Demystifying the growth of superconducting Sr 2 RuO 4 thin films

We report the growth of superconducting Sr 2 RuO 4 thin ﬁlms by molecular-beam epitaxy on (110) NdGaO 3 substrates with transition temperatures of up to 1.8 K. We calculate and experimentally validate a thermodynamic growth window for the adsorption-controlled growth of superconducting Sr 2 RuO 4 epitaxial thin ﬁlms. The growth window for achieving superconducting Sr 2 RuO 4 thin ﬁlms is narrow in growth temperature, oxidant pressure, and ruthenium-to-strontium ﬂux ratio. © 2018 Author(s). article content, except where otherwise noted, is a Creative

In a previous publication, 30 we introduced the thermodynamics of molecular-beam epitaxy (TOMBE) diagram to discuss the adsorption-controlled growth of ruthenates. The TOMBE diagram is particularly helpful for visualizing the growth window of compounds where multiple volatile gas species are inherently involved in the growth. In the case of Sr 2 RuO 4 , like other complex oxide ruthenates, the gas species involved in calculating the growth window are O 2 (g) and RuO x (g) (x = 2 or 3).
The region shaded in red in the TOMBE diagram of the Sr-Ru-O ternary system ( Fig. 1) illustrates the adsorption-controlled growth window of Sr 2 RuO 4 , where Sr 2 RuO 4 (s) is in equilibrium with RuO x (g). The growth window in Fig. 1 has been calculated for an incident excess ruthenium flux of 1.3 × 10 13 /cm 2 ·s, consistent with the growth conditions used in this manuscript. The growth window for phase-pure Sr 2 RuO 4 , shaded red region in Fig. 1, is rather narrow adding to the challenge for realizing superconducting Sr 2 RuO 4 thin films. The growth window is narrow due to the small difference in Gibbs formation energies between Sr 2 RuO 4 (s) and Sr 3 Ru 2 O 7 (s). 31 On the higher temperature and higher oxygen pressure side of the dotted red line, it is thermodynamically favorable for Sr 2 RuO 4 to break down into SrO(s) and RuO x (g), while on the lower temperature and lower oxygen pressure side of the dotted green line, the formation of Sr 3 Ru 2 O 7 (s) becomes thermodynamically favorable. Figure S1 of the supplementary material illustrates the effect of varying the excess ruthenium on the growth window with the incident ruthenium flux fixed at 2 × 10 13 atoms/cm 2 ·s. As the excess ruthenium flux (determined by the ruthenium-to-strontium flux ratio) is reduced, the growth window for Sr 2 RuO 4 expands.
The narrow growth window we calculate for Sr 2 RuO 4 in Fig. 1 agrees with the observation of other groups that the growth window for superconducting Sr 2 RuO 4 thin films is very narrow in terms of parameters such as the growth temperature 24 and ruthenium-to-strontium flux ratio. 26 This narrow growth window is the most significant challenge in reproducibly growing superconducting Sr 2 RuO 4 thin films, requiring careful optimization of the interdependent growth parameters.
