Reorientation of the diagonal double-stripe spin structure at Fe1+yTe bulk and thin-film surfaces

Establishing the relation between ubiquitous antiferromagnetism in the parent compounds of unconventional superconductors and their superconducting phase is important for understanding the complex physics in these materials. Going from bulk systems to thin films additionally affects their phase diagram. For Fe1+yTe, the parent compound of Fe1+ySe1−xTex superconductors, bulk-sensitive neutron diffraction revealed an in-plane oriented diagonal double-stripe antiferromagnetic spin structure. Here we show by spin-resolved scanning tunnelling microscopy that the spin direction at the surfaces of bulk Fe1+yTe and thin films grown on the topological insulator Bi2Te3 is canted out of the high-symmetry directions of the surface unit cell resulting in a perpendicular spin component, keeping the diagonal double-stripe order. As the magnetism of the Fe d-orbitals is intertwined with the superconducting pairing in Fe-based materials, our results imply that the superconducting properties at the surface of the related superconducting compounds might be different from the bulk.

T he physics of many transition metal oxides (TMOs) is dominated by strong electronic correlations, which leads to exotic ground states and excitations with a dominant role of electronic charge and spin degrees of freedom. For example, for cuprate-based high-temperature superconductors there have been growing evidence that charge and spin density wave (SDW)-like states are inherent to these materials with a significant impact on the corresponding excitation spectrum [1][2][3] . Indeed, spin and charge ordering appear to be a key feature for understanding the physics of high-temperature superconductors 4,5 . Furthermore, among the correlated electron systems the recently discovered iron-based superconductors 6 are of particular interest for the understanding of the interplay between superconductivity and magnetism. Especially, the iron-chalcogenide system Fe 1 þ y Se 1 À x Te x has gained high interest due to the surprisingly high T C superconductivity in single-layer films of FeSe [7][8][9] and its unique interplay between magnetism and superconductivity 10 . For bulk single crystals, FeSe exhibits a superconducting transition temperature T C of no higher than 10 K (ref. 11) but in a single-unit cell (UC) thick film grown on SrTiO 3 T C can be increased above 100 K (ref. 9). This finding has spurred numerous investigations aiming at the understanding of how superconductivity evolves in transition metal chalcogenides from bulk to ultra-thin films. In particular, scanning tunnelling microscopy (STM) with atomic-scale resolution has proven to be an indispensable tool for revealing the real-space electronic structure 12,13 . However, most of the recent STM studies on TMO and iron-based superconductors have been focusing only on the charge degrees of freedom. With the recent developments in spin-polarized STM (SP-STM) 14,15 , which accesses both charge and spin degrees of freedom on the atomic length scale, detailed investigations of TMO compounds and iron-based superconductors have now become possible.
As Fe 1 þ y Te exhibits diagonal double-stripe antiferromagnetic (DDS) spin order, contrasted with single-stripe antiferromagnetic (AFM) order in iron pnictide superconductor parent compounds, the study on its mechanism of magnetic order has recently attracted a lot of attention. It provides a non-polar charge-neutral Te-terminated surface on cleaving [16][17][18] . Furthermore Fe 1 þ y Te can be grown in situ by molecular beam epitaxy with high quality 19,20 . In bulk, Fe 1 þ y Te is the non-superconducting parent compound of the transition metal chalcogenide system Fe 1 þ y Se 1 À x Te x 10 and exhibits the DDS magnetic structure below its Néel-temperature T N [21][22][23] . Depending on its excess iron concentration y, the Néel temperature varies from T N E60-70 K 24 . Using neutron diffraction, it has been shown that in the bulk the Fe spins within the DDS structure are pointing along the diagonal of the Fe-Fe square network 22,23 . The crystal structure and corresponding DDS order are schematically shown in Fig. 1a,b. The magnetic phase transition of bulk Fe 1 þ y Te is accompanied by a structural phase transition, with the structure changing from a tetragonal to a monoclinic phase for which the lattice constant a Te is slightly larger than the lattice constant b Te 22,25 . The DDS structure itself shows a commensurate AFM modulation along the a Te direction with a wave length of l AFM ¼ 2a Te and has a ferromagnetic coupling along the b Te direction 22,23,26 .
