Comparative Scanning Tunneling Microscopy Study on Hexaborides

We compare STM investigations on two hexaboride compounds, SmB$_6$ and EuB$_6$, in an effort to provide a comprehensive picture of their surface structural properties. The latter is of particular importance for studying the nature of the surface states in SmB$_6$ by surface-sensitive tools. Beyond the often encountered atomically rough surface topographies of {\it in situ}, low-temperature cleaved samples, differently reconstructed as well as B-terminated and, more rarely, rare-earth terminated areas could be found. With all the different surface topographies observed on both hexaborides, a reliable assignment of the surface terminations can be brought forward.


I. INTRODUCTION
The hexaborides of cubic structural type CaB 6 (P m3m) represent a very versatile class of compounds 1 . LaB 6 features a very low work function of about 2.7 eV 2 while electron-doped CaB 6 is a ferromagnetic material, albeit with low magnetic moment 3,4 , and CeB 6 exhibits quadrupolar ordering 5 . The hexaborides are often highly conductive. From Hall measurements it was shown 6 that the majority of the hexaborides has one charge carrier per rare-earth atom, with the exceptions of divalent Eu and Yb with very low charge carrier densities and SmB 6 exhibiting intermediate valence 7,8 .
The material SmB 6 has attracted special attention recently as it was proposed to host topologically non-trivial surface states 9 . This material falls into the category of so-called Kondo insulators 10,11 in which the insulating properties are brought about by hybridization between conduction bands (here d-bands) and localized fstates. In consequence, a narrow gap opens up at sufficiently low temperatures (below the Kondo temperature T K ) while the f -electrons provide the strong spinorbit coupling required for the development of topologically protected surface states predicted by band structure calculations [12][13][14] . Subsequently, considerable experimental effort was made to verify the topological nature of the surface states, in particular through angleresolved photoemission spectroscopy (ARPES) with spin resolution 15,16 . Though there is a consensus on the existence of a conducting surface state 17,18 , its topological nature is a matter of ongoing debate. For instance, the surface states observed by ARPES measurements have been interpreted in terms of Rashba splitting 19 . One crucial aspect 20,21 , namely a Γ 8 quartet ground state of the Sm f 5 configuration, has recently been observed experimentally 22 , but is in contrast to some band structure calculations 13,23,24 . Here, the strong correlations of the Kondo insulator as well as its intermediate valence complicate band structure calculations 25 . An additional complication is the complex (001) surface of SmB 6 itself due to its polar nature 26 . Because of the cubic structure of SmB 6 , in situ cleaved surfaces usually required for surface-sensitive techniques like ARPES or Scanning Tunneling Microscopy/Spectroscopy (STM/S) are often atomically rough or reconstructed [27][28][29][30] . But even in case of atomically flat surfaces the interpretation of the surface termination in STM is controversial 31,32 . In an effort to make progress in this complex situation we here compare topographies obtained by STM on SmB 6 and EuB 6 . The latter material is interesting in its own right due to its complex band structure 33 , ferromagnetic properties 34 and polaron formation 35 . We note that a comparative study of YbB 6 , CeB 6 and SmB 6 , primarily based on ARPES results, was recently brought forward 36 .

II. EXPERIMENTAL SECTION
Single crystals of SmB 6 and EuB 6 were grown by an Al flux method [37][38][39] . The orientation of the single crystals was checked by Laue diffraction. The lattice constants are a = 4.133Å for SmB 6 and a = 4.185Å for EuB 6 .
