dispersion of the system is shown in Figure 4(a), more details). where the previously calculated vF = 7.1 × 105 m/s was used to The energy dispersion of the system with the above set of match the experiment. The warping parameter λ was set to 250 parameters is shown on the left-hand side of Figure 4(b), with eV·Å3 by fitting the theoretical CE map at 0.440 eV (right- the TSS band presenting a gap of 240 meV as a consequence of hand side of Figure 4(a)) to the measured one (Figure 3(a)). the nonvanishing net magnetization induced by the magnetic This value confirms a similar warping strength compared to dopants. Furthermore, the TRS is broken, and the surface of other TIs such as Bi2Te3.61 The energy values (with respect to the TI becomes a quantum anomalous Hall (or Chern) the DP) in the theoretical CE maps (Figure 4(a)) were chosen insulator.1,65 As seen on the CE maps (right-hand side of to match the experiment (Figures 3(a)−(c)). As expected, the Figure 4(b)), the TRS breakdown results in the transition from hexagonal warping can be clearly distinguished far from the the 6-fold to a 3-fold rotational symmetry (see section V in DP, whereas when approaching the DP, the CE maps round SM), so that the warped FS evolves from hexagonal (pristine) off, as in the experiment (Figure 3(a)−(c)). to trigonal (doped system), as in the experiments (Figures To introduce the effect of the RE dopants in the former 3(d)−(f)). Interestingly, the obtained value of Δ is up to 1 Hamiltonian (eq 1), a magnetic moment can be coupled to the order of magnitude larger than previous expectations.66−69 TI TSS via an exchange interaction47 through a Zeeman-like Although higher values have been predicted or expected,70,71 term. The Hamiltonian takes the final form (see SM, section up to our knowledge, this is the first time that the exchange V) coupling has been estimated by direct comparison to H = vF(k x k y x ) + ( k3 cos 3 ) experimental results. Such a relatively high value of the y z (2) exchange coupling Δ makes Bi2Se2Te doped with RE a good where Δ stands for the exchange coupling and θ for the candidate system for the realization of the QAHE. azimuthal angle of the momentum. Δ is a fitting parameter of Experimentally, the change in the warping symmetry is also our model. At this point the model keeps using the previously evidenced, just as in the theoretical model, by the induced obtained values of vF and λ, that is 7.1 × 105 m/s and 250 eV· inversion asymmetry in the TSS band dispersion in Figure Å3, in such a way that the only difference between the pristine 3(g),(h), measured along the K direction (red and blue and Er-doped models is the inclusion of the Zeeman-like term dashed lines in Figures 3(a) and (d)), and in the momentum 6253 https://doi.org/10.1021/acs.nanolett.3c00587 Nano Lett. 2023, 23, 6249−6258 Nano Letters pubs.acs.org/NanoLett Letter Figure 5. Topological surface state (TSS) band structure evolution upon Er doping showing signatures of the magnetically induced bandgap at the Dirac point (DP). (a)−(d) TSS bandmaps for pristine Bi2Se2Te and 0.15, 0.3, and 0.6 Er monolayer-doped Bi2Se2Te, respectively, acquired with a photon energy of hν = 52 eV and at T = 15 K. (e)−(h) Energy distribution curves (EDC) extracted from the TSS bandmaps in (a)−(d). EDCs at the point are highlighted following the color correspondence, and the fitting procedures followed for the momentum distribution curves (MDC) and EDC analysis are described in section VII in the SM. The TSS and top valence band dispersions obtained from the MDC fittings are indicated by red and blue dots on the TSS ARPES bandmaps in the top panels. Similarly, EDC fitting results are displayed in the bottom panel. The indicated band dispersion for 0.6 Er ML is, contrary to the other coverages, just a guide to the eye due to the impossibility of performing appropriate fits because of the low signal-to-noise ratio. Purple arrows indicate the DP energy, which is upshifted as the Er coverage is increased. distribution curves (MDCs) close to the EF, depicted above As previously described, the transition from hexagonal to each TSS bandmap. The Fermi wavevectors kF for 0.3 ML Er/ trigonal of the TSS symmetry when an out-of-plane magnetic Bi2Se2Te (blue MDC, Figure 3(h)) are asymmetric with