STM data obtained for Fe 1 þ y Te bulk and thin film samples have revealed atomic resolution of the Te-terminated surface and a superstructure on top of the atomic corrugation having a periodicity of l ¼ 2a Te [18][19][20][27][28][29] . The observation of this additional l ¼ 2a Te periodicity is mainly discussed in two contradictory models. On one hand, the interpretation for the 2a Te superstructure is given in terms of a charge density wave (CDW), where the charge density of the top Te layer is modified by the SDW of the underlying AFM order of the Fe layer. The strong dependence on the bias voltage V bias suggests a complex interplay between the charge and the magnetic order 18,20,27,30 . In contrast to a common representation of spin and charge modulations in correlated electron systems 31 , in this case the CDW would have the same periodicity as the SDW. Opposed to this interpretation, experiments performed with magnetically sensitive tips, which were prepared by attaching excess Fe atoms to the tip apex, give additional insight based on spin-polarized tunnelling 28,29 . The 2a Te superstructure can unambiguously be assigned to a direct imaging of the DDS order of the underlying Fe lattice. However, in previous studies the absolute orientation of the spins within the AFM structure could not be revealed.
In this work we investigated the Fe 1 þ y Te surface of bulk samples and of thin Fe 1 þ y Te films grown on Bi 2 Te 3 by SP-STM, revealing the DDS structure in both sample systems. Moreover, by using Fe-coated W-tips in a vector-magnet system, we were able to rotate the tip magnetization direction both within the surface plane as well as perpendicular to the surface. As we thereby have access to the different components of the spin direction of the sample, we could unambiguously prove that the spin direction within the surface DDS structure is canted with respect to the crystallographic b Te direction.

Results
SP-STM on the surface of Fe 1 þ y Te bulk and thin films. In spinpolarized STM, the tunnelling current depends on the relative orientation of the tip magnetization and the local spin direction of the sample. The total tunnelling current I t can be described by where I 0 is the spin-averaged tunnelling current and I p is the spin-polarized tunnelling current, which is proportional to the product of the spin polarization P t of tip and the energy integrated spin polarization P s of the sample, I p pP t Á P s Á cos(b). Here, b is the angle between the spin directions of the tip and the sample 32 .
In general, Fe-coated W-tips have a magnetization direction perpendicular to the tip axis and thus parallel to the surface of the sample. Therefore, Fe-coated W-tips exhibit sensitivity to an a priori unknown in-plane component of the sample magnetization. By applying an external magnetic field of about 1 T, the magnetization direction of the tip will be reoriented parallel to the applied field direction 33 . However, the corresponding Zeeman energy of 0.1 meV is too weak to affect the spin structure of Fe 1 þ y Te, as the exchange interactions between neighbouring Fe atoms in the DDS structure are on the order of 10 meV (ref. 34), and there is a considerable magnetic anisotropy energy of about 0.5 meV per Fe atom 28 . By application of the external magnetic field in different orientations and recording constant-current SP-STM images, we can therefore image the particular component of the sample spin structure in the given direction of the magnetic field.
