Surface reconstructions and electronic structure of metallic delafossite thin films

In recent years, metallic oxides with a delafossite structure have captured significant attention due to their extraordinary structural and electronic characteristics. PtCoO₂ single crystals are distinguished by their unparalleled high conductivity per carrier. Similarly, PdCoO₂ single crystals possess the longest mean free path of up to 20 μm at 4 K, surpassing all other known oxide materials.^1–3 The structure of these delafossites consists of layers of platinum (or palladium) that create a single, closed electron pocket at the center of the Brillouin zone at the Fermi level (E_F), which is pivotal for the high conductivity in PtCoO₂ (PdCoO₂) single crystals.^4–6 The CoO₂ layers adjacent to these conductive platinum (or palladium) layers serve as insulating spacers, leading to the out-of-plane resistivity being more than 1000 times higher than the in-plane resistivity in PdCoO₂ single crystals at low temperature.^1,7 Notably, PtCoO₂ films maintain relatively high conductivity even with reduced dimensionality, exhibiting diminished sensitivity to film thickness in comparison to copper.⁸ Among delafossite compounds, PdCrO₂ is particularly remarkable for its unique combination of antiferromagnetic order (AFM) at around 37 K while maintaining its metallic conductivity.^9,10 It exhibits a finite interlayer coupling between palladium layers and adjacent insulating CrO₂ layers, making this an interesting system to study Kondo-like couplings in a hidden Mott material.^9–13 

With their unique layered structures, metallic delafossites offer opportunities to create novel low-dimensional materials with distinctive properties and functionalities. The polar layers in delafossites, denoted as A¹⁺ (A = Pt, Pd) and $BO21−$ (B = Co, Cr) in the bulk, exhibit distinct surface states when cleaved in vacuum, effectively addressing the challenges posed by polar surfaces.¹⁴ The A polar surfaces facilitate pronounced electron doping and stabilize the surface states of platinum and palladium layers, whereas hole-doped surface states emerge at the BO₂ terminations. The CoO₂-terminated surface displays a substantial spin splitting of the surface states, arising due to a strong breaking of the inversion-symmetry at the surface.¹⁵ The ferromagnetism observed in the palladium surface state opens up possibilities for creating two-dimensional ferromagnets.^14,16 The superlattice structures of PdCoO₂ and PdCrO₂, characterized by structural symmetry breaking, provide a potential avenue for studying interlayer electron interactions. In addition, the Fermi surface of PdCrO₂, which has predominantly palladium character, undergoes a magnetic reconstruction into a $3×3$ pattern driven by AFM order at low temperatures.^9–13 Despite the significant promise held by low-dimensional delafossites, interpretation of surface reconstruction in thin films is complicated by the simultaneous presence of surface states and electronic reconstructions driven by AFM order. This complexity underscores the need for further detailed investigations to decipher the intricate phenomena underlying these observations.

Through the powerful combination of molecular-beam epitaxy (MBE) and angle-resolved photoemission spectroscopy (ARPES), we have grown films of PtCoO₂, PdCoO₂, and PdCrO₂ with controlled terminations, enabling a detailed investigation into their electronic structures. These delafossites exhibit distinct surface reconstructions, including a new 2 × 2 surface reconstruction in PdCrO₂ that has never been previously reported for any delafossite material. Utilizing first-principles density functional theory (DFT) calculations, we demonstrate that surface reconstructions induced by excess oxygen significantly reduce the surface energy for A terminations, while BO₂ terminations exhibit relative stability compared to A terminations. In order to show a comprehensive comparison of the metallic delafossites – PtCoO₂, PdCoO₂, and PdCrO₂—We present side-by-side ARPES, low-energy electron diffraction (LEED), reflection high-energy electron diffraction (RHEED), and first-principles calculations of these materials in the subsequent figures.

