Aberration-Corrected Scanning Transmission Electron Microscopy of La₂CuO₄-based Superconducting Interfaces at the Stuttgart Center for Electron Microscopy

Introduction

High-quality functional complex oxide heterostructures are excellent systems for studying interface phenomena arising from the interaction between neighboring layers [1,2]. Depending on the choice of the constituents, different microscopic phenomena can occur at the interfaces, including electronic and orbital reconstruction, magnetic exchange interactions, crystal-structure distortions, chemical intermixing or breaking of the crystal symmetry [3].
In this context, one recent exciting finding was the observation of high-temperature interface superconductivity (HT-IS) at the interface between epitaxially grown strontium-over-doped metallic (M) lanthanum cuprate (La_1.55Sr_0.45CuO₄) and under-doped insulating (I) La₂CuO₄ (LCO) layers [4], none of which is superconducting if taken alone. The full understanding of HT-IS is a very important step towards the disclosure of mechanisms for high-temperature superconductivity (HTSC) [4,5], being potentially able to shed light on questions related to the formation of superconducting interfaces [4], its dimensionality and locus [6], and the impact of the crystal structure and atom positions on the superconducting properties [7,8]. Numerous studies employing advanced experimental methods as well as innovative approaches have addressed these questions [6,7,9-13].
In order to explain the HT-IS in M–I lanthanum cuprate bilayers, a model based on the electronic charge transfer due to a difference in the hole chemical potentials between the over-doped and under-doped phases has been invoked [6,13]. As a consequence of such a redistribution, a doped region having the optimal hole concentration for HT-IS is formed in the nominally insulating phase (namely, the second CuO₂ plane in LCO away from the interface). In such bilayers, the superconducting critical temperature (T_c) was also found to be dependent on the deposition sequence (e.g. M-I or I-M), where the top layer adopts the out-of-plane lattice parameter of the bottom phase as a result from electrostatic interactions ("Madelung strain") and a linear relation between T_c and c was revealed [7]. Such findings open an exciting scenario for the enhancement of the superconducting critical temperature in M–I lanthanum cuprate heterostructures, which could in principle be obtained by appropriately tuning the out-of-plane lattice parameter of the bottom layer.
The development of spherical aberration (C_s) correctors [14] in (scanning) transmission electron microscopy ((S) TEM) provides sub-Ångstrom spatial resolution. In STEM, the annular bright-field (ABF) imaging technique is capable of imaging light elements [15-17], such as oxygen, which makes ABF especially interesting for the investigation of perovskite oxides [18,19]. ABF images can be simultaneously recorded with high-angle annular dark-field (HAADF) images [20] and correlated with spectroscopic techniques such as electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray (EDX) spectroscopy. Moreover, it is well-known that the properties of complex perovskite-type oxide structures (mostly ABO₃ and A₂BO₄ type structures and their derivatives) are strongly influenced by small structural changes of the BO₆ octahedral network [21,22]. Thus, the understanding how the octahedral distortions are correlated with the dopant distribution and how they modify the functionality of complex oxide heterostructures is of significance. Although octahedral distortions at interfaces of various heterostructures have recently been widely studied via ABF imaging [18,19,22-25], the present understanding of octahedral networks and their distortions in A₂BO₄ systems is still limited.
In this work, we demonstrate the indispensable role played by aberration-corrected STEM for the determination and interpretation of interfacial octahedral distortions in oxide heterostructures, in particular for La₂CuO₄-based superconducting interfaces. We have comprehensively studied La_1.6A_0.4CuO₄–La₂CuO₄ bilayers (with A = Ca, Sr, Ba) and two-dimensionally (2D) doped La₂CuO₄ superlattices (SLs), which were grown via the atomic-layer-by-layer oxide molecular beam epitaxy technique (ALL-oxide MBE) [26], by employing analytical high-resolution STEM techniques. Through atomically-resolved STEM-EELS investigations we demonstrate how the dopant size affects the dopant distribution, and thus the superconducting mechanism of the system. Moreover, by analyzing the cation and anion strain-induced displacements at picometer resolution, we demonstrate that the size mismatch between the dopant and the host La³⁺ cations has a direct influence on the structure and in particular on the out-of-plane strain state [27].

