Structural distortions, especially layer buckling, are key to understanding and controlling the ferroic properties of hexagonal ternary intermetallics (composition ABC) [1][2][3]. For example, consider the parent centrosymmetric ZrBeSitype structure (space group P6 3 /mmc), which consists of planar graphitic (BC ) n-layers that are "stuffed" with an A n+ spacer [Fig. 1(a)]. Compounds with this structure are typically semimetals or Dirac semimetals, e.g., LaCuSn [4] and BaAgBi [5]. Upon decreasing the A n+ cation size via isovalent substitution, the (BC ) n-planes typically buckle in a unidirectional pattern due to increased interlayer interactions, to yield the polar LiGaGe-type structure [2,6] [space group P6 3 mc,Fig. 1(b)]. Here, the polar distortion gives rise to polar metallicity in the metallic state (e.g., LaAuGe, LaPtSb [7,8]) and predicted hyperferroelectricity in the insulating state (e.g., LiZnAs, NaZnSb), in which the long-range polarization is robust against the depolarizing field [2,9]. In such compounds the properties are determined by both the magnitude and the long-range ordering of the planar buckling, d, defined as the displacement along the c axis between dissimilar atoms in the buckled BC plane [2]. Due to this breaking of inversion symmetry, Weyl nodes are also predicted to exist in many LiGaGe-type ABCs (e.g., KMgBi, LiZnBi) [1,10,11]. Tuning the magnitude and sign of buckling is proposed to change the crystal momenta and chirality of the Weyl nodes, or cause them to merge into a single Dirac point [1]. All of these predicted properties are defined by the buckling d in the system; therefore it is crucial to understand the origins of the buckling observed in these structures.

Recent experiments and theory suggest that in addition to cation size, the electron count may be an important handle * jkawasaki@wisc.edu for controlling the layer buckling. Whereas most stable ABCs have 18 (or 8) valence electrons per formula unit corresponding to a filled s 2 p 6 d 10 (or s 2 p 6 ) configuration, the family LnAuSb (Ln = lanthanide) has 19 valence electrons. The extra electron destabilizes the unidirectionally buckled LiGaGetype structure, instead favoring a highly buckled structure with significant Au-Au interlayer bonding [Fig. 1(c),YPtAstype] [6]. Importantly, although the resulting dimer buckled structure is centrosymmetric, the magnitude of buckling in the AuSb planes is predicted to be much larger than that observed in the LiGaGe-type polar structure [6]. First-principles calculations also suggested that LaAuSb hosts a Dirac cone within 100 meV of the Fermi energy [6]. Therefore, an understanding of the coupling between electronic structure (electron count) and layer buckling in LnAuSb may be a path towards tuning the buckling, and hence ferroic properties, of LiGaGe-type compounds.

Here we use molecular beam epitaxy (MBE) to demonstrate the first epitaxial growth of LaAuSb. Our large area single-crystalline films enable detailed structure and electronic property measurements and provide a path towards integration in layered heterostructures. The films are single crystalline and epitaxial to the c-plane Al 2 O 3 substrate, as measured by x-ray diffraction (XRD) and reflection highenergy electron diffraction (RHEED). Scanning transmission electron microscopy (STEM) measurements reveal that the AuSb layer buckling is four times larger than the buckling in the 18-valence compounds LaPtSb and LaAuGe. Photoemission spectroscopy measurements of the valence bands are consistent with density functional theory calculations and suggest that buckling results from an electronic instability that is suppressed in the buckled Au-Au dimer structure. Our results provide a route towards tuning the layer buckling and potential ferroic order in hexagonal ABCs. LaAuSb films were grown in a custom MBE system (MANTIS Deposition) on Al 2 O 3 (0001) substrates (MTI) at a growth temperature of 650 • C as measured by a pyrometer. The lattice mismatch between LaAuSb and Al 2 O 3 is 3.2% tensile. Following the film growth, most samples were capped with amorphous Ge to prevent oxidation upon removal from the vacuum system. La and Au fluxes of 1.5 × 10 13 atoms/cm 2 s were supplied from effusion cells, as measured by an in situ quartz crystal monitor (QCM). Due to the high relative volatility of Sb, a 30% excess flux of Sb (2 × 10 13 atoms/cm 2 s) was supplied using a cracker cell, similar to the strategy used for cubic Heusler compounds [13][14][15]. Absolute fluxes were calibrated ex situ by Rutherford backscattering spectrometry (RBS). in which we observe only the expected sharp 000l reflections and no secondary phases. For comparison we also plot a 2θ scan of a LaAuGe film (blue online), which has 18 valence electrons and crystallizes in the undimerized LiGaGe-type structure [7]. The presence of the 0002, 0006, 00010, and 00014 superstructure reflections in the LaAuSb confirms the doubling of the unit cell along the c axis, consistent with Au-Au dimerization. For samples grown at temperatures below 500 • C, we do not observe the half-order superstructure reflections, suggesting a loss of long-range order. The superstructure-ordered sample grown at 650 • C displays sharp Kiessig fringes [Fig. 3(b)]. The fringe spacing, averaged up to the fifth order, of 0.21 • corresponds to a film thickness of 41 nm, or 98 f.u., in good agreement with the 100 f.u. expected from RHEED oscillations and QCM fluxes. Rocking curve widths for the film and substrate are sharp and approximately equal (3.32 and 3.5 arc sec, respectively), indicating a high degree of in-plane ordering [Fig. 3(d STEM measurements confirm the Au-Au dimerized structure with a high degree of AuSb layer buckling. These measurements were performed using a FEI Titan STEM equipped with a probe corrector using an operating voltage of 200 kV. High-angle annular dark-field (HAADF) STEM images were collected with a 24.5-mrad probe semiconvergence angle, a 18.9-pA probe current, and a HAADF detector range of 53.9-269.5 mrad. The sample was prepared for analysis using focused ion beam (FIB) milling. A FIB lamella was lifted out and attached to a Cu support grid prior to the final FIB milling to a thickness of ≈100 nm. The final milling step was done using Ar ion milling using a Fischione Nanomill operated at 900 V, bringing the sample to a final thickness of ≈20-40 nm before being transferred to the TEM column.