Metallic delafossite thin films of PtCoO₂, PdCoO₂, and PdCrO₂ are synthesized in a Veeco Gen10 MBE system on (001) sapphire substrates. The atomic structure of delafossites, exemplified by PtCoO₂, is illustrated in Fig. 1(a). The growth process is described in detail in the supplementary material. Figure 1(b) presents the results of PtCoO₂ films’ growth in an adsorption-controlled regime, highlighting the narrow growth window for achieving single-phase PtCoO₂ films. The atomic force microscopy image in Fig. 1(c) reveals 180° in-plane rotation twins within these films, in agreement with prior reports of the epitaxial growth of PtCoO₂, PdCoO₂, and PdCrO₂ films on (001) Al₂O₃ substrates.^17–25 The pure-phase nature of the PtCoO₂ films is confirmed by θ–2θ x-ray diffraction scans in Fig. 1(d). Resistivity vs temperature measurements of a 13.3-nm-thick PtCoO₂ film, conducted using a Quantum Design Physical Property Measurement System (PPMS) employing a four-point van der Pauw geometry, are shown in Fig. 1(e). As the 4-nm-thick PdCoO₂ buffer layer is quite flat as shown in the supplementary material (Fig. S1), its resistance has been subtracted out of the resistance measurement of the PtCoO₂ film (assuming a simple parallel resistance model). The resistivity of the PtCoO₂ film is subsequently calculated using the average thickness of the PtCoO₂ film. The residual resistivity ratio (RRR = ρ_300K/ρ_4K) of this PtCoO₂ film is 1.91 in its as-grown state (i.e., without any ex situ post anneal). For comparison, the RRR of a PtCoO₂ single crystal is 52.5.³ The resistivity of our PtCoO₂ film shows a similar linear temperature dependence behavior at high temperatures to that observed in the single crystals. The resistivity comparison between the film and the single crystal is shown in the supplementary material (Fig. S1). The microstructure of the PtCoO₂ film is investigated by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images in Fig. 1(f) and electron energy-loss spectroscopy (EELS) maps found in the supplementary material (Fig. S4). Details on the growth method, as well as the structural and electrical characterization of PdCrO₂ films, can be found in the supplementary material (Figs. S2 and S3). All PtCoO₂ films investigated in this study exhibit a mixed termination of platinum and CoO₂, a result of the adsorption-controlled method utilized to produce them.²⁴ The palladium termination of the PdCoO₂ film and the CrO₂ termination of the PdCrO₂ films were achieved via the shutter-controlled growth method employed for their growths, as described in prior work.^22,24 Note that not all delafossite films with the described terminations exhibit surface reconstructions. For example, no reconstruction features are present in the Pd- and CoO₂- terminated PdCoO₂ films described in Ref. 24. This points to a multitude of routes to compensate for the polar surface charge in these materials and a delicate balance of energetics. The precise conditions for stabilizing the different reconstructions observed in these delafossite films, thus, require further study.

ARPES measurements were employed to investigate the bulk states and surface reconstructions of metallic delafossite films. ARPES measurements were conducted using lab-based ARPES systems, which consist of a Scienta Omicron VUV 5000 emitting He-I photons at 21.2 eV and He-II photons at 40.8 eV, and a Fermion Instruments BL1200s discharge lamp for neon-I photons at 16.85 eV.²⁶ The detection of emitted electrons was performed using a VG Scienta R4000 electron analyzer. Prior to ARPES measurements, all films were exposed to air and then underwent re-annealing in ozone at a background partial pressure of 5 × 10⁻⁶ Torr at 480 °C for 5 min.

In Figs. 2(a), 2(c), and 2(e), we compare the Fermi surfaces of PtCoO₂, PdCoO₂, and PdCrO₂ films, respectively. Specifically, Fig. 2(a) highlights a hexagonal pocket, denoted as the α band. This intense band is centered at the Γ point and represents the platinum-driven band of PtCoO₂, consistent with observation from previous studies on PtCoO₂ single crystals.² Interestingly, in addition to the bulk α band, additional band features labeled as α′ bands are observed both at E_F and 150 meV below it, as shown in Figs. 2(a) and 2(b). These α′ bands occupy a similar momentum position to those of the reconstructed bands in PdCrO₂ at low temperatures.^11,13 While the known additional bands in the PdCrO₂ case arise due to band folding at the magnetic Brillouin zone boundary, we will show below that these new states in PtCoO₂ films reflect a new surface reconstruction. This observation is corroborated by the observation of the same α′ bands identified in another PtCoO₂ film using 16.85 eV photons, whereas these bands were absent in the ARPES data obtained with 40.8 eV photon energy, as shown in Figs. S6 and S7 in the supplementary material. The absence might be related to the photon energy dependence of the relevant photoemission cross section.