For STM investigations, two ultra-high vacuum (UHV) systems were used 40 . A 4 He system allows for base temperatures below 5 K; if a heating stage is used the base temperature is typically ∼6 K (a temperature sensor is incorporated into the heating stage). If not stated otherwise, the STM/STS data reported in the following were obtained at ∼6 K. Our 3 He-based system operates down to a base temperature of ∼0.3 K and allows to apply magnetic fields up to 12 T perpendicular to the investigated surface. Electrochemically etched tungsten tips were used if not stated otherwise. Tunneling spectroscopy was conducted by using a lock-in technique and adding a small ac modulation voltage V mod of 0.1 or 1.0 mV (depending on bias voltage V , see respective figure caption) with a frequency of 117 Hz to the bias voltage. Some of the STM data reported in the following were obtained in a so-called dual-bias mode. In these cases, two different bias voltages V were applied for the forward and backward scan of the fast scan direction. This mode of operation allows to obtain topographic images with two different V at the same sample position (within the piezoelectric hysteresis of the scanner, typically giving offsets well below 1% of the total scan size of the two topographies). In doing so, drift corrections can be neglected and parameters like temperature T or magnetic field, sample history, surface termination, or tip condition are identical. Even if the tip changes, it then influences the data for both V at very similar sample positions.
All samples reported here were cleaved in situ along a (001) crystallographic plane at a temperature of ∼20 K using identical cleaving stages in both UHV systems. After cleaving, the sample needs to be transferred into the respective STM head during which time (in the order of 10 s) the sample temperature is not controlled. We here provide results based on 24 cleaves of SmB 6 (on 8 of which we did not find any atomically flat surface area) and 5 cleaves on EuB 6 .

A. SmB6
In order to obtain information on the nature of the surface states the applied probe needs to be surface sensitive. One obstacle in investigating SmB 6 with highly surface-sensitive tools like ARPES or STM are the different surface terminations. Due to the cubic structure of the hexaborides, the majority of the cleaved surface areas is rough on an atomic scale 31 . This may result in a modified local structure which, in turn, may influence the properties (specifically of Sm) at the surface 41,42 .
Upon searching, a (2 × 1) surface reconstruction can usually be found 28,30,43 . The (2 × 1) reconstruction was also observed by low-energy electron diffraction 36,44,45 as well as by STM on LaB 6 46 . Clearly, if we assume that the compared to an unreconstructed polar surface. Yet, other STM studies did not report this reconstruction 29 or interpreted it differently 32 . It should also be noted that such a reconstruction may have repercussions on the metallic surface state 47 .
In Fig. 1 we present such a (2 × 1) reconstructed surface area. The height scan taken along the blue line as indicated in the topography is consistent with the aforementioned idea of each second row of Sm atoms missing. This is corroborated by a change in height on and between these rows of atoms of the order 40-50 pm; yet, an order of magnitude smaller height oscillations for the (2 × 1) reconstructed surface was also reported 30,43 . The reconstruction is likely formed during the cleaving process or subsequently upon some additional diffusion of surface atoms. In both cases, one may expect domains of (2 × 1) and (1 × 2) reconstructed areas and dislocations between the Sm rows by one lattice constant, both of which can easily be recognized in the topography, Fig. 1.
Rarely we also found atomically flat surface areas as shown in Fig. 2. Similar surface topographies have been presented before [27][28][29]32,43,48,49 . It was shown, however, that the obtained topography depends on applied bias voltage V , and even a contrast reversal was observed for V = 0.2 V and −3.0 V 32 . In the following we make use the dual-bias mode described in Section II as it allows to visualize exactly the same surface area without relying on defects on top of the investigated surface (the appearance of defects may change with V , see Fig. 2). We have chosen values of V small compared to the barrier height Φ (see also below) yet larger than the hybridization gap of less than 20 meV 29,50-54 . In Fig. 2 dual-mode topographies for V = ± 0.2 V (upper) and ±0.02 V (lower) are compared. Note that here different samples were investigated at somewhat different temperatures of T ∼ 6 K (upper) and 1.7 K (lower). Qualitatively, the topographies for given temperature agree very well, i.e. there is no contrast inversion of reversed V . There are subtle inhomogeneities in the background at T ∼ 6 K; we can only speculate that they result from a not fully developed conducting surface state because we so far did not observe such inhomogeneities at T ≤ 1.7 K (see also discussion of Fig. 7 below). We note that very similar inhomogeneities are reported on atomically flat surfaces, Fig. S1B in 30 .
