Strain control of oxygen kinetics in the Ruddlesden-Popper oxide La1.85Sr0.15CuO4

Oxygen defect control has long been considered an important route to functionalizing complex oxide films. However, the nature of oxygen defects in thin films is often not investigated beyond basic redox chemistry. One of the model examples for oxygen-defect studies is the layered Ruddlesden–Popper phase La2−xSrxCuO4−δ (LSCO), in which the superconducting transition temperature is highly sensitive to epitaxial strain. However, previous observations of strain-superconductivity coupling in LSCO thin films were mainly understood in terms of elastic contributions to mechanical buckling, with minimal consideration of kinetic or thermodynamic factors. Here, we report that the oxygen nonstoichiometry commonly reported for strained cuprates is mediated by the strain-modified surface exchange kinetics, rather than reduced thermodynamic oxygen formation energies. Remarkably, tensile-strained LSCO shows nearly an order of magnitude faster oxygen exchange rate than a compressively strained film, providing a strategy for developing high-performance energy materials.

The in-plane strain was then determined by: in − plane strain = − (2) Transport measurements were obtained using a Quantum Design physical property measurement system using the typical Van der Pauw geometry. Temperature-dependent Hall coefficient of the annealed films are illustrated in Supplementary Fig. 2. The electronic structure of strained LSCO films was probed using fluorescence yield X-ray absorption spectroscopy performed at beam line 4-ID-C of the Advanced Photon Source at Argonne National Laboratory. Figure 1. Structural characteristics of epitaxial La 1.85 Sr 0.15 CuO 4 films. a, Xray diffraction spectra of LSCO films grown on LSAO (a = 3.756 Å) and LAO (a = 3.788 Å) single-crystal substrates. The (00l) peaks of LSCO film on each substrate show that the LSCO is grown along the (001) direction and confirms the high quality of the films and absence of secondary phases. b, Reciprocal space mapping of the (1 0 11) peak of LSCO films grown on each substrate illustrates the fully strained state of the LSCO.

Supplementary Figure 2. Strain and oxygen-dependent Hall coefficient. Hall coefficient strained LSCO films grown on LAO (tensile) and LSAO (compressive).
Compressively strained films show little change in the Hall coefficient, whereas tensile-strained films show a strong deviation among oxygen-annealed (red), as-grown (black), and vacuum-annealed (blue).

Supplementary Note 2 Defect calculations: energetics and formation volumes
Our approach to calculating defect formation energies in the present work uses the wellestablished defect thermodynamics methods used in previous works. [1][2][3] Briefly, the defect formation energy form E α ∆ for oxygen defects of type α (vacancy or interstitial) in LSCO is defined as: where L 0 is the matrix of lattice constants for the relaxed, undefected cell, and L is the matrix of lattice constants of the relaxed cell containing the defect under study. Supplementary Table 3 summarizes the calculated values of the V cc (c-axis) component of the volume relaxation tensor for each defect type. As stated in the main text, vacancies result in a c-axis reduction (especially for equatorial vacancies), and interstitials result in a c-axis expansion (especially for oxide interstitials).

Defect Type V cc (Å 3 )
Oxide Supplementary Figure 3 contains plots of the calculated defect formation energy under as-grown conditions as a function of strain for each defect type. In general, the functional relationship between the defect formation energy with strain is quadratic. Overall, the variation in formation energy with strain is small, around 100-200 meV. In particular, for the stable vacancy and interstitial species, the variation of formation energy with strain is < 100 meV. We note here that at larger strain states, the variation in defect formation energy may become larger to the point where the defect energetics play a more sizable role in the measured stoichiometry of strained LSCO thin films. However, for the lower strain states considered in this study, the strain response of the oxygen stoichiometry is due to changes in the oxygen surface exchange kinetics, and not due to the changes in the oxygen defect thermodynamics.

Estimation of k* for LSCO under arbitrary (T, P), effect of strain and time to fill oxygen sites
In this work, we drew upon previously published data for surface exchange in LSCO to compute qualitative, approximate k* values as a function of temperature, pressure, and strain state. We used these computed values of k* under each annealing condition to then estimate the time required to fill enough oxygen sites to result in the measured c-axis values reported in Fig.   3 of the main text. From the work of Claus et al., 6 we extracted data of k* as a function of temperature at ambient oxygen pressure P(O 2 ) = 0.2 atm. The Arrhenius relationship from the data in their work is: From the work of Lee, et al., 7 the authors report the pressure dependence of k* in LSCO as: The samples in the current work and the work of Lee et al. 7 are thin films of LSCO. Therefore, we can use the measured k* value from Lee, et al., Eq. (6) and Eq. (7) to obtain approximate, qualitative values of k* at different (T, P). As Eq. (6) was obtained from k* measurements on polycrystalline LSCO, we are making the assumption that the activation barrier for k* for polycrystalline and thin film samples is the same. This assumption is necessary because, to our knowledge, the activation barrier for thin film LSCO has not been experimentally measured, and is reasonable as our goal is only to show the approximate, qualitative differences in lattice response times between different annealing conditions and the qualitative effect of strain on k* based on other reported materials data. As a sensitivity check, we find that the lattice response times vary by about +/-0.8 log units when the activation barrier for k* varies by +/-250 meV. This variation would not impact any of the qualitative conclusions of the study.
Supplementary Table 5 Table 5. Computed values of k* for unstrained LSCO based on the extracted relationships and data from previously published work. The data for k* (geometric average with the as-grown state) are the data points for zero strain plotted in Figure 5 of the main text.
The last component for estimating the range of k* is the effect of strain. To our knowledge, no experiments have been performed that specifically measure the variation in k* as a function of strain in any Ruddlesden-Popper material. Thus, the best approximation we can make is to draw upon data for a similar material, the perovskite La 1- Although the values reported in Fig. 5 Figure 3 of the main text (plus additional values from annealing at other temperatures), the change in c-axis between the as-grown state and the other annealing conditions, the calculated change in number of oxygen interstitials required to realize the requisite change in c-axis, and the time required to fill all oxygen interstitials (in log minutes) assuming that LSCO has a range of k* values corresponding to k* in tension (higher k*, shorter time to fill oxygen interstitials) and k* in compression (lower k*, longer time to fill oxygen interstitials).
Finally, now that the values of k* and O interstitial concentration are in the correct units, the value of oxygen flux can be calculated and turned into units of time. The oxygen flux O R has units of (#O/cm 2 -s). Multiplying this value by the cross-sectional area of the films, which is 1.25x10 -6 cm 2 , we obtain an oxygen current in (#O/s). Inverting this quantity to (s/#O) and multiplying by the number of required interstitials and film volume (the films are 25 nm thick, so the volume is 3.125x10 -12 cm 3 ) and converting to minutes yields the time needed to fill the necessary number of O sites in the lattice.