In a palladium-terminated PdCoO₂ film, analogous new band features referred to as β′ bands were found as shown in Figs. 2(c) and 2(d). The PdCoO₂ bulk state, denoted as the β band, primarily exhibits palladium character according to prior work on PdCoO₂ single crystals.^14,27,28 It is important to note that the β′ bands in the PdCoO₂ film differ from the symmetry of surface states attributed to palladium and CoO₂ layers, as discussed in previous work.^14,24,29 Thus, the presence of the α′ bands in PtCoO₂ films and the β′ bands in PdCoO₂ films is new territory compared to prior work.

The band structure of the PdCrO₂ film is shown in Figs. 2(e) and 2(f). Although the band structures of PdCoO₂ and PtCoO₂ are similar, that of PdCrO₂ exhibits distinctive behavior. This band structure exhibits a hexagonal pocket β band centered at Γ point, representing the primary palladium character of the bulk state, in line with previous reports on PdCrO₂ single crystals.^11,13 The bulk bands observed in PtCoO₂, PdCoO₂, and PdCrO₂ films are consistent with our independent DFT calculations (see Fig. S11 in the supplementary material).²⁸ Nonetheless, the PdCrO₂ film also presents additional band features, denoted as β″ bands, which have not been reported in any prior delafossite materials. Note that the data for the β″ band in our PdCrO₂ film were obtained above the AFM transition temperature, suggesting that this band’s presence is not associated with the AFM order in PdCrO₂. Nevertheless, the β″ bands are also present in the ARPES result of this PdCrO₂ film taken at 6 K, as shown in the supplementary material (Fig. S5). Moreover, the β″ band exhibits distinct dispersion compared to the reconstructed bands driven by AFM order in PdCrO₂ single crystals. In addition, the β″ bands are also present in a thinner PdCrO₂ film (4 nm thickness) as shown in Fig. S8 in the supplementary material. Nonetheless, not all the PdCrO₂ films with CrO₂ termination exhibit the β″ bands. Figure S9 in the supplementary material shows the dispersions at the M point of the PtCoO₂ and PdCrO₂ films.

We further compare the dispersion of these additional bands in the metallic delafossite films along the Γ-K direction, as illustrated in Fig. 3. Figures 3(a), 3(d), and 3(g) display the momentum dispersion curves at E_F of the PtCoO₂, PdCoO₂, and PdCrO₂ films, respectively. The high-intensity α band in Fig. 3(a) and the highly dispersive β bands observed in Figs. 3(d) and 3(g) correspond to the platinum and palladium bulk state in PtCoO₂, PdCoO₂, and PdCrO₂ films, as previously shown in Figs. 2(a), 2(c), and 2(e). The α′ band in the PtCoO₂ film and the β′ band in the PdCoO₂ film exhibit similar dispersion, as illustrated in Figs. 3(c) and 3(f). Conversely, the β″ band in the PdCrO₂ film displays a distinct k_F position compared to the α′ band in the PtCoO₂ film and the β′ band in the PdCrO₂ film, as shown in Fig. 3(i). In addition, Fig. 3(a) reveals the subtle presence of an additional γ band in the PtCoO₂ film, a feature also shown in Fig. 2(a). This γ band could potentially be associated with a platinum surface state, similar to the palladium surface state observed in PdCoO₂ single crystals.¹⁴ Given the analogous behavior of the α′ band in the PtCoO₂ film and the β′ band in the PdCoO₂ film, our analysis now focuses on the comparison between the PtCoO₂ and PdCrO₂ films.

To investigate the surface reconstructions of the PtCoO₂ film and the PdCrO₂ films, we analyzed their LEED images displayed in Figs. 4(a) and 4(c). In the composite LEED image of the PtCoO₂ film [Fig. 4(a)], the reciprocal lattice of PtCoO₂ is marked by red solid diamonds, as shown by the red solid hexagonal zone in the center. A distinct $3×3$ reconstruction with a 30° rotation is indicated by the green diamonds along with a less pronounced 4 × 4 reconstruction signified by the yellow hexagons. The $3×3$ reconstruction with a 30° rotation is simplistically denoted as $3×3$⁠. The green zones (solid lines) and yellow zones (dashed lines) denote the pronounced $3×3$ and the subtle 4 × 4 reconstructed orientations, respectively. Importantly, these reconstruction patterns observed in the PtCoO₂ LEED image correspond precisely with those observed in the RHEED image along the [100] direction in reciprocal space, as evidenced by comparing the white dashed line in Fig. 4(a) with the peak positions in the RHEED image [Fig. 4(b)]. Similarly, the LEED image for the PdCrO₂ film [Fig. 4(c)] displays the reciprocal lattice of PdCrO₂ denoted by red solid diamonds, with a strong 2 × 2 reconstruction denoted by blue hexagons and a weak $3×3$ reconstruction represented by green diamonds. The blue zones (solid lines) and green zones (dashed lines) represent the strong 2 × 2 and the weak $3×3$ reconstructed orientations, respectively. Once again, the reconstructions identified in the LEED images are seen to be consistent with the peaks observed in the RHEED image along the [100] direction, as indicated in Figs. 4(c) and 4(d), ensuring a consistent interpretation of the surface reconstructions across different imaging techniques.

A detailed analysis of the Fermi surface measured on the PtCoO₂ film is performed by extracting the bulk α band at E_F in Fig. 2(a) and folding it with the $3×3$ reconstruction. The corresponding results are presented in Fig. 4(e), where we observed a striking match between the additional band features at E_F (α′ band) and the folded band with the $3×3$ reconstruction. Despite its presence in both the LEED and RHEED analyses of the PtCoO₂ film, we did not observe any additional 4 × 4 reconstruction at E_F. It is worth noting that the intensity of the 4 × 4 reconstruction is considerably weaker compared to the $3×3$ reconstruction, which may account for its limited visibility. Similarly, we folded the bulk band of the PdCrO₂ film at E_F, which revealed an almost exact correspondence between the additional β′ band and the band folded with the 2 × 2 reconstruction, as presented in Fig. 4(f). Interestingly, the band structure of the PdCrO₂ film at E_F did not exhibit the $3×3$ reconstruction suggested by the LEED result. This discrepancy could be attributed to the relatively weak $3×3$ reconstruction compared to the 2 × 2 reconstruction, as evidenced in the LEED analysis of the PdCrO₂ film presented in Fig. 4(f).

Our findings provide conclusive evidence for the primary $3×3$ surface reconstruction in the PtCoO₂ film, which is also observed in the PdCoO₂ film. In addition, the main 2 × 2 reconstruction has been firmly identified in the PdCrO₂ film. Evidence of these reconstructions is consistently detected by the ARPES, LEED, and RHEED measurements on our films. Nonetheless, such specific reconstructions have not been previously reported in delafossite materials, which are usually prepared by cleavage of single crystals, prompting further investigation into their origin. Figure 4 elucidates the consistency between the RHEED data and the reconstructions observed in LEED results. We further conduct a comparative analysis of the RHEED images of the PdCoO₂ film [in Figs. 2(c) and 2(d)] at various stages of growth, enabling real-time monitoring during the growth process. These RHEED images, presented in Fig. S10 in the supplementary material, reveal the emergence of one-third-order peaks during the annealing of the as-grown PdCoO₂ film in distilled ozone and persist throughout the cooling process. Remarkably, these one-third-order peaks in the PdCoO₂ film mirror those seen in the PtCoO₂ film [Fig. 4(b)], corresponding to the $3×3$ reconstruction. This observation suggests a potential link between the $3×3$ reconstruction and excess oxygen on the film surface, implying that excess oxygen on the surface may mitigate the polar surface charge by reducing the surface energy. Note that the PdCoO₂ film possesses a full layer of palladium termination, introducing a positive charge. The additional oxygen helps to neutralize this polar surface charge, thus lowering the surface energy. Addressing the challenges of polar surfaces can be approached in various ways; for instance, when the PtCoO₂ film is grown by co-deposition, the result is a mixed termination by platinum and CoO₂. It is important to mention that all films are subjected to annealing in distilled ozone to provide fresh surfaces prior to the ARPES measurement; thus, there are multiple steps during growth and annealing where excess oxygen is supplied and could, thus, attach to the film surface should it be energetically favorable to do so.

Given the limitations of STEM to clearly resolve surface atoms, we next discuss the potential surface scenarios compatible with $3×3$ and 2 × 2 reconstructions through DFT calculations. We have chosen to omit scenarios leading to the weak 4 × 4 reconstruction observed in PtCoO₂ due to the complexity introduced by their large supercell sizes. For the $3×3$ reconstruction, the scenarios considered include the presence of one oxygen vacancy (⁠$3×3$ −1/3 oxygen), an excess of A-site atoms on a BO₂-terminated surface (⁠$3×3$ + n/3 A-site), and an excess of oxygen atoms on an A-terminated surface (⁠$3×3$ + n/3 oxygen), where n equals 1 or 2. Similarly, for the 2 × 2 reconstruction, we explore the possibility of one oxygen vacancy (2 × 2 − 1/4 oxygen), an excess of A atoms on the BO₂-terminated surface (2 × 2 + n/4 A-site), and an excess of oxygen atoms on an A-terminated surface (2 × 2 + n/4 oxygen), where n is 1, 2, or 3. In addition, we have calculated the pristine surfaces, denoted as BO₂- and A-site termination in Fig. 5. For each scenario, we search for the lowest energy surface atomic configuration and then calculate its surface energy relative to the pristine BO₂-terminated surface. The results are illustrated in Fig. 5, with computational details available in the supplementary material (Fig. S12).

For all three compounds studied, the surface energies associated with creating an oxygen vacancy or adding excess A-site atom(s) on BO₂-terminated surfaces are found to be positive, often exceeding 0.5 eV per unit cell area (panels 1 and 3 in Fig. 5). This indicates that both removing oxygen from and adding A atom(s) onto the BO₂-terminated surface are energetically costly processes. Conversely, the introduction of excess oxygen atoms on A-terminated surfaces significantly lowers the surface energy, as shown in panel 5 in Fig. 5. In certain cases, this adjustment leads to negative surface energies when compared to the BO₂-terminated surface, suggesting that adding oxygen to A-terminated surfaces is energetically favorable and could lead to more stable surface configurations.

The above results further support the hypothesis that the reconstructions observed in PtCoO₂ (mixed termination) and PdCoO₂ (palladium termination) films could be attributed to excess oxygen, which effectively reduces the surface energy. In our ARPES and LEED results, the $3×3$ reconstruction is manifest on both PtCoO₂ and PdCoO₂ films. Nonetheless, our calculations indicate that scenarios leading to the $3×3$ reconstruction do not consistently exhibit the lowest surface energy. This discrepancy might originate from the limitation of DFT in accurately determining surface energies or could be due to additional complexities present on the experimental film surfaces that are not fully accounted for in the DFT models. For instance, the mixed termination observed in PtCoO₂ could alter the energy landscape in ways not captured by our DFT simulations. Therefore, while our DFT calculations align with our ARPES and LEED findings in suggesting that excess oxygen contributes to the observed reconstructions, they do not conclusively determine the size of the reconstructed supercell. In the case of PdCrO₂ films grown with CrO₂ terminations, scenarios involving excess oxygen are not applicable. This leaves the 2 × 2 reconstruction with 1/4 A-site addition as a scenario with relatively low surface energy, aligning with our experimental observations and presenting a possible explanation for the surface structure of PdCrO₂ films.

In conclusion, we have successfully synthesized high-quality PtCoO₂, PdCoO₂, and PdCrO₂ films by MBE, followed by a comprehensive investigation of their surface reconstructions using a combination of ARPES, LEED, and RHEED. Our investigations have unveiled the presence of surface reconstructions in these films, including a $3×3$ reconstruction in PtCoO₂ films with mixed platinum–CoO₂ terminations and in palladium-terminated PdCoO₂ film, as well as a distinctive 2 × 2 reconstruction is seen in CrO₂-terminated PdCrO₂ films. These findings, which are corroborated by ARPES, LEED, and RHEED analyses, highlight surface reconstructions in these films that have not been previously reported in delafossite single crystals. These new reconstructions are likely closely linked to the polar terminations of the as-grown thin films, where the additional atoms on pristine surfaces could potentially lower their surface energy. DFT calculations shed light on the relative instability of surfaces terminated with A (A = Pt, Pd) atoms compared to those terminated with BO₂ (B = Co, Cr), as evidenced by their higher formation energies. Nonetheless, the presence of excess oxygen can significantly mitigate these energies, leading to reconstructed configurations. Our results show general consistency (with some discrepancies) between the calculated and experimentally observed sizes of the reconstructed supercells. By elucidating the distinct surface reconstructions from the surface states associated with different terminations in metallic delafossites, as well as from the electronic reconstructions driven by magnetic order, our work not only contributes to the understanding of surface phenomena in delafossite materials but also sets the stage for further exploration of highly two-dimensional studies in this intriguing class of materials.