To investigate the surface termination in more detail we present in Fig. 3 topographies on areas exhibiting steps of less than one unit cell height a 28 . Such steps are perfectly suited to gain information about the different surface terminations. Again, the topographies obtained in dual mode with V ± 0.2 V agree on a qualitative level. The white arrows in Fig. 3 indicate the main crystallographic directions 100 and 010 . Height scans taken along the blue lines, i.e. parallel to one of the main crys-tallographic directions and at overall unchanged height, clearly indicate lateral distances between corrugations consistent with the lattice constant a, while such taken along descending height (red arrows) exhibit less obvious corrugations (possibly related to crystallographic imperfections within such regions of changing overall height). Within elevated areas (bright regions), however, the corrugations appear to run along the diagonal, i.e. 110 , directions. This is consistent 27,28 with a Sm-terminated surface where also, in addition to the Sm atoms, the apex atoms of the B-octahedra are seen, see discussion of Fig.  8 below as well as the crystal structure shown in Fig. 4.
We now turn to the height scans taken along the red arrows in the topographies which, again, follow a 100 direction but also include a height change. Atomic distances corresponding to a can be seen for V = +0.2 V, but less well for V = −0.2 V. Clearly, the total change in height depends to some extent on V : It amounts to about 130 pm for V = +0.2 V and ∼100 pm for −0.2 V. Yet, both numbers appear to be consistent with the expected step height upon going from a Sm-to a B-terminated surface considering the inter-octahedron B distance of 164.6 pm. Given the fact that distances of a are observed along the main crystallographic directions on this (001) plane such a step height is difficult to interpret otherwise; a viable alternative is the opposite assignment (i.e. going from a B-terminated surface down to a Sm- terminated one) which would, however, involve breaking up of B-otcahedra, i.e. intra-octahedral bond breaking. Estimates of the surface energy 29,31 indicate a slight preference for inter-octahedral bond breaking but impurities or sample inhomogeneities and defects may change these estimates locally. Indeed, a donut-like structure was interpreted as breaking inter-octahedral bonds 27 .
In order to gain further insight into the different terminations exposed in Fig. 3 tunneling spectroscopy was conducted. The STS curves shown in Fig. 4 correspond in color to the areas marked in Fig. 3 (right) over which the spectra were averaged. These spectra can be compared to those obtained on small areas of atomically flat surfaces, but differ from those seen on larger areas in that there is no pronounced maximum in dI/dV at around −20 mV 28 . The orange spectrum attained on the elevated part of the topography Fig. 3 exhibits a well developed hump at V ∼ +10 mV 27,28,45 . It is tempting to compare this hump to the conspicuous maximum observed on Smterminated surface of larger areas 27,28 . Note that we did not observe ( Fig. 4 and 28 ) a pronounced shift in energy of features at negative V as reported elsewhere 49 .
The discussion above indicated that a (2 × 1) reconstruction is energetically favorable with respect to the polar nature of a Sm-or B-terminated surface. However, a similar effect is conceivable if the (2 × 1) reconstruction is not long-ranged, but realized only locally. The lines of Sm may then meander 28,31 not giving rise to a superstructure 52 . Part of such a "disordered" reconstructed surface is shown in Fig. 5. In such a case, a similar change in height upon going from the topmost Sm atoms to the underlying B layer is expected as in Fig. 3. The height scan, Fig. 5 (right), along the red line marked in the topography indeed supports this assertion.
In one instance, we observed a topography as presented in Fig. 6. The height scan may be interpreted as every third row of atoms missing. Here, the height change between the upper and lower rows of atoms is only about 30 pm, similar to 28 or slightly smaller (Fig. 1) than the case of (2 × 1) reconstructions. The exact number, however, may depend on details of the tip, i.e. how well it may penetrate between the rows of atoms, and may even be much smaller 30,43 .