In Fig. 1, we give an introduction to both Fe 1 þ y Te samples used in this work. The first investigated sample shown in Fig. 1c,d is the surface of cleaved bulk Fe 1 þ y Te (yB0.07). Figure 1c displays a typical spin-resolved constant-current image of the bulk Fe 1 þ y Te surface, which shows clear atomic resolution of the Te-terminated surface (a detailed analysis of the investigated spin contrast is discussed later on). Compared with previously reported results 18,28,30 , a large area of the Fe 1 þ y Te surface is free of excess Fe atoms, which is due to the annealing procedure as described in the Methods section. This annealing procedure leads to the formation of Fe clusters containing all the excess Fe (outside of the field of view of Fig. 1c) and large areas with no surface excess Fe atoms in between these clusters. The surface is atomically flat but shows a small variation in the apparent height, which is probably caused by excess Fe atoms between the sub-surface layers. By calculating the Fourier transform (FT) of Fig. 1c, the lattice periodicity is displayed as bright Bragg spots labelled as q a Te and q b Te in Fig. 1d, where q a Te has a higher intensity than q b Te (cf. refs 20,28,30). In addition to the atomic periodicity the constant-current image in Fig. 1c shows the typical superstructure, which has a periodicity of l ¼ 2a Te along the a Te direction. The presence of this superstructure is visible as additional spots in the FT (labelled with q AFM ) with a wave vector of q AFM ¼ 1 2 q a Te . Overall, the cleaved surface shows all the characteristics previously reported for Fe 1 þ y Te (cf. refs 20,27,28).
The second investigated sample is a thin Fe 1 þ y Te film grown on Bi 2 Te 3 ( Fig. 1e-g). A large-scale STM topography of the sample area is displayed in Fig. 1e together with the height profile along a line shown in Fig. 1f. From atomically resolved images taken on the different visible layers and their apparent heights, we deduce the structure of the layers as sketched in Fig. 1g. The first UC thin layer of FeTe, which has an apparent hight of B3.5 Å (Fig. 1e), is embedded into an incomplete Bi 2 Te 3 quintuple layer. Owing to the interaction with the underlying substrate it exhibits a network of stripe-like dislocations, leading to a rough surface (not resolved in the large scale image of Fig. 1e). On top of the embedded layer, the growth of an additional FeTe layer has started and forms a second layer island with a height of 6.5 Å, which is roughly equal to the c axis lattice constant (6.26 Å) 23 of the bulk Fe 1 þ y Te UC as shown in Fig. 1a. This second layer has an atomically flat surface. In this work we focused on SP-STM measurements on top of the second layer islands indicated by the white arrow in Fig. 1e. In Fig. 1h, an atomically resolved image of the surface on the second layer Fe 1 þ y Te island is shown. We do not observe excess Fe atoms on the surface, but we cannot exclude that there is a small amount of excess Fe atoms sitting in the van der Waals gap in between the two FeTe layers. In addition to the atomic corrugation the characteristic 2a Te superstructure is visible as indicated in the inset of Fig. 1h, which is very similar to the one at the bulk Fe 1 þ y Te surface shown in Fig. 1c. This is also visible in the FT displayed in Fig. 1i, which coincides with the FT pattern in Fig. 1d; the atomic lattice shows peaks of different intensity (labelled with q a Te and q b Te ) and also the 2a Te superstructure peaks are visible (labelled with q AFM ). Therefore, the spin-resolved STM image of the second layer Fe 1 þ y Te island It is noteworthy that for this particular data the tips' spin polarization is perpendicular to the sample spin orientation. Therefore, a non-zero magnetic field had to be used to rotate the tip magnetization, to observe the 2a Te spin contrast. White arrows denote the lattice directions a Te and b Te . Inset: magnified image showing the atomic lattice of the surface Te atoms with a 2a Te periodic superstructure. (i) The FT of h with the same assignment of the different peaks as in d. exhibits a very similar spin structure as the surface of bulk Fe 1 þ y Te. It is noteworthy that for both the bulk samples and the thin film samples, the 2a Te superstructure is observed only if the tip is magnetically coated, or if a nominally uncoated tip picks up surface Fe atoms or a cluster of FeTe due to a tip-sample contact, as also shown in ref. 28. Images taken with a zero spin polarization at the foremost atom of the tip show only the atomic contrast from the topmost Te atoms with a periodicity of a Te and b Te (Supplementary Fig. 1).
