Strain-relaxation and critical thickness of epitaxial La_1.85Sr_0.15CuO₄ films

Epitaxial strain has been demonstrated as a powerful tool for tuning the physical properties of layered structure types, such as the Ruddlesden-Popper (RP) phases, A₂BO₄, where A = a lanthanide or alkaline earth metal and B = a transition metal.^1–4 For example, the electronic bandwidth in the spin-orbit-coupling compound, Sr₂IrO₄,⁴ and oxygen diffusion in the ionic conductor, La₂NiO_4+δ,^2,5 are strongly influenced by strain. Perhaps, one of the best illustrations of the strain effect in a RP phase is in regards to the superconducting cuprates, La_2−xSr_xCuO₄. The superconductivity in these compounds is highly sensitive to structural perturbations induced by hydrostatic pressure owing to their anisotropic structure.^6–8 Thus, it is no surprise that epitaxial strain has been explored as a means to tune this anisotropy in order to increase the critical temperature for superconductivity, T_c. In fact, it has become a general rule of thumb that compressive strain can enhance T_c, whereas tensile strain may suppress the T_c.^1,9,10 The former is associated with an increased separation between the Cu and apical oxygen atoms,^11,12 whereas the latter is attributed to increased lattice buckling of the CuO₂ planes.¹³ These observations imply that a strong relationship exists between the RP structure and properties.

One approach to probing the effects of strain upon the superconductivity is by exploring films of different thicknesses. This approach allows one to investigate both the strain relaxation behavior and the critical thickness for the onset of superconductivity (d_c). Therefore, this method provides a systematic way to investigate the structure and property relationships for a large range of strain values. Previously, the thickness-dependent superconductivity in optimally doped La_1.85Sr_0.15CuO₄ (LSCO) was explored.^9,14–17 However, these studies lacked sufficient discussion of the structural response to (1) strain relaxation for both superconducting and non-superconducting films, (2) variable thicknesses, or (3) LSCO films not exposed to highly oxidizing ambients, all of which can prevent an accurate determination of the lattice response and d_c. Recently, oxygen vacancies, which are known to promote hole depletion and lower T_c in LSCO,^18,19 have been reported to be increasingly formed by tensile strain due to a significantly reduced oxygen vacancy formation energy.^10,20,21 Therefore, the thickness-dependence of LSCO (i.e., change in the degree of strain) must be revisited in order to determine the role of oxygen vacancy formation upon the superconducting T_c in strain-relaxed LSCO films. A study such as this is necessary to reliably interpret the underlying mechanism of strain control of superconductivity.

With the knowledge of oxygen vacancy formation in tensile-strained films,^10,20,21 we report on the thickness-dependent structural and T_c changes of LSCO films grown under a large magnitude of tensile and compressive strain. By systematically tuning the strain of LSCO films by varying both the lattice mismatch with the substrate and film thickness, we observed different d_c values for LSCO on each substrate. Moreover, this approach led us to find highly contrasting stability of the superconductivity and oxygen sublattice depending on the type of strain. We found that compressive-strained films showed the smallest d_c and more robust superconductivity, whereas tensile-strained films were very vulnerable for suppression of superconductivity due to strain-mediated oxygen loss.