High substrate temperatures are critical for achieving superconducting Sr 2 RuO 4 thin films; we attribute this to two underlying reasons. The first is that high substrate temperature enhances the adatom surface migration length, which increases the spacing between out-of-phase boundaries. 28 These out-of-phase boundaries propagate through the thickness of the film and can act as pair breakers, thus suppressing the fragile superconductivity in Sr 2 RuO 4 thin films. 27 The second is that high  substrate temperature is essential for overcoming any reaction kinetic bottlenecks and promotes growth within this thermodynamic window. 30 Sr 2 RuO 4 thin films were grown using a Veeco GEN10 molecular-beam epitaxy system. Strontium was evaporated from a low-temperature effusion cell, while an electron beam evaporator was used for ruthenium. All of the elemental source materials had a purity of 99.99%. Distilled ozone (∼80% O 3 + 20% O 2 ) was used as the oxidant, which was introduced into the chamber using a water-cooled, electropolished 316L stainless steel tube with a 4.6 mm inner diameter pointed at the substrate with an angle of inclination of 40 • from the normal of the substrate and that terminates a distance of 9.6 cm from the center of the substrate. The tube provides an enhancement in the local oxidant pressure by a factor of ∼4× over the background chamber pressure. An optical pyrometer operating at a wavelength of 1550 nm was used to measure the substrate temperature. (110) NdGaO 3 substrates, from CrysTec GmbH, were etched using HF-NH 4 OH and then annealed at 950 • C in flowing oxygen to yield a GaO 2 -terminated surface. 32 The Sr 2 RuO 4 thin film, characterized in detail in this manuscript, was grown on a (110) NdGaO 3 substrate within the adsorption-controlled growth window outlined in Fig. 1. We used a strontium flux of 2.2 × 10 13 atoms/cm 2 ·s and a ruthenium flux of 2.4 × 10 13 atoms/cm 2 ·s corresponding to an excess ruthenium flux of 1.3 × 10 13 atoms/cm 2 ·s for the growth of Sr 2 RuO 4 . The film was grown at a substrate temperature of 900 • C and a chamber background pressure of 8 × 10 −7 Torr of (∼80% O 3 + 20% O 2 ). At the end of the growth, both the strontium and ruthenium shutters were closed simultaneously and the sample was rapidly cooled to below 250 • C under the same ozone pressure as was used during growth. The growth conditions used here fall within the narrow growth window calculated in the TOMBE diagram in Fig. 1. This illustrates the accuracy of the calculations and confirms that our growth temperature is sufficiently high so that kinetic barriers are negligible and the growth can be accurately described by thermodynamics.
X-ray diffraction (XRD) measurements along the specular crystal truncation rod (CTR) were carried out in a Rigaku SmartLab high-resolution diffractometer with Cu-K α1 radiation (λ = 1.5406 Å). A Ge 220 double-crystal monochromator was used in the incident side optics for the XRD θ-2θ measurement. The XRD θ-2θ scan of a 55 nm thick Sr 2 RuO 4 film grown on a (110) NdGaO 3 substrate (notations following the Pbnm non-standard setting of space group #62) is shown in Fig. 2. All of the peaks in the XRD θ-2θ scan can be indexed to either the (001)-oriented Sr 2 RuO 4 film or the (110) NdGaO 3 substrate (asterisks). The out-of-plane lattice constant of the film is c = 12.772 ± 0.007 Å at room temperature, which is slightly larger than the room-temperature value of 12.746 Å for Sr 2 RuO 4 single crystals, 33 consistent with the film being subject to a modest amount of in-plane compressive misfit strain imposed by the substrate. Specifically, the misfit strain in the Sr 2 RuO 4 at room temperature on the (110) NdGaO 3 substrate 34 is −0.39% along the [001] in-plane direction of the substrate and −0.16% along the [110] in-plane direction of the substrate. From an elastic stiffness calculation, 33 = −c13 c33 ( 11 + 22 ), where 11 , 22 , and 33 are the principal strains in the Sr 2 RuO 4 film and c 13 and c 33 are the coefficients of the elastic stiffness tensor of Sr 2 RuO 4 in Voigt notation, 35 this strain is expected to yield an out-of-plane film spacing 12.770 Å, which is in good agreement with the 12.772 ± 0.007 Å spacing observed. Rocking curve measurements around the 006 reflection of the Sr 2 RuO 4 film and the 220 reflection of the NdGaO 3 substrate are shown in Fig. 2(b). In addition to the Ge 220 double-crystal monochromator on the incident side, a Ge 220 two-bounce analyzer was also used on the detector side to improve the resolution of the rocking curve measurements. The slits on the incident and receiving side optics were set to 1 mm. The full width at half maximum (FWHM) of the Sr 2 RuO 4 film (20 arcsec) is comparable to the FWHM of the NdGaO 3 substrate (15 arcsec) indicating that the structural quality of the film is comparable to that of the underlying substrate.