Magnetic field-dependent SP-STM on bulk Fe 1 þ y Te. After introducing the two different sample systems used in this work we will now discuss our results obtained with different orientations of the tip magnetization starting with the surface of bulk Fe 1 þ y Te and out-of-plane tip sensitivity. Figure 2a,b show constant-current maps of the same surface area obtained with an Fe-coated tip. They were recorded in a magnetic field of 1 T with opposite out-of-plane field directions, which forces the tip magnetization to point up and down. The two SP-STM images show the characteristic 2a Te superstructure, which is also visible by the q AFM peak displayed in the corresponding FTs in Fig. 2c,d. In contrast to different interpretations such as charge ordering phenomena 18,20 , this additional superstructure has been attributed to a direct imaging of the DDS order of Fe 1 þ y Te by SP-STM 28,29 . Our experiments show that this is indeed the case and confirm that spin-polarized tunnelling is the origin of the additional 2a Te superstructure by applying external magnetic fields. By comparing the superstructure with the atomic lattice, a phase shift by one lattice unit is observed for opposite magnetic field directions (cf. insets of Fig. 2a,b). By subtracting the constant-current maps in Fig. 2a from that in Fig. 2b, an image of the out-of-plane components of the spin structure is obtained in Fig. 2e, which mainly shows a stripe pattern with a periodicity of 2a Te along the a Te direction. This is also reflected by the FT of the difference image in Fig. 1f. Here, only the peak q AFM remains and the Bragg peaks q a Te and q b Te related to the atomic lattice have vanished. On the other hand, the sum image of the constantcurrent maps in Fig. 2a,b, which is shown in Fig. 2g together with its FT in Fig. 2h, does not reveal the 2a Te periodic stripe pattern, but merely the Bragg peaks q a Te and q b Te . This observation directly confirms the results from ref. 28 and proves spin-polarized tunnelling contrast due to the DDS spin structure of Fe 1 þ y Te. The maximum spin contrast appears between every second Fe lattice site located between two neighbouring Te sites. This can be explained by the fact that spin-polarized tunnelling primarily results from the 3d states of Fe being located below the top Te layer.
However, from the strong spin contrast we see using the outof-plane sensitive magnetic tip, we can additionally conclude that the surface AFM structure has a considerable out-of-plane spin component. Considering the magnetic structure of bulk Fe 1 þ y Te as known from neutron diffraction 21-23 depicted in Fig. 1b, this leads to the conclusion that the surface spins are reoriented with respect to the corresponding bulk layers.
To analyse the in-plane surface spin components of the DDS structure of bulk Fe 1 þ y Te, we performed experiments within a vector-magnet system, which enables to rotate the tip magnetization direction within the film plane. For this purpose a magnetic field with a fixed amplitude was applied parallel to the surface and then stepwise rotated for each taken SP-STM image recorded. The results are shown in Fig. 3 for the magnetic field amplitude of 1 T. Figure 3a shows an overview of the atomically resolved Fe 1 þ y Te surface with a magnetic field applied under an angle of  a ¼ À 16°relative to the given magnetic field coordinate system. On top of the atomic corrugation, the strong 2a Te superstructure is visible running continuously through the whole image from the bottom left to the top right. The blue square indicates the area where the investigations with rotated magnetic fields were performed and the red arrow indicates a defect used as a marker for the atomic-scale registry. On rotating the magnetic field parallel to the surface, the intensity of the 2a Te superstructure was measured by taking spin-resolved constant-current maps for each field direction ( Fig. 3b-d, see full set of images in Supplementary  Fig. 2). The intensity of the superstructure was then extracted from the amplitude of the q AFM peak in the FTs (Fig. 3e-g). In addition to the q AFM peak, the intensity of the Bragg peaks q a Te and q b Te were recorded as a reference, to confirm that the tip did not change during the full magnetic field sweep. These intensities are shown in Fig. 3j as a function of the magnetic field angle. In Fig. 3b,c, the tip magnetization direction is pointing in opposite directions within the surface plane. It is again apparent that the 2a Te superstructure observed for both field directions exhibits a phase shift of one lattice unit and is merely a result of the spinsensitivity of the tip. This is verified by calculating the difference and sum of Fig. 3b,c shown in Fig. 3h,i, where only the magnetic signal 2a Te of the superstructure, or the purely electronic signal with