moment is introduced is expected to be accompanied by a respect to the point, as compared to pristine Bi2Se2Te (red bandgap opening at the DP because of the TRS breaking.47 MDC, Figure 3(g)), as a consequence of the different vF of the A more detailed and comprehensive picture on the TSS two branches of the TSSs, of (8.0 ± 0.3) × 105 and (1.2 ± 0.1) band dispersion around the DP can be gathered from the EDC × 106 m/s for the branches corresponding to the vertex and fits (Figure 5(e)−(h)), particularly in those obtained at the the flat face of the trigonal TSSs, respectively. A similar point, extracted along vertical dashed lines in Figure 5(a)−(d) asymmetric band dispersion of the TSS was predicted for the and highlighted in the same colors as in Figure 5(e)−(h). The MnBi2Te4(0001) surface AFM state alongside the same TSS fits for the colored EDCs in Figure 5(e)−(g) are shown in warping transition.48 Figure S11 in section VII in the SM. For the pristine sample The evolution of the TSS as a function of the Er coverage is (Figure 5(e) and Figure S11(a)) the DP is clearly defined by shown in Figure 5. TSS ARPES bandmaps along the K the intersection of the two linear dispersive branches (orange direction for pristine, 0.15, 0.3, and 0.6 ML Er/Bi2Se2Te are EDC), resulting in a single, punctual, and sharp peak with a shown in Figure 5(a)−(d), respectively (second derivative maximum intensity at 440 meV. After the Er deposition, a bandmaps shown in Figures S9 and S10 in section VII in the broadening of the intensity is clearly evidenced around the DP, SM). The corresponding energy distribution curves (EDCs) as as reflected in Figure 5 and more clearly in the second a function of the Er coverage are presented in Figure 5(e)− derivative bandmaps in Figures S9 and S10 in section VII in (h), where the EDCs acquired precisely at the point and the SM, which would be an indication of a possible bandgap thus crossing the DP (along vertical dashed lines in Figures opening at the DP. Indeed, this energy broadening and the gap 5(a)−(d)) are highlighted following the color correspondence. opening are unequivocally evidenced in the EDCs in Figures Here, orange, cyan, green, and red lines stand for pristine, 0.15, S11(c) and (e) where, instead of a single peak as for the 0.3, and 0.6 ML Er/Bi2Se2Te, respectively. The band pristine sample, two peaks are necessary for the correct fitting dispersions have been obtained from the MDC and EDC in the energy region close to the DP. Moreover, the dispersion fittings, whose results are indicated by red and blue dots in of this double peak structure can be extracted from the EDC Figure 5 (a detailed analysis on the MDC and EDC fitting fittings in the vicinity of the Γ point (Figure S12) and is procedure is included in SM, section VII). The dispersion indicated by red and blue dots in Figure 5(f),(g). The obtained from the pristine sample (Figures 5(a) and (e)) characteristic linear dispersion of relativistic massless Dirac displays linear branches which clearly cross at the DP. Red and Fermions of the pristine sample seems to be renormalized to a blue dots for the doped samples (Figure 5(b)−(h)) indicate parabolic-like dispersion, showing a plateau in the EDC the upper and bottom band dispersions relative to the DP. intensity in the vicinity of the point, while the cusp-like 6254 https://doi.org/10.1021/acs.nanolett.3c00587 Nano Lett. 2023, 23, 6249−6258 Nano Letters pubs.acs.org/NanoLett Letter shape of the top of the VB is preserved. This would be another Massimo Tallarida − ALBA Synchrotron Light Source, 08290 indication of the bandgap between the top of the bulk VB and Barcelona, Spain the bottom of the TSS. Similar XPS and ARPES results have Adriana I. Figueroa − Departament de Física de la Matéria been found after 0.3 Dy ML deposition and are summarized in Condensada, Universitat de Barcelona, 08028 Barcelona, section IV in the SM. All the details on the procedures Spain; Catalan Institute of Nanoscience and Nanotechnology followed for the fitting of the MDCs and EDCs, as well as for (ICN2), CSIC and BIST, Campus UAB, 08193 Barcelona, the determination of the TSS dispersions and the gap opening Spain; orcid.org/0000-0002-8498-9383 for the different samples, are included in Figures S9−S13 in Vera Marinova − Institute of Optical Materials and section VII in the SM. Technologies, Bulgarian Academy of Sciences, Acad. G. As discussed at the beginning of the manuscript, similar Bontchev, 1113 Sofia, Bulgaria; orcid.org/0000-0002- bandgap openings have already been experimentally observed 3499-0212 and attributed to TRS by magnetic impurities for numerous Kevin García-Díez − ALBA Synchrotron Light Source, 08290 transition metal magnetic impurities7 or Dy substitutional Barcelona, Spain; Catalan Institute of Nanoscience and dopants.41 Nevertheless, the magnetically induced warping Nanotechnology (ICN2), CSIC and BIST, Campus UAB, transition also resulting from the TRS breaking has not been 08193 Barcelona, Spain; orcid.org/0000-0001-8093- reported so far. 904X In this work, by doping the surface of a TI with RE atoms, Aitor Mugarza − Catalan Institute of Nanoscience and the magnetically induced evolution of the warping of the TSS Nanotechnology (ICN2), CSIC and BIST, Campus UAB, from hexagonal to trigonal has been demonstrated by means of 08193 Barcelona, Spain; ICREA Institució Catalana de ARPES experiments. This shape transition has been predicted Recerca i Estudis Avançats, 08010 Barcelona, Spain; to be accompanied by a bandgap opening at the DP, and orcid.org/0000-0002-2698-885X indeed, signatures of such an effect have also been observed in Sergio O. Valenzuela − Catalan Institute of Nanoscience and the present study. Additionally, the DP has been proven to be Nanotechnology (ICN2), CSIC and BIST, Campus UAB, tunable toward the EF through charge transfer between the RE 08193 Barcelona, Spain; ICREA Institució Catalana de adatoms and the substrate. The TSS band dispersion of the Recerca i Estudis Avançats, 08010 Barcelona, Spain; doped system is reproduced by including a Zeeman-like term orcid.org/0000-0002-4632-8891 in the low energy Hamiltonian describing the system. This Rodolfo Miranda − Instituto Madrileño de Estudios modification entails two important consequences, the first of Avanzados, IMDEA Nanociencia, 28049 Madrid, Spain; them being the just above-described breaking of the hexagonal Departamento de Física de la Materia Condensada, Instituto symmetry and the second one the opening of a gap at the DP “Nicolás Cabrera” and Condensed Matter Physics Center of the TSS. Both phenomena have been observed in the (IFIMAC), Universidad Autónoma de Madrid (UAM), ARPES measurements. Moreover, we find that in order to Campus de Cantoblanco, 28049 Madrid, Spain theoretically describe the experimental results a large exchange Julio Camarero − Instituto Madrileño de Estudios Avanzados, coupling is needed, of the order of 0.1 eV. Thus, the large IMDEA Nanociencia, 28049 Madrid, Spain; Departamento exchange coupling and the DP tunability make the controlled de Física de la Materia Condensada, Instituto “Nicolás doping of TIs with REs an excellent approach to realize the Cabrera” and Condensed Matter Physics Center (IFIMAC), QAHE at higher temperatures. Universidad Autónoma de Madrid (UAM), Campus de Cantoblanco, 28049 Madrid, Spain; orcid.org/0000- ■ * ASSOCIATED CONTENT sı Supporting Information 0003-0078-7280 Francisco Guinea − Instituto Madrileño de Estudios The Supporting Information is available free of charge at Avanzados, IMDEA Nanociencia, 28049 Madrid, Spain; https://pubs.acs.org/doi/10.1021/acs.nanolett.3c00587. Donostia International Physics Center, 20018 San Sebastián, Spain; Ikerbasque, Basque Foundation for Science, 48009 Additional experimental data and details on the sample Bilbao, Spain growth methods and the theoretical model (PDF) Jose Angel Silva-Guillén − Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, 28049 Madrid, Spain; ■ AUTHOR INFORMATION Corresponding Author orcid.org/0000-0002-0483-5334 Complete contact information is available at: Miguel A. Valbuena − Instituto Madrileño de Estudios https://pubs.acs.org/10.1021/acs.nanolett.3c00587 Avanzados, IMDEA Nanociencia, 28049 Madrid, Spain; orcid.org/0000-0002-0585-5636; Notes Email: miguelangel.valbuena@imdea.org The authors declare no competing financial interest. Authors Beatriz Muñiz Cano − Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, 28049 Madrid, Spain; ■ ACKNOWLEDGMENTS IMDEA Nanociencia and IFIMAC acknowledge financial orcid.org/0000-0002-9338-7077 support from the Spanish Ministry of Science and Innovation Yago Ferreiros − Instituto Madrileño de Estudios Avanzados, through, respectively, “Severo Ochoa” (Grant CEX2020- IMDEA Nanociencia, 28049 Madrid, Spain 001039-S) and “María de Maeztu” (Grant CEX2018-000805- Pierre A. Pantaleón − Instituto Madrileño de Estudios M) Programmes for Centres of Excellence in R&D. This Avanzados, IMDEA Nanociencia, 28049 Madrid, Spain project has received funding from the Community of Madrid Ji Dai − ALBA Synchrotron Light Source, 08290 Barcelona, (CM) through project P2018/NMT-4321 (NANOMAG- Spain COST), from Spanish Ministry of Economic Affairs and 6255 https://doi.org/10.1021/acs.nanolett.3c00587 Nano Lett. 2023, 23, 6249−6258 Nano Letters pubs.acs.org/NanoLett Letter Digital Transformation (MINECO) through projects ferromagnet-topological insulator heterostructure devices. Appl. Phys. SPGC2018-098613-B-C21 (SpOrQuMat), EQC2019- Lett. 2013, 103, 202409. 006304-P (Equipamiento científico), and PID2020- (12) Hou, Y.; Kim, J.; Wu, R. Magnetizing topological surface states 116181RB-C31 (SOnanoBRAIN) and from Spanish Ministry of Bi2Se3 with a CrI3 monolayer. Science advances 2019, 5, eaaw1874. (13) Chang, C.-Z.; Zhang, J.; Feng, X.; Shen, J.; Zhang, Z.; Guo, M.; of Science and Innovation (MICINN) and the Spanish Li, K.; Ou, Y.; Wei, P.; Wang, L.-L.; et al. Experimental observation of Research Agency (AEI/10.13039/501100011033) through the quantum anomalous Hall effect in a magnetic topological grants PID2021-123776NB-C21 (CONPHASETM), insulator. Science 2013, 340, 167−170. PID2019-107338RB-C65, and PID2019-111773RB-I00. (14) Chang, C.-Z.; Zhao, W.; Kim, D. Y.; Zhang, H.; Assaf, B. A.; ICN2 was funded by the CERCA Programme/Generalitat de Heiman, D.; Zhang, S.-C.; Liu, C.; Chan, M. H.; Moodera, J. S. High- Catalunya and supported by the Spanish Ministry of Economy precision realization of robust quantum anomalous Hall state in a and Competitiveness, MINECO, under Contract No. SEV- hard ferromagnetic topological insulator. Nat. Mater. 2015, 14, 473− 2017-0706. A.I.F., V.M., and S.O.V. acknowledge support from 477. European Union’s Horizon 2020 FET-PROACTIVE project (15) Otrokov, M. M.; Klimovskikh, I. I.; Bentmann, H.; Estyunin, D.; Zeugner, A.; Aliev, Z. S.; Gaß, S.; Wolter, A.; Koroleva, A.; Shikin, TOCHA under Grant Agreement No. 824140. LOREA was A. M.; et al. Prediction and observation of an antiferromagnetic cofunded by the European Regional Development Fund topological insulator. Nature 2019, 576, 416−422. (ERDF) within the Framework of the Smart Growth Operative (16) Rienks, E. D.; Wimmer, S.; Sánchez-Barriga, J.; Caha, O.; Programme 2014-2020. B.M.C. acknowledges support from Mandal, P. S.; Růzǐ čka, J.; Ney, A.; Steiner, H.; Volobuev, V. V.; CM (PEJD-2019-PRE/IND-17048). F.G. and P.A.P. acknowl- Groiß, H.; et al. Large magnetic gap at the Dirac point in Bi2Te3/ edge support from the European Commission, within the MnBi2Te4 heterostructures. Nature 2019, 576, 423−428. Graphene Flagship, Core 3 (Grant No. 881603), from CM (17) Garnica, M.; Otrokov, M. M.; Aguilar, P. C.; Klimovskikh, I.; (Grant NMAT2D) and (MAD2D-CM)-MRR MATERIALES Estyunin, D.; Aliev, Z. S.; Amiraslanov, I. R.; Abdullayev, N. A.; AVANZADOS-IMDEA-NC. Y.F. acknowledges financial sup- Zverev, V. N.; Babanly, M. B.; et al. Native point defects and their implications for the Dirac point gap at MnBi2Te4 (0001). npj port through the Programa de Atraccion de Talento de la Quantum Materials 2022, 7, 1−9. Comunidad de Madrid, Spain, Grant No. 2018-T2/IND- (18) Grauer, S.; Schreyeck, S.; Winnerlein, M.; Brunner, K.; Gould, 11088. A.I.F. is a Serra Húnter fellow. The authors acknowl- C.; Molenkamp, L. Coincidence of superparamagnetism and perfect edge Jordi Prat and Pierluigi Gargiani for their invaluable quantization in the quantum anomalous Hall state. Phys. Rev. B 2015, technical support during experiments. 92, 201304. (19) Pan, L.; Liu, X.; He, Q. L.; Stern, A.; Yin, G.; Che, X.; Shao, Q.; ■ REFERENCES (1) Hasan, M. Z.; Kane, C. L. Colloquium: Topological insulators. Zhang, P.; Deng, P.; Yang, C.-Y.; et al. Probing the low-temperature limit of the quantum anomalous Hall effect. Science advances 2020, 6, eaaz3595. Rev. Mod. 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