In order to investigate the strain-relaxation mechanism, a series of compressive- and tensile-strained LSCO (a_bulk = 3.777 Å, c_bulk = 13.226 Å)²² films were grown using pulsed laser epitaxy on LaSrAlO₄ (LSAO, a = 3.756 Å), LaAlO₃ (LAO, a = 3.788 Å), (LaAlO₃)_0.3(SrAl_0.5Ta_0.5O₃)_0.7 (LSAT, a = 3.868 Å), and SrTiO₃ (STO, a = 3.905 Å) single-crystalline substrates to produce different biaxial strains (−0.56, 0.29, 2.35, and 3.28%, respectively) (see Figure 1(a)). Due to the large lattice mismatch for LSCO grown on STO and LSAT, we were only able to grow partially strained films. Further modulation of the strain was achieved by varying thickness. Optimal growth conditions were determined from samples with the narrowest x-ray rocking curves and no secondary phases. Typically, full-width-at-half-maximum values of ∼0.05° or less in rocking curve ω scans were obtained from well-optimized films grown at 700 °C in 100 mTorr of oxygen on all substrates, except those films grown on LAO, which required a lower temperature of 550 °C. It is unclear the exact reason for the lower optimal temperature for films on LAO, though it might be attributed to a smaller lattice mismatch. After growth, all samples were cooled in 100 Torr of oxygen to room temperature. Previous studies had employed more rigorous oxidation environments by using ozone for layered cuprate growth, which is significantly more oxidizing than molecular oxygen.^1,9,10 We found our optimal growth conditions to be insufficient to fully oxidize LSCO, but we did not further oxidize them through thermal post-annealing or ozone use during growth in order to identify the intrinsic strain effect on the oxygen concentration. This fact also allows for a thorough discussion of the strain-relaxation mechanism without the structural effects induced by oxygen interstitials (i.e., c-lattice expansion) commonly observed for LSCO treated in an extremely oxidizing environment. The in-plane (a) and out-of-plane (c) lattice parameters were determined from high-resolution x-ray diffraction, and the thickness was calculated from the x-ray reflectivity spectra. Transport properties were characterized in the van der Pauw geometry using a Quantum Design Physical Property Measurement System.

In order to determine the d_c for observing superconductivity, the thickness-dependent sheet resistance for LSCO grown on each substrate was examined as shown in Figs. 1(b)-1(e) and summarized in Fig. 1(f). We found that the d_c (T_c) are approximately 10 nm (11.9 K), 40 nm (5.5 K), 50 nm (5.9 K), and 100 nm (7.3 K) for LSCO grown on LSAO, STO, LSAT, and LAO substrates (respectively). Additionally, while T_c values for these films are smaller than the bulk value of 40 K,¹⁸ earlier reports on growth of LSCO on STO showed that thicknesses as high as 800 nm reached only ∼33 K.¹⁵ We note that the highest T_c obtained for our LSCO on STO was 29 K for a significantly lower thickness of 75 nm, only slightly lower than our maximum value of 29.7 K for LSCO on LSAO and the bulk value of 33 K obtained from our target (not shown). However, the lower T_c that we see for thinner films near d_c on each substrate implies that there must be strong structural modifications occurring during film relaxation of LSCO on each substrate.

We investigated the structural relaxation since this could lead to a near bulk-like lattice and to determine whether the revival of superconductivity at the d_c is related. The out-of-plane (c) and in-plane (a) lattice parameter responses to increasing film thickness were investigated as shown in Figures 2(a) and 2(b). As one might expect, compressive strain produces an elongated c-lattice parameter, whereas tensile strain results in a smaller out-of-plane lattice parameter. As the films relax, the lattice parameters for LSCO under both strain states begin to converge towards bulk values.

Since the lattice mismatch between LSCO and LSAT and STO substrates is significantly large, relaxation occurs immediately. Conceivably, these substrates induce relaxation quickly due to the energy cost for maintaining a fully strained film, which agrees well with our observation of a relaxed 15 nm film on STO. In contrast, films grown on LSAO and LAO are fully strained up to a thickness of 35 nm and 80 nm films (respectively), but undergo relaxation for the larger thicknesses studied. It is perhaps not surprising that t_c for films on LAO is nearly double the value for films on LSAO since the lattice mismatch is nearly half as small (0.29% for LAO and −0.56% for LSAO). That being said, even small tensile strain is enough to suppress the superconductivity, which supports the conventional wisdom that tensile strain increases buckling of the CuO₂ planes detrimental to superconductivity.¹³ 

When we consider the elastic properties of LSCO, we can see that suppression of superconductivity cannot be solely explained by the buckling effect as is commonly assumed. In Figure 3, we plot the out-of-plane strain, ε_OOP = (c − c_b)/c_b, versus the in-plane strain, ε_IP = (a − a_b)/a_b, where a_b and c_b are reference lattice parameters²² in order to identify whether strain varies uniformly with increasing thickness and different substrates. A linear trend for films under in-plane compressive strain and tensile strain up to ∼0.25% is observed, the slope of which, ν^∗, is equivalent to −2ν/(1 − ν), where ν is the Poisson ratio.²³ We determined a ν ∼ 0.32, which is in good agreement with the value of ν = 0.3 obtained for bulk LSCO and other layered oxides.^24,25 The linearity that we observe for the less strained (thicker) films on LSAT and STO further supports that the variation in the unit cell size from the bulk value in Fig. 2 is due to the elastic deformation rather than stoichiometry issues. However, a significant deviation from linearity is evident for the region where the in-plane tensile strain is greater than 0.25%. It is perhaps no coincidence that this value for tensile strain coincides with a generally contracted out-of-plane lattice parameters (right axis) less than ∼13.21 Å, smaller than the anticipated values for ideal LSCO under the same in-plane strain. More importantly, this region includes the subset of films (open symbols) that are not superconducting below d_c, even for relatively thick films, where any contribution from the finite thickness effect is minimal at best.^26–29 An example can be seen from the 5 nm thick compressive-strained LSCO film, which is not superconducting despite having a large out-of-plane lattice parameter of 13.27 Å. While the origin for the deteriorated conduction attributed to the finite thickness effect in this film is not known precisely, some factors may include a decrease in the density of states at the Fermi level, variation of the electronic bandwidth, strong localization of carriers, and reaching a percolation threshold.^26–29 It is important to mention that superconductivity has been observed down to one CuO₂ plane in multilayer cuprate systems,³⁰ which may suggest that the finite thickness effect is not a feasible explanation for this 5 nm film on LSAO containing multiple CuO₂ planes. However, multilayer structures do not provide an accurate interpretation of finite thickness effects occurring in single layer films since the interface composition may be different and coupling between layers may play a role in the conduction mechanism.²⁷ These observations are intriguing in that they provide a set of spatial requirements that must be met for observing superconductivity in strained LSCO films.

We attribute the deviation from Poisson behavior and the c-lattice contraction to tensile-strain induced oxygen vacancy formation owing to the reduced oxygen activation energy, i.e., the energy required to move oxygen ions from one site to another, rather than lattice buckling.^20,21 While lattice contraction is unexpected with oxygen vacancy formation, preferential oxygen vacancy formation within the equatorial position for as-grown or oxygen reduced LSCO has been reported to contract the c-lattice parameter in tensile-strained LSCO, whereas compressive strain maintains a robust, oxygen-stoichiometric structure.²⁰ 

The large sensitivity of the structure to oxygen vacancy formation will likely play a large role upon the mechanism of strain-relaxation in these films. In fact, previous studies have identified that strain relaxation may occur via an oxygen-defect mediated process^25,31–33 rather than the classical Matthews-Blakeslee theory³⁴ taking into account the formation of dislocations. Therefore, with the knowledge that tensile strain stabilizes oxygen vacancies coupled with the potential for an oxygen-vacancy-driven relaxation mechanism, a new perspective to the thickness-dependent T_c behavior can be uncovered since the T_c is a sensitive indicator for oxygen non-stoichiometry.^18,19 As shown in Figure 4, relaxation of tensile strain leads to a higher T_c, which agrees with a film lattice that converges towards a bulk-like state as tensile strain (thickness) is reduced (increased). It is then highly feasible that the relaxation of this strain will result in a more oxygen-stoichiometric film as in the case of the LSCO film on STO with T_c = 29 K. The fact that a compressive strain as high as −0.26% has the same T_c as this unstrained film indicates that the oxygen stoichiometry between the two is quite similar.

In conclusion, we have shown through a systematic study of the strain relaxation behavior in optimally doped LSCO epitaxial thin films that a strong relationship exists between the structure and properties. We found that the superconductivity is suppressed for films with tensile strain more than 0.25% and a contracted c-lattice parameter, which coincide with a deviation from Poisson behavior. The lack of superconductivity in these films appears to be linked to strain-driven oxygen non-stoichiometry in the as-grown state. Thus, it is crucial to take into account the role of strain on the oxygen stoichiometry in layered oxides such as RP phases in order to reliably interpret the structural impact upon their physical properties induced by strain relaxation.

This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences, and Engineering Division. S.K.P. was supported in part by NRF Korea (No. 2011-0031933) for his contribution on growth optimization and data analysis.