the lattice periodicity, respectively, remain. By comparing the intensities of the two Bragg peaks q a Te and q b Te , and the DDS q AFM peak extracted from the FTs of these images shown in Fig. 3e,f, we can conclude that both SP-STM images exhibit the same amplitudes for the atomic corrugation and the 2a Te superstructure, respectively, as shown in the plot of Fig. 3j. In contrast, in the SP-STM image and its FT for a field direction of 84° (Fig. 3d,g), the amplitude of the atomic corrugation remains at the same level but the amplitude of the 2a Te superstructure is strongly reduced. Overall, the resulting angular dependence plotted in Fig. 3j reveals a periodic variation of the q AFM peak intensity with a periodicity of 180°, whereas the intensities of the Bragg peaks do not show significant changes. As shown by the fitted line, the q AFM intensity nicely follows a |cos(a)|-dependence, which is expected for spin-polarized tunnelling into an AFM spin structure on the rotation of the tip magnetization. The maximum of the intensity was found to be at À 19°. The corresponding in-plane spin direction of the DDS structure is indicated by the green arrow in Fig. 3a. We can thus deduce that the DDS spin structure of the surface layer has an in-plane component, which deviates by 19°from the b Te direction, the spin direction of the DDS spin structure in the bulk layers of Fe 1 þ y Te. Moreover, considering the similar q AFM intensity for the outof-plane case (Fig. 2c,d) and for the maximum in-plane contrast case (Fig. 3j), we can conclude that the DDS spin structure at the surface is additionally rotated out of the surface plane by roughly 45°.
Magnetic field-dependent SP-STM on Fe 1 þ y Te films on Bi 2 Te 3 . For comparison, we will now discuss the results obtained for a thin Fe 1 þ y Te film grown on a Bi 2 Te 3 substrate. All SP-STM data in Fig. 4 were obtained in the same surface area on the top of a two UC high Fe 1 þ y Te island for magnetic fields of 2.5 T applied in opposite out-of-plane directions (Fig. 4a,b) and for magnetic fields of 1.2 T applied in opposite in-plane directions (Fig. 4e,f). As for the measurements discussed above, the characteristic 2a Te superstructure is observed in all four SP-STM data sets. The FTs in the insets of Fig. 4a,b,e,f also show the same q AFM pattern as for the bulk samples. By comparing the position of the maximum of the 2a Te superstructure relative to the underlying Te lattice, for example, at the position indicated by the red arrow, the Fe 1 þ y Te thin-film system also reveals a phase shift by one lattice constant upon inverting of the tip's magnetization direction in the out-ofplane and in the in-plane direction. This is also obvious from the difference images in Fig. 4c,g, reflecting the images of the out-ofplane and in-plane components of the spin structure, respectively. Therefore, we can conclude that the surface of the thin film Fe 1 þ y Te on Bi 2 Te 3 exhibits the same DDS spin structure as the bulk samples. In addition, to analyse the direction of the surface spins, the magnetic field dependence of the intensities of the q AFM peak and of the Bragg peaks q a Te and q b Te were extracted for the out-of-plane and for the in-plane direction and are shown in Fig. 4d,h, respectively (full series of magnetic field dependent SP-STM images is given in the Supplementary Figs 3 and 4). For zero magnetic field, the 2a Te superstructure has vanished and the intensity of the q AFM peak is basically zero. For this particular tip, the initial tip magnetization at zero magnetic field is thus almost perpendicular to the spin direction in the Fe 1 þ y Te surface layer. It is noteworthy that the absence of the 2a Te superstructure for this case again implies that there is no contribution to the superstructure from a CDW, in conflict with previous results 18,20,27 . On increasing the magnetic field in the out-ofplane direction the intensity of q AFM starts changing, as the magnetization direction of the tip is continuously rotated from the in-plane to the out-of-plane direction as shown in Fig. 4d. For both the negative and the positive field direction, the intensity of q AFM saturates when the tip magnetization is fully rotated into the out-of-plane direction. For the in-plane direction a similar behaviour is observed as shown in Fig. 4h. On increasing the magnetic field, the tip continuously rotates into the direction of the magnetic field, where a strong magnetic contrast is deduced by the increase in the q AFM intensity. From the similar saturation values of the q AFM intensities in Fig. 4d,h, we can conclude that the out-of-plane component of the DDS spin structure in the surface layer of the Fe 1 þ y Te thin film has a similar strength as the in-plane component, that is, the spin structure is rotated by roughly 45°out of the surface plane.