La₂CuO₄ bilayers: Probing dopant size effects on HT-IS

The bilayer structures were grown on LaSrAlO₄ (LSAO) (001) substrates, where the growth process starts with an over-doped metallic layer followed by an undoped insulating layer. A structural model of the ALL-oxide MBE grown bilayers is given in Fig. 1a. Figure 1b–d show atomically resolved HAADF images which cover the substrate and the nominal metallic and insulating layers demonstrating a high quality of the bilayers as well as perfect coherent interfaces and the absence of extended defects, such as misfit dislocations and/or stacking faults. Initial XRD measurements have revealed that the shortest c -axis lattice constant (13.22 Å) was observed for the LCCO/LCO bilayers, whereas the c -axis lattice parameters are 13.28 Å and 13.37 Å for the LSCO/LCO and LBCO/LCO bilayers, respectively. Such findings nicely correlate with the nominal cationic radii in nine-fold coordination [28], as a consequence of Madelung strain [7]. For the LCCO/LCO, LSCO/LCO and LBCO/LCO systems, the superconducting critical temperatures (T_c) are ~17 K, ~36 K and ~39 K, respectively [29].

Fig. 1

a) Structural model of the bilayers grown on the LSAO substrate and STEM–HAADF images showing coherent interfaces of b) Ba-(LBCO), c) Sr- (LSCO), and d) Ca-(LCCO) doped bilayers. The HAADF images were taken along the [100] direction of the LSAO substrate. e) Transport measurements as resistance versus temperature for differently doped bilayers. Figures reproduced with permission from Ref. [36].

Dopant distribution

In order to gain deeper insight into the interfacial structure and on the present c vs T_c relation in comparison with the literature, atomically resolved imaging and spectroscopy were carried out. Figure 2a, b present HAADF images of the LCCO/LCO bilayer. An atomically resolved image at a higher magnification of the highlighted region in Fig. 2a is presented in Fig. 2b. Figure 2c shows the intensity profile of the HAADF image taken from the Ca-doped bilayer presented in Fig. 2a. In the HAADF image, Ca-doped areas exhibit a darker contrast, due to Z -contrast (Z_La = 57 and Z_Ca = 20) [20,30], and the HAADF intensity increases in the first 1–2 unit cells (uc) indicating a Ca-depleted region in the LCCO layer. Figures 2d, 2f, and 2h show RGB (the colors red, green and blue represent Cu, La and the dopant, respectively) atomic resolution maps of Ca-, Sr- and Ba-doped bilayers as measured by EELS. The average profiles of the dopant distributions obtained from the EELS maps are shown below each RGB map in Figs 2e, 2g and 2i. The RGB maps and the average profiles of the dopant distributions for each bilayer exhibit characteristic differences. The Sr-doped bilayer shows the most homogeneous distribution among the dopants (Figs 2f and 2g). The abruptness of the LSCO/LCO interface can be estimated from the decay of the Sr distribution from the M layer into the I layer as 1.6 ± 0.4 nm, which is in fairly good agreement with the values for the interfacial width reported in the literature [4]. Conversely, the distribution of the Ca and Ba dopants in the LCCO/LCO and LBCO/LCO bilayers is less homogeneous. The atomically resolved EELS RGB map (Fig. 2h) and the averaged profile of the Ba dopant (Fig. 2i) indicate that the Ba concentration increases towards the nominal LBCO/LCO interface and obviously demonstrates the tendency of Ba to segregate towards the free surface of the film. Most importantly, as a consequence of such Ba migration, the LBCO/LCO interface is quite smeared and considerably wider than for the other dopants, i.e. the interfacial width for LBCO is 2.6 ± 0.6 nm. As far as the LCCO/LCO bilayer is concerned, we observe a tendency that Ca accumulates at the interface between the substrate and the epitaxial layer, followed by a depletion of Ca in the 1^st and 2^nd uc (Figs 2d and 2e). This behavior is most likely linked with the compressive in-plane strain state in the film. In this case, the extent of cationic intermixing at the M–I interface and the interfacial width is estimated to be ~1.4 ± 0.4 nm. For the determination of the distribution widths for each dopant, several line scans acquired from different regions of the samples are averaged to improve the statistics.
Our investigations highlight the profound influence of the dopant on the final structural properties of the bilayers, and accordingly on the electrical transport properties [29]. We observe a major impact of the dopant size on the in-plane strain state of the films, in a similar way as has already been demonstrated by Lee et al . for a related perovskite system [27]. In particular, when Ba²⁺ is the dopant, i.e. in the LBCO/LCO bilayers, a maximum in-plane strain is induced due to the large misfit. As the HAADF images show perfect epitaxial growth of all films without any defects which could relieve strain, the only way to obtain strain relaxation in the case of the Ba-doped system is by the rearrangement of dopants within the film, i.e. the segregation of excess Ba towards the film surface.
Remarkably, we observed a strong deviation from the expected linear dependence of T_c on the c -axis lattice parameter for the M–I bilayers, with T_c of the LBCO/LCO bilayer being lower than expected (over 60 K), while the c-axis lattice parameter is increased [29]. In order to explain this context, we need to consider the dopant distribution at each M–I interface. In particular, the average cationic intermixing extent is as high as 2 uc in the case of the LBCO/LCO bilayers. The anomalous Ba redistribution is a consequence of Ba segregation towards the film surface, which results in a particularly broadened M–I interface. This finding accounts for the reduced T_c of the LBCO/LCO bilayers as demonstrated for a related LCO-based system for which a spread interface leads to a classical doping model, the so-called "homogeneous doping" [31], in which the hole concentration is increased in correspondence to the randomly distributed ionic dopant point defects, rather than to an interface effect, defining the final local physical properties. In such a situation (only homogeneous doping is active), one expects T_c not to exceed the values which are obtained in doped bulk single-phase systems, i.e. the maximum T_c ~ 40 K is obtained for optimally doped LBCO samples which are epitaxially grown on LaSrAlO₄ (001) substrates [32]. For both the LCCO/LCO and LSCO/LCO bilayers, despite a certain dopant redistribution is present at the interface; the superconducting and structural properties are consistent with HT-IS. Notably, for the LSCO/LCO interface as investigated by Gozar et al . [4], Sr is redistributed into the nominally undoped phase for a depth of about 1 uc, i.e. 1.3 nm, in agreement with our observations on both LCCO/LCO and LSCO/LCO structures.