The high-precision images seen in Fig. 4 were obtained by applying a nonrigid registration [16] to the HAADF image series. Accurate positions of atomic sites were derived by fitting each peak on the HAADF image to a two-dimensional Gaussian function. Sampling across 26 Au-Au pairs, we measure a Au-Au bond length of b = 3.10 ± 0.02 Å, which is in good agreement with the 3.12 Å expected from powder diffraction refinement [6]. Averaging over 51 Au-Sb pairs, we find a planar buckling of d = 0.80 ± 0.02 Å also in good agreement with the 0.75 Å observed in bulk powder diffraction [6]. This buckling is approximately four times larger than the bucklings observed in LiGaGe-type compounds with similar stoichiometry. In comparison, LaAuGe and LaPtSb have d of 0.18 ± 0.01 Å and 0.22 ± 0.01 Å, respectively [7].

Magnetotransport properties were measured using a Quantum Design Physical Property Measurement System (PPMS). The resistivity versus temperature dependence at zero magnetic field shows strong metallic behavior with a residual resistivity ratio (RRR) of ρ 300K /ρ 2K = 2.25 [Fig. 5 multiple carriers since LaAuSb is expected to be a semimetal. Therefore to extract the densities and mobilities we fit to a two-band model of the form [17]

where n e (n h ) and µ e (µ h ) are the electron (hole) densities and mobilities, respectively. We first fit the slope of ρ xy vs B in the range 7-8 T to constrain the difference in carrier densities. We then adjust the concentrations and mobilities to fit ρ xy (B) over the full field range, checking that these parameters are also consistent with the zero-field resistivity ρ xx (0) = 1/(n e eµ e + n h eµ h ).

A representative fit of ρ xy at 2 K is shown by the solid red curve in Fig. 5(b), bottom panel. The extracted carrier densities and mobilities versus temperature are shown in Fig. 5(a), middle and bottom panels, respectively. We find weakly varying electron and hole densities of order 10 20 cm -3 , consistent with expectations for a semimetal, and mobilities approaching 1000 cm 2 /V s in the low-temperature limit (2 K).

To investigate the origins of the Au dimer buckling and its relation to electronic structure, photoemission spectroscopy measurements were performed at beamline 29-ID of the Advanced Photon Source (APS), using a Scienta R4000 analyzer (angular acceptance angle of 14 • ) and incident photon energies in the range 300 to 2000 eV (Fig. 6). The Fermi level was determined via reference measurements on a gold screw that is in electrical contact with the sample. To protect the surfaces, these samples were transported to the APS using an ultrahigh vacuum suitcase (pressure less than 10 -9 Torr, no Ge cap). For comparison with experiment, DFT calculations were performed using the Perdew-Becke-Ernzerhof (PBE) parametrization of the generalized gradient approximation including fully relativistic spin-orbit coupling effects (GGA + SO), as implemented in WIEN2K [18]. Further details about the calculation parameters can be found in Ref. [6]. For the dimerized structure we used the bulk atomic positions as reported in Ref. [6]. The calculated electronic structure is also consistent with Ref. [6].

We observe good qualitative agreement between the measured angle-integrated valence band spectrum (Fig. 6, black symbols) and the GGA + SO calculation for the dimerized structure [Fig. 6(b), shaded red curve]. The measured valence band width is approximately 1 eV and decreases to a sharp but finite minimum at the Fermi energy, consistent with the behavior expected for a semimetal or Dirac semimetal [6].

We also compare the photoemission measurement to a GGA + SO calculation for LaAuSb in a hypothetical undimerized LiGaGe-type structure [Fig. 1(b)]. For this hypothetical structure we fix the in-plane lattice constant and the out-of-plane functional unit spacing to those of the dimerized YPtAs-type structure and apply the same buckling d but in a uniform direction with a B-C-B-C layer stacking sequence. We find that this structure exhibits a sharp peak in the density of states just above the Fermi energy, which is expected to be unstable [Fig. 6(b), blue curve]. In comparison, for the dimerized structure there is a strong suppression in the density of states resulting in a pseudogap at the Fermi energy. Our measurements and comparisons with theory suggest an electronic origin for the dimerization, akin to a Peierls distortion, and consistent with the formal electron count of La 3+ 2 (Au-Au) 0 Sb 3- 2 suggested previously by first-principles calculations [6]. In this picture, the Au-Au dimerization is responsible for suppressing the density of states at E F .

In summary, we demonstrated the epitaxial singlecrystalline growth of the 19-valence-electron compound LaAuSb. Due to the strong electronic driving force for Au-Au dimerization, the resultant AuSb layer buckling is four times larger than the buckling observed in 18-electron ABCs. Our epitaxial films exhibit relatively large mobility and magnetoresistance with carrier concentrations consistent with those of a compensated semimetal. Lastly, we showed that our measured valence band structure is consistent with the proposed dimerized electronic structure, providing strong evidence for an electronic driving force towards Au-Au dimerization, and therefore buckling, in these 19-valence-electron-count compounds.