Discussion
In summary, we provide a direct proof that spin-polarized tunnelling is responsible for the observation of the 2a Te superstructure in STM on Fe 1 þ y Te by using well-defined spinsensitive Fe-coated W-tips. Measurements under applied magnetic fields reveal that the 2a Te superstructure can only be interpreted in terms of direct SP-STM imaging of the DDS order of the Fe 1 þ y Te surface. This confirms previous SP-STM results with magnetically sensitive tips on Fe 1 þ y Te 28,29 and does not support the interpretation of a 2a Te CDW-order discussed in refs 18,20,27. Most notably, both DDS spin structures, the one at the surface of bulk Fe 1 þ y Te and thin Fe 1 þ y Te grown on Bi 2 Te 3 , have a strong component in the out-of-plane direction along the c axis, of similar strength as the component in the surface plane. Measurement of the in-plane components of the surface spinstructure of bulk Fe 1 þ y Te showed that the spin-direction also deviates from the b Te axis direction. Neutron scattering, which is sensitive to the bulk magnetization, revealed a dominant spin direction of the DDS structure along the b Te axis direction 22,23,26 . A tiny component of the magnetization along the a-and c axes has been mainly attributed to local moments of excess iron atoms, which are located in the van der Waals gap between the FeTe layers 23 . In contrast, our experiments indicate a strong image of e,f. Scale bars 5.8 nm wide (ac,e-g). The magnetic field dependence of the intensity of q a Te , q b Te and q AFM in the FTs for out-of-plane magnetic fields is plotted in d and for magnetic fields applied in the in-plane direction in h. The colour coding of the corresponding symbols match the circular markings in the FTs. Since the absolute value of the FT contains no phase information the amplitude of the q AFM peak was multiplied by À 1 for negative field directions to illustrate the observed phase shift of the DDS superstructure. component of the surface magnetization out of the b Te axis direction, in favour of a reorientation of the ordered magnetic moments at the surface of Fe 1 þ y Te. The central question is, thus, what drives this surface reorientation of the spin direction by keeping the overall DDS order.
Owing to its layered crystal structure Fe 1 þ y Te has a quasi-twodimensional electronic structure with a very small exchange interaction between the Fe atoms from different layers 34 . It has been shown that the relative orientations of the spins within the DDS spin structure are already determined by the three nearestneighbour exchange interactions of the Fe atoms within the a-b plane of a given Fe 1 þ y Te layer, which are on the order of 10 meV (ref. 35). On the other hand, the absolute orientation of the spins within the DDS spin structure is determined by the magnetic anisotropy energy, which is only on the order of 0.5 meV in the bulk layers 28 . Our result of an overall DDS surface spin structure, which is preserved but reoriented with respect to the bulk layers, suggests that the rather strong exchange interactions within the layers are largely unaffected by the effects occurring at the surface, whereas these effects have a qualitative impact only on the weaker magnetic anisotropy energy. The magnetic anisotropy energy usually has two main contributions, the magneto-crystalline contribution and the dipolar stray field contribution. While the former could be affected by a relaxation of the surface layer with respect to the bulk layers, the latter is usually weak for an AFM spin structure as the DDS structure. We therefore propose that a possible lattice relaxation of the topmost Fe 1 þ y Te layer could be responsible for the observed reorientation.
Our findings may have important implications for the investigations of the related superconducting material Fe 1 þ y Se 1 À x Te x using surface-sensitive techniques. The superconducting pairing in Fe-based superconductors is intertwined with the magnetism in the iron d-orbitals 36 . Our results show that the spin direction at the surface is very different from the bulk. By strong spin-orbit interaction 37 , this will have a considerable effect on the energetics of the d-orbitals and could thereby also change the superconducting properties at the surface with respect to the bulk 38 . Finally, comparable SP-STM studies could offer insight into the origin of the strongly increased T C of the monolayer FeSe grown on SrTiO 3 compared with bulk FeSe 7-9 .
In conclusion, we have shown that SP-STM experiments with Fe-coated W-tips are well suited to investigate correlated electron systems such as Fe 1 þ y Te with a complex electronic and magnetic structure. However, a complete characterization requires SP-STM experiments performed in three-dimensional vector-field systems offering field-dependent studies with arbitrary field orientation.

Methods
Sample and tip preparation. High-quality Fe 1 þ y Te single crystals were synthesized using the flux method 39 where the excess Fe ratio y was kept as low as possible. The measured composition of the crystals using single crystal X-ray diffraction resulted in yE7%. The samples were cleaved in situ at room temperature and measured in ultra-high vacuum (UHV) with a background pressure better than 3 Â 10 À 10 mbar. For all SP-STM measurements the bulk samples were moderately annealed at 100°C after cleaving, which removes the surface excess iron and leads to an atomically flat surface. In addition, ultra-thin Fe 1 þ y Te films were grown in situ on Bi 2 Te 3 substrates. Single crystals of Bi 2 Te 3 were synthesized using a Stockbarger method and were well characterized using angle-resolved photoemission spectroscopy (ARPES) 40 . Fe-chalcogenide thin-film preparation was carried out in a UHV system with a base pressure better than 3 Â 10 À 10 mbar. The Bi 2 Te 3 crystals were cleaved in situ under UHV conditions and Fe 1 þ y Te thin films were prepared by depositing 0.5-1 monolayer Fe onto the clean Bi 2 Te 3 surface at room temperature followed by a 15 min annealing cycle at B300°C. Fe deposited on Bi 2 Te 3 reacts with the substrate on annealing, most probably via a substitutional process replacing Bi by Fe. This preparation was performed similar to the method described in ref. 41 for FeSe on Bi 2 Se 3 . Here, the main difference in the growth is that the Fe 1 þ y Te islands do not show the moirépattern observed for FeSe on Bi 2 Se 3 but a smooth atomically flat surface. To prepare spin-sensitive tips, electrochemically etched W-tips were shortly heated to B2,000°C (flash) and afterwards a thin Fe film of B10 nm thickness was deposited onto the tip apex by e-beam deposition 14,32 .
Experimental techniques. The STM experiments were performed in two homebuilt low-temperature UHV-STM systems at the base temperature of 6.5 K 42,43 . One of them was used for the data shown in Figs 2 and 4, to apply either out-ofplane magnetic fields up to 2.5 T or in-plane magnetic fields in a given direction up to 1 T 42 . The other was used for the data shown in Fig. 3, to continuously rotate a magnetic field of 1 T in the surface plane 43 . All STM data were recorded in constant-current mode with a fixed sample bias voltage V bias and a constant set-point for the tunneling current I t . The FTs were calculated from the absolute value of the complex two-dimensional fast FT, which is proportional to the power spectral density.
Data availability. The authors declare that the main data supporting the findings of this study are available within the article and its Supplementary Information files. Extra data are available from the corresponding author upon request.