It should be noted again that our assignment of Smor B-terminated surfaces depends largely on the exact cleave, i.e. whether inter-or intra-octahedral bonds are broken. Albeit the former is, as mentioned above, energetically favorable, the latter may also occur as suggested by the observation of so-called donuts 27,31 .
In Fig. 7  ing lattice is not disturbed beyond the defects. Other defects, #5 (orange) and #6 (black) in the lower right panel, appear to be incorporated into the lattice as also the immediate lattice sites seem influenced. Albeit conceivable, there is no evidence for an exchange of B by Al in pure SmB 6 55 (note that this refers to substitution of individual B atoms by Al, not to Al inclusion of nonnegligible size 56,57 ). In the Th-Pd-B system it was found that Pd may replace two adjacent B atoms belonging to neighbouring octahedra 58 . Along the same line one may speculate that a similar replacement of adjacent B atoms by impurities near the surface may result in the observed slight displacement of surface atoms. Qualitatively different are the defects #3 (light blue) and #4 (magenta). Here, the lateral position (again, the vertical dashes indicate distances of a) and the height oscillation of the protrusions appear to remain unchanged while the height level is either raised (#3) or lowered (#4) by about 15-20 pm over distances of about 2 lattice constants from the center of the defect. We speculate that the defect itself is located in a subsurface layer, possibly on a Sm site, leaving the B-octahedra intact. It should be noted that this type of defect seems qualitatively different from the background inhomogeneity of Fig. 2. Albeit a clear assignment of either one of these features to structural or electronic inhomogeneities is speculative at present, it is obvious that a clean surface is a prerequisite for their observation. It should also be noted that dents of about 80 pm have so far only been observed on Sm-terminated surfaces 28 . The topography of such dents is very similar to the surface structure of La-terminated LaB 6 where La atoms are missing from the topmost layer 59 . Therefore, it should be highly instructive to investigate Sm-deficient samples Sm 1−x B 6 and attempt to correlate the Sm-deficiency x with the occurrence of these dents.

B. EuB6
In contrast to SmB 6 , the ferromagnetic semimetal EuB 6 has so far only scarcely been investigated by STM 35 even though its electronic structure is not fully understood, see 33,60 and references therein. Hence, STS-in particular by using a spin-polarized tip-may provide fresh insight. In the following, we focus on the surface topography.
In Fig. 8 we compare the topographies of rare-earth terminated samples EuB 6 and SmB 6 . In both cases, atomically flat and clean surface areas could be found after cleaving. The blue lines in the topographies indicate where the height scans parallel to the crystallographic 100 directions were taken. The corrugations of heights 30-40 pm are spaced apart by one respective lattice constant a. However, at the center of the square arrangements of these main corrugations in the topography (resulting from the cubic structure) additional humps are seen, also forming a regular, square arrangement. This is evidenced by the red height scans along the diagonal 110 directions, with the distances between the main and the interjacent smaller corrugations corresponding to a/ √ 2. Based on the distances and orientations, the higher protrusions were assigned 27,28 to the rare-earth atoms and the smaller ones to the apex of the B octahedra, again assuming breaking inter-octahedral bonds upon cleaving. We emphasize that the observation of in- terjacent smaller corrugations along 110 is pivotal for the assignment of the surface termination, yet requires sufficiently large, atomically flat and clean surface areas. However, the consistent observation of this type of surface topography on two different members of the hexaboride family makes a plausible case.
