Epitaxial growth and electronic properties of mixed valence YbAl₃ thin films

Intermetallic compounds containing certain rare-earth elements with an open f-shell, such as Yb, Ce, U, Eu, etc., in a periodic arrangement form the so-called Kondo lattice that exhibits a plethora of emergent exotic properties such as unconventional superconductivity,¹ quantum criticality,² hidden order,³ and non-Fermi liquid behavior.⁴ Understanding how these emergent properties arise from competing energy scales, and the possibility to rationally manipulate these interactions, is essential for any prospect of exploiting these properties for potential applications. Growing these intermetallics in epitaxial thin film form opens up new avenues for dimensional confinement and strain engineering of the Kondo lattice,⁵ investigation of proximity effects,⁶ and the creation of tunable electronic states via artificial superlattices.⁷ 

In intermetallic YbAl₃, the Yb valence fluctuates between two configurations, Yb²⁺(f¹³) and Yb³⁺(f¹²).⁸ Its ground state is non-magnetic and has a Kondo temperature of T_K ≈ 670 K. Transport and thermodynamic measurements indicate that there exists another low temperature scale, T* ≈ 34 K–40 K, below which Fermi-Liquid-like behavior has been found to emerge.⁹ Moreover, it undergoes a much slower crossover from the high temperature local moment regime to the low temperature Fermi liquid regime than predicted by the Single Impurity Anderson Model (SIAM).^9,10 These observations along with the anomalies in the temperature-dependent soft x-ray photoemission spectroscopy measurements of bulk and Lu-doped single crystals suggest that Kondo lattice effects play an important role.^11,12 The microscopic mechanism governing this behavior, however, remains enigmatic. One reason is that YbAl₃ does not naturally cleave, which has precluded measurements of its electronic structure by momentum-resolved techniques such as angle resolved photoemission spectroscopy (ARPES) and spectroscopic imaging scanning tunneling microscopy (SI-STM). Measurements of fractured or scraped single crystals are complicated by multiple crystallographic faces¹³ and issues with surface quality, coupled with a propensity of the YbAl₃ surface to form oxides.¹⁴ One way of circumventing this difficulty is to synthesize epitaxial thin films and to measure them in situ with spectroscopic probes. Here, we report the first progress along this direction.

Thin films were grown on MgO substrates in a Veeco GEN10 MBE system with a liquid nitrogen cooled cryoshroud with a base pressure below 2 × 10⁻⁹Torr. Prior to growth, MgO substrates were annealed in vacuum for 20 min at 800 °C. Epitaxial (001) YbAl₃ films were achieved by first depositing a 1–2 nm thick aluminum buffer layer, followed by a LuAl₃ buffer layer on which YbAl₃ was grown. For the deposition of the LuAl₃ and YbAl₃ elements were co-deposited onto a rotating substrate from Langmuir effusion cells at a growth rate of ≈0.4 nm/min. During growth in situ reflection high-energy electron diffraction (RHEED) was used to monitor the surface evolution. After growth, the films were immediately transferred under ultra-high vacuum (5 × 10⁻¹⁰Torr) into an analysis chamber where low-energy electron diffraction (LEED) and in situ photoemission spectroscopy were performed. Bulk structural characterization was performed ex situ by four-circle x-ray diffraction (XRD) using Cu K_α radiation. The atomic scale structure of the YbAl₃ thin film was studied by aberration-corrected scanning transmission electron microscopy (STEM) and electron energy loss spectroscopy (EELS) performed on a FEI Titan Themis 300. Cross-sectional TEM specimens were prepared using a FEI Strata 400 Focussed Ion Beam with a final milling step of 2 keV to reduce surface damage. Films were further characterized by atomic force microscopy (AFM), scanning electron microscopy (SEM), and resistivity measurements.

Both YbAl₃ and its structural analogue LuAl₃ crystallize in a cubic AuCu₃ (L12) structure where Yb/Lu atoms occupy the vertices of the unit cell and Al atoms occupy the face-centered positions (Fig. 1(c)). Various compounds belonging to the same space group, such as AuCu₃ have been reported to show an order-disorder transition, where above a certain temperature the disordered face-centered cubic (FCC) phase is stabilized.¹⁵ In the disordered FCC phase, the occupation probability of all the lattice sites becomes $14$ for Yb/Lu and $34$ for Al atoms. Diffraction measurements can distinguish the cubic ordered phase, as its diffraction peaks should be observed for all values of h, k, ℓ indices, while for the disordered phase, the structure factor becomes zero when indices are mixed between odd and even h, k, ℓ indices. YbAl₃ and LuAl₃ have lattice constants of a = 4.2 Å and a = 4.19 Å, respectively. The lattice constants of MgO and aluminium are 4.21 Å and 4.05 Å, respectively, which provide a good lattice match to the LuAl₃ or YbAl₃ film. MgO and Al have a different space group (⁠$Fm3¯m$⁠) than that of ordered YbAl₃/LuAl₃ (⁠$Pm3¯m$⁠), but the surface atomic arrangement of the oxygen atoms on the (001) surface of MgO and the Al atoms on the Aluminum (001) surface provide an excellent template for the epitaxial integration of YbAl₃/LuAl₃ on MgO substrates with aluminum as a buffer layer (Figs. 1(a)–(c)). The face-centered sites and vertices are inequivalent for (⁠$Pm3¯m$⁠), and thus, the LuAl₃/YbAl₃ layers can nucleate either where the LuAl₃/YbAl₃ is in perfect registry with that of the Al unit cell (left domain in Fig. 1(d)) or where it is shifted by (⁠$12, 12$⁠, 0) (right domain in Fig. 1(d)), leading to the formation of anti-phase domains (Fig. 1(d)). Our EELS map confirms that there is negligible inter-diffusion across the boundary between the YbAl₃ and LuAl₃ layers (Fig. 1(e)).

In Fig. 2(a), we show an out-of-plane θ-2θ XRD scan. Prominent 001 and 003 Bragg peaks can be easily identified, confirming the films have the ordered L12 structure.¹⁶ Moreover, the observation of only 00ℓ film peaks establishes that our films are single phase with the desired (001) YbAl₃ out-of-plane orientation. Analysis of the peak positions reveals that the LuAl₃ layer is relaxed while YbAl₃ is strained to the underlying LuAl₃ layer. An azimuthal $ϕ$ scan of the (110) YbAl₃ film peak is shown in Fig. 2(b). The $ϕ$ scan in combination with the θ-2θ scans establishes the epitaxial relationship of YbAl₃/LuAl₃ with respect to MgO where (001)[100] YbAl₃/LuAl₃||(001)[100] MgO. Rocking curve measurements were performed on the 001 film peak and the 002 substrate peak, shown in Fig. 2(c). The full width at half maximum (FWHM) of the film peak was found to be 0.32° while that for the substrate peak was 0.03°.

The growth process was initiated first by depositing an aluminum buffer layer at a substrate temperature of 500 °C. RHEED patterns taken after the deposition process shown in Fig. 3(b) reveal large transmission spots indicative of 3D grains. Although depositing aluminum at elevated temperatures results in a rough surface, it also nucleates epitaxially oriented grains providing a template for the growth of epitaxially oriented YbAl₃/LuAl₃ layers. Growing YbAl₃/LuAl₃ directly on MgO or depositing the Al buffer layer at a lower temperature resulted in a mixed orientation where a secondary orientation with (111) YbAl₃/LuAl₃||(001) MgO was observed. Films grown directly on MgO were also found to be much rougher by AFM as YbAl₃/LuAl₃ layers do not wet the MgO (001) surface well. Subsequently, a second buffer layer of LuAl₃ was deposited at a substrate temperature of 200 °C and annealed in vacuum at 350 °C for 30 min. The deposition of the LuAl₃ buffer layer was also important to achieve epitaxial YbAl₃ films, as growing YbAl₃ directly on the aluminium buffer layer resulted in secondary phases. As the LuAl₃ growth proceeded, the RHEED pattern became more and more two-dimensional as individual grains coalesced into a flat surface (Fig. 3(d)). Thicker LuAl₃ buffer layers and post-annealing resulted in better quality films. Finally, the sample was cooled down to 200 °C for the deposition of the YbAl₃ layer. The growth temperature was ramped up to 315 °C after initiating growth at 200 °C. During growth, half-order peaks can be seen in RHEED images taken along the [100] azimuth (Fig. 3(e)), indicating that the YbAl₃ film grows with the ordered L12 structure (Fig. 1(c)).

In situ LEED patterns (Fig. 4(a)) indicate that the surface of the films is ordered with no additional surface reconstruction. The smoothness of the films was confirmed by AFM measurements (Fig. 4(b)) revealing a smooth surface with an rms roughness of only ≈1.8 Å over a 1 μm × 1 μm field of view. SEM and corresponding energy dispersive x-ray spectroscopy (EDX) measurements on a 35 nm thick LuAl₃ film with a 1.2 nm aluminum buffer shown in (Figs. 4(c) and 4(d)) reveal small aluminum-rich regions where excess aluminum has precipitated out. This observation is in agreement with the Yb–Al phase diagram (at temperatures relevant to our study a two-phase Al + YbAl₃ region exists).¹⁷ The expulsion of excess aluminum from the film ensures robustness of the growth method against slight flux mismatch, ensuring correct stoichiometry of our films.

Having investigated the structural aspects of our thin films, we now turn to their electronic properties. Four-point resistivity measurements were performed in a van der Pauw geometry using both a home-built dipper setup and a Quantum Design PPMS system. The temperature-dependent resistivity for a 20 nm YbAl₃/1.6 nm LuAl₃/1.2 nm Al and 35 nm LuAl₃/1.2 nm Al thin films are shown in Figs. 5(a) and 5(b), respectively. The resistivity curves are found to be qualitatively similar to that obtained for corresponding single crystals.¹⁸ The resistivity of YbAl₃ is plotted as a function of T² in the inset of Fig. 5(a), which shows that the film deviates from T² Fermi liquid behavior (⁠$ρ(T)=ρ0+AT2$⁠) above T^* ≈ 37 K, similar to single crystals,⁹ albeit with a lower residual resistivity for the single crystals. The roughness of the aluminum buffer layer employed at the beginning of the growth process and the presence of anti-phase domain boundaries could be potential contributors to both the higher residual resistivity and wide rocking curves (Fig. 2(c)) of our thin films. The T² coefficient of resistivity in our thin films is A = 6 × 10⁻⁴ ± 1 × 10⁻⁴μΩ cm/K² similar to the earlier reported values for single crystals.^19,20 Assuming a similar value of γ = 45 mJ/mol K² in our thin films as in single crystals, we obtain a Kadowaki Woods ratio (A/γ²) of ≈3 × 10⁻⁷μΩ cm mol² K²/mJ², which is orders of magnitude lower than the universal behavior observed in many f electron systems, A/γ²= 1 × 10⁻⁵μΩ cm mol² K²/mJ².²¹ This apparent discrepancy can be reconciled by incorporating corrections due to the large degeneracy (N = 8) of the Yb 4f J = 7/2 in the ground state that gives a value of A/γ²= 3.6 × 10⁻⁷μΩ cm mol² K²/mJ².²² 

Finally, Fig. 6 shows in situ photoemission spectra (PES) at normal emission obtained from these films. All measurements were taken using a monochromatized VUV5000 helium discharge lamp using a photon energy of 21.2 eV and a Scienta R4000 analyzer in a UHV chamber with base pressure better than 5 × 10⁻¹¹Torr. The observed spectra show two sets of characteristic features corresponding to f¹³ and f¹² final states, respectively, indicative of YbAl₃ being a mixed valence compound. This is again consistent with earlier measurements of YbAl₃ single crystals.^11,23 Spectral peaks very close to the Fermi level with a binding energy of 0.03 eV and 1.34 eV, respectively, constitute features derived from Yb²⁺f¹³ final states, where the former is derived from the Yb²⁺f¹³ J = 7/2 final state, also known as the Kondo resonance peak, while the latter is the spin orbit split peak derived from the Yb²⁺f¹³ J = 5/2 final state. Peaks marked with asterisks in Fig. 6 at binding energies 0.6 eV and 1.9 eV are corresponding surface core levels. The difference in binding energies between the bulk and surface doublets in our measurements is found to be ≈0.6 eV, consistent with earlier PES measurements.^11,23 Spectral features observed at binding energies between 5 and 11 eV are derived from the Yb³⁺f¹² final states. Estimating the intensity of the photoemission peaks derived from Yb²⁺ and Yb³⁺ final states, we obtain, in our thin films, a mean Yb valence of 2.78 ± 0.06 at 21 K. The Yb valence estimated from our thin films is consistent with earlier low energy photoemission (2.77 at 10 K)²³ and x-ray spectroscopy measurements (2.78 at 20 K),^24,25 but is higher than that estimated from soft x-ray PES (2.65 at 20 K).¹¹ Uncertainty in background subtraction leads to an uncertainty of ≈4% in our valence estimation, but our high energy resolution allows contributions from the surface states to be easily separated from that of the bulk states.

In conclusion, we have demonstrated that epitaxial thin films of YbAl₃ (001) can be grown on MgO (001) by judicious choice of buffer layers and an optimized growth strategy. By providing access to pristine sample surfaces, our thin film approach could help elucidate microscopic mechanisms underlying the properties of YbAl₃ by directly measuring the single particle spectral function in both real and momentum space via surface spectroscopic probes such as ARPES and STM. Furthermore, our approach opens the possibility to engineer the properties of YbAl₃ and other mixed valence compounds via interfacial engineering or fabrication of heterostructures.

This work was supported by the National Science Foundation through DMR-0847385 and by the Cornell Center for Materials Research with funding from the NSF MRSEC Program (DMR-1120296), and by the Research Corporation for Science Advancement (2002S). This work made use of the Cornell Center for Materials Research Shared Facilities which are supported through the NSF MRSEC Program (DMR-1120296). The FEI Titan Themis 300 was acquired through NSF-MRI-1429155, with additional support from Cornell University, the Weill Institute, and the Kavli Institute at Cornell. S.C. acknowledges helpful discussions with J. T. Heron and H. P. Nair.