In addition to these lab-based XRD measurements, we also performed synchrotron-based nonresonant XRD measurements on other superconducting Sr 2 RuO 4 films grown on (110) NdGaO 3 at beamline A2 at the Cornell High Energy Synchrotron Source (CHESS). Synchrotron data were taken using an incident energy of 14.5 keV (λ = 0.855 Å) and a Dectris Eiger X 1M area detector, to more thoroughly map the reciprocal space of these samples. A representative segment of an off-specular CTR with in-plane momentum transfer q along [001] NdGaO 3 is shown in Fig. 2(c)  the (110) NdGaO 3 substrate are aligned with the same q , showing that the in-plane lattice constants of the film and substrate are equal illustrating that even a 132 nm thick Sr 2 RuO 4 film on (110) NdGaO 3 is commensurately strained. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was performed on an aberration-corrected FEI Titan Themis operating at 300 keV with a probe convergence semi-angle of 21.4 mrad and inner and outer collection angles of 68 and 340 mrad, respectively. Cross-sectional STEM specimens were prepared with the standard focused ion beam (FIB) lift-out process using an Omniprobe AutoProbe 200 nanomanipulator on an FEI Strata 400 FIB. Atomic resolution STEM images (Fig. 3) of the same 55 nm thick superconducting Sr 2 RuO 4 film, characterized in Fig. 2, reveal relatively few structural defects within the field of view (∼73 nm). The observed epitaxial orientation relationship is (001) Sr 2 RuO 4 (110) NdGaO 3 and [100] Sr 2 RuO 4 [001] NdGaO 3 , consistent with prior work. 36 The spacing between out-of-phase boundaries propagating through the thickness of the film is greater than the in-plane coherence length (ξ ab (0)) of ∼66 nm measured on Sr 2 RuO 4 single crystals 11 indicating that the growth temperature is high enough to minimize the incorporation of these defects that can destroy superconductivity. There are some regions [ Fig. 3(b)] especially near the substrate-film interface where the local stoichiometry corresponds to that of Sr 3 Ru 2 O 7 , which is likely due to the narrow growth window for Sr 2 RuO 4 . Such structural variation was observed in several superconducting films. Note that inclusions of Sr 3 Ru 2 O 7 and SrRuO 3 are also seen in single crystals of Sr 2 RuO 4 grown slightly outside the optimal conditions. 37 The presence of these impurity phases in Sr 2 RuO 4 single crystals leads to a suppression of the measured T c . 37 An atomic force microscope (AFM) image of the same 55 nm thick Sr 2 RuO 4 film is shown in Fig. 4. The RMS roughness is ∼7.2 Å. Resistivity as a function of temperature for more than 80 Sr 2 RuO 4 films grown on (110) NdGaO 3 was measured in a four-point rectangular geometry from room temperature to 4 K to screen out films that do not have a sufficiently high in-plane residual resistivity ratio (RRR) [ρ ab (300 K)/ρ ab (4 K)]. Films deemed phase pure by XRD, grown in the SrO(s) + RuO x (g) region of the TOMBE diagram, consistently have ρ ab (4 K) > 5 µΩ·cm and do not superconduct above 0.4 K. Only films with ρ ab (4 K) < 4 µΩ·cm, corresponding to RRRs > 30-33, were observed to undergo a superconducting transition above 0.4 K, the measurement limit of our low-temperature setup described below. This is similar to the case of growth outside the stability window for epitaxial yttrium barium copper oxide thin films (with nominal composition YBa 2 Cu 3 O 7 ), 38 which are non-superconducting when grown outside of the thermodynamic stability window. 39 Resistivity as a function of temperature for the same sample characterized by XRD, STEM, and AFM (Figs. 2-4, respectively) is shown in Fig. 5(a), indicating a RRR of 69.