Based on DFT calculations it was suggested that the work function for a Sm-terminated surface of SmB 6 is about 2 eV, and at least twice as high on a B-terminated surface 29 . We therefore started to investigate the tunneling barrier height Φ, which is related to the work functions of the sample and the tip (Φ s and Φ t , respectively). The tunneling current I decreases exponentially with increasing tip-sample distance ∆z, i.e. I(z) ∝ exp(−2κ ∆z). The barrier height Φ can be calculated from κ 2 = 2me 2 Φ, where m e is the bare electron mass. Figure 9 shows two curves I(∆z) obtained on a clean B-terminated EuB 6 surface shown in the inset. The barrier heights for the two exemplary curves are Φ = 4.7 eV and 5.6 eV, i.e. they vary by almost 1 eV. Unfortunately, because of their highly infrequent occurrence we were not able so far to measure Φ on a Eu-terminated surface. It therefore remains to be seen whether a measurement of the barrier height can help in identifying the termination of clean EuB 6 surfaces.
In the case of SmB 6 , both the investigation of slightly Gd-substituted samples with W tunneling tips and of pristine SmB 6 with Cr tips resulted in a strong suppression of the surface state 61 . In fact, the dI/dV curves in close proximity to magnetic defects and taken with magnetic tip are akin to spectra obtained with W tip on pristine SmB 6 at 20 K, a temperature high enough such that the surface states do not significantly contribute to the tunneling spectra. These observations are expected for topologically nontrivial surface states close to atoms carrying a sizable magnetic moment arising from an exchange interaction 62,63 . Given this achievement in utilizing Cr tips as well as the magnetic properties of EuB 6 we also started to investigate surfaces of EuB 6 with magnetic Cr tunneling tips. One particularly intriguing example, attained in dual-bias mode for V = ±0.2 V, is presented in Fig. 10. The dual-bias mode is important as an only partial contrast reversal for the two different V -values is observed, rendering a position adjustment of subsequently obtained images based solely on defects less reliable. This partial contrast reversal also complicates the assignment of the observed features: While the prominent bright lines seen for V = +0.2 V correspond in height (see green scan line and green height profile) to Sm atoms, Fig. 5, and might be interpreted as Eu atoms, the same lines appear dark, i.e. as dents, for V = −0.2 V. We note that by utilizing a magnetic tip, contrast changes may be expected mostly on surfaces of magnetic materials. Importantly, the height profiles measured along these lines did not show any contrast reversal upon reversing V (compare the blue and red height scans in Fig. 10). The corrugations along these lines exhibit a periodicity of 2a. Taken together, one may speculate about the formation of magnetic Eu dimers on the surface of EuB 6 . Clear of these lines, there is no obvious indication for a formation of such dimers: The green height scan exhibits corrugations (away from the aforementioned line) with distances corresponding to a. However, the apparent changes in contrast in areas between the line features upon reversal of V render this picture incomplete, at least. Clearly, measurements in magnetic fields are called for, but so far we were not able to locate such a topographic feature in our STM system with magnetic field capabilities.

IV. CONCLUSIONS
Investigating topographies on a large number of SmB 6 and EuB 6 samples revealed different surface terminations which show similarities between these two hexaborides. Such similarities are obvious for the rare-earth termi-nated surfaces, a termination that is rather rare 27,28 but essential when attempting an assignment of the different terminations. In addition, utilizing a dual-bias mode allowed a comparison of topographies obtained with different bias voltages on exactly identical surface areas without relying on defects. Along with the observations of step heights less than a, these observations made a reliable assignment of the rare-earth and B-terminated surfaces possible. Apart from these atomically flat terminations, we observed different line structures which may correspond to lines of rare-earth atoms on top of an otherwise B-terminated surfaces. Some of these structures exhibited intriguing properties, also if probed by magnetic tips, which warrants further study.

V. ACKNOWLEDGEMENT
We thank Silvia Seiro, Ulrich K. Rößler, Frank Steglich, Hao Tjeng and Jens Wiebe for support and discussions.
Financial support from the Deutsche Forschungsgemeinschaft within the priority program SPP1666 is gratefully acknowledged. Work at Los Alamos was performed under the auspices of the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering.