Local structure of superconducting $(\mathrm{La},\mathrm{Sr}{)}_2{\mathrm{CuO}}_4$ under strain: Microscopic mechanism of strain-induced $T_c$ variation

High-quality polarized x-ray absorption spectroscopy data for $(\mathrm{La},\mathrm{Sr}{)}_2{\mathrm{CuO}}_4$ thin-film single crystals reveal strain-dependent local disorder (in the oxygen radial distribution) that correlates with the superconducting critical temperature. The temperature-dependent in-plane oxygen displacement shows that local lattice distortion strongly depends on strain, i.e., the biaxial tensile strain develops domains with the bond-stretching-type local distortion which is weakened by the compressive strain. We suggest that the two-dimensional strain modifies electronic inhomogeneity that influences the superconducting critical temperature through superfluid density, rather than band structure effects.

Figure 1

Cu $K$-EXAFS oscillations and Fourier transform. (a) Experimental fluorescence yield spectra for 100 channels of a pixel array detector. Using a grazing-incidence geometry $(\theta =1°)$ and fine adjustment of azimuthal angle $\left(\varphi \right)$, artifacts due to the substrate scattering and standing waves are eliminated. (b) In-plane polarized Cu $K$-EXAFS oscillations as functions of wave number $k$ for 100-nm-thick $(\mathrm{La},\mathrm{Sr}{)}_2{\mathrm{CuO}}_4$ (LSCO) thin-film single crystal grown on ${\mathrm{LaSrAlO}}_4$ (LSAO) substrate. The upper row shows the data for thin film (solid line) and that of bulk single crystal (dashed line) taken at $10\mathrm{K}$ and the lower row shows the data taken at various temperatures.

Figure 2

(a) Fourier transform (FT) magnitude functions of the Cu K-EXAFS oscillations for a LSCO thin-film single crystal grown on LSAO substrate. Complex FT was performed over the $k$-range $3–18{\mathrm{\AA }}^{-1}$ using a Hanning window. (b) The experimental nearest neighbor contributions compared with those of theoretical calculations.

Figure 3

Mean-square relative displacement ${\sigma }_{\mathrm{Cu}\text{−}\mathrm{Op}}^2$ plotted as a function of temperature (K) for the $\mathrm{Cu}\text{−}{\mathrm{O}}_{\mathrm{p}}$ distance in $(\mathrm{La},\mathrm{Sr}{)}_2{\mathrm{CuO}}_4$ (LSCO) thin-film single crystals grown on ${\mathrm{SrTiO}}_3$ (STO) and ${\mathrm{LaSrAlO}}_4$ (LSAO) substrates, referred to as LSCO/STO and LSCO/LSAO, respectively. The arrows indicate positions of the superconducting critical temperature $\left(T_c\right)$ and the onset temperature of local distortion $\left(T^{*}\right)$. The upper inset indicates the difference ${\sigma }_{\mathrm{Cu}\text{−}\mathrm{Op}}^2$ values for the two samples, showing the mean strain-induced broadening of radial distribution function. The dashed line is an eye-guide.

Figure 4

Temperature dependence of oxygen displacement in strained LSCO, ${\sigma }_{\mathrm{Cu}\text{−}\mathrm{Op}}^2$ vs $T$ under compressive strain (left row) and under tensile strain (right row). The arrows indicate positions of $T_c$ and $T^{*}$ (the same with Fig. 3). The inset at $T_c$ shows the temperature derivatives of resistivity $d\rho ∕dT$. The inset figures show ${\sigma }_{\mathrm{Cu}\text{−}\mathrm{Op}}^2$ vs $T∕T_c$. Upturn and drop parts of relative displacement ${\sigma }_{\mathrm{Cu}\text{−}\mathrm{Op}}^2$ are denoted as $\mathrm{\Delta }{\sigma }_{\mathrm{coh}}^2$ and $\mathrm{\Delta }{\sigma }_{\mathrm{dis}}^2$, respectively.

Figure 5

Local lattice distortions. (a) Tetragonal distortions in LSCO under strain. $\mathrm{\Delta }{R}_{\mathrm{Cu}\text{−}\mathrm{Op}}$ for LSCO grown on ${\mathrm{SrTiO}}_3$ (LSCO/STO) and on ${\mathrm{LaSrAlO}}_4$ (LSCO/LSAO) elongates and is shortened, respectively, by $0.01\mathrm{\AA }$. (b) Schematic illustration of in-plane RDF for undistorted and specific distortions. Oxygen displacement is indicated for the three cases of local distortions, i.e., Q2-type Jahn–Teller distortion, low-temperature-tetragonal and low-temperature-orthorhombic, which result in the long $\mathrm{Cu}\text{−}{\mathrm{O}}_{\mathrm{p}}$ distances by $\approx 0.1\mathrm{\AA }$.