The superconducting transition was measured in a Quantum Design Physical Property Measurement System (PPMS) equipped with a 3 He insert to measure electrical transport as a function of temperature from 300 K down to 0.4 K. Electrical contacts were made by wire bonding aluminum wires from gold pads on the PPMS sample holder directly to the surface of the 5 mm × 10 mm film in a four-point linear geometry. Each of the wire bonds was spaced apart by ∼2 mm along the longer dimension of the sample. Note that the film was not patterned, so the current is not constrained in how it flows. The superconducting transition for the same film characterized in Figs. 2 and 3 is shown in Fig. 5(b), measured at zero magnetic field with an excitation current of I = 100 µA. The T c is 1.8 K. The full width of the superconducting transition in temperature (∆T ∼ 0.4 K) is relatively broad compared to single crystals (∆T < 0.1 K), as shown in Fig. 5(c). This is likely due to the presence of percolative superconducting pathways, which have a higher T c than the majority of the film. The residual resistivity of the highest-quality Sr 2 RuO 4 superconducting film, we have grown to date, is ∼1.5 µΩ·cm, which is relatively high when compared to ∼100 nΩ·cm for the highest purity Sr 2 RuO 4 single crystals. 13 This suggests that with further reduction in impurities and planar defects in our films, it might be possible to attain an even higher T c and a sharper superconducting transition. Figure 5(d) shows the magnetoresistance of the same film measured at 0.45 K with the magnetic field applied along the [001] direction of the film. A tangent-line construction gives an upper critical field of H c2 c (0.45 K) = 2.0 kOe. The suppression of the zero resistance state with an applied magnetic field confirms that the resistive transition measured here [ Fig. 5(b)] is indeed the result of superconductivity. As is evident from Fig. 5(c), the onset of superconductivity of our Sr 2 RuO 4 films grown on (110) NdGaO 3 is higher than that for Sr 2 RuO 4 single crystals and higher than any other reports for Sr 2 RuO 4 thin films. Note that all prior reports of superconducting Sr 2 RuO 4 films involved growth on (100) (LaAlO 3 ) 0.29 -(SrAl 1/2 Ta 1/2 O 3 ) 0.71 (LSAT) substrates. [24][25][26] The misfit strain, at room temperature,  14,15 To test this hypothesis more carefully, future work on epitaxial thin films should focus on quantitatively disentangling factors that enhance T c (e.g., lattice strain) from those that suppress T c (e.g., defects) following the pioneering work on single crystals. 12,14,15 In summary, we have outlined and demonstrated an adsorption-controlled growth window for Sr 2 RuO 4 thin films using molecular-beam epitaxy. We provide an explanation based on thermodynamic calculations for the origin of the narrow growth window for achieving superconducting thin films. We hope that this work clarifies some of the mysteries surrounding the growth of superconducting Sr 2 RuO 4 thin films. Finally, growth within this window has yielded superconducting Sr 2 RuO 4 thin films with a T c of up to 1.8 K on (110) NdGaO 3 substrates, the highest reported to date for Sr 2 RuO 4 thin films.
See supplementary material for additional TOMBE diagrams illustrating the expanded growth window for Sr 2 RuO 4 attained by tuning the excess ruthenium flux.

Supplementary Material
Fig. S1: TOMBE diagram calculated for a fixed incident ruthenium flux of 2.00×10 13 atoms/cm 2 ·s and excess ruthenium fluxes of (a) 1.01×10 13 atoms/cm 2 ·s, (b) 1.5×10 13 atoms/cm 2 ·s, and (c) 1.95×10 13 atoms/cm 2 ·s. It is evident that a reduction in the excess ruthenium flux causes the thermodynamic growth window for adsorption controlled growth window for Sr2RuO4 (shaded red) to expand in both growth temperature and oxygen pressure.