Fig. 2

Atomic-column resolved STEM and EELS spectrum imaging. (a) HAADF image showing the growth quality, a defect-free structure and coherent interfaces of LCCO/LCO. (b) High magnification of the area highlighted by the red rectangle in (a). (c) Intensity profile along the black arrow in (a), averaged across the horizontal direction. In (d), (f), and (h), RGB elemental maps (La = green, Cu = red, dopant = blue) are shown. In (e), (g) and (i) the dopant distributions of the Ca-, Sr- and Ba-doped bilayers, as obtained from the maps in (d), (f) and (h), are displayed. Figures reproduced with permission from Ref. [29].

Visualizing Jahn–Teller effects at interfaces

After having revealed the dopant distributions, we focus on the correlative impact on the structure of the octahedral network. The CuO₆ octahedron in the parent La₂CuO₄ phase is elongated along the c -axis by the Jahn–Teller (JT) effect [33] and exhibits two long and four short Cu–O bonds [34]. It is reported that, in such systems the incorporation of dopants determines the compression of the octahedron (i.e. a decrease of the Cu–O apical distances) [35] defined as an anti-Jahn–Teller (AJT) effect [33].
In this context, we simultaneously acquired HAADF (Fig. 1) and ABF images (Fig. 3) of the interfaces of all samples, thus imaging all atomic columns in the crystal structure, namely La/Sr–O, Cu–O, and O [36]. To quantitatively analyze and measure the local lattice distortions, we mapped all atomic positions from the images by first locating the center-of-mass and then iteratively refining a 2D Gaussian fitting procedure for each atomic column [37]. Figure 3a–c shows the unambiguously atomic-column resolved ABF images. In Fig. 3d, the measurement of the interatomic distances is defined. The red arrow shows the distance between apical oxygen atoms, the green arrow shows the distance between oxygen atoms in the basal plane.
By averaging the dopant intensity profiles from elemental Ba-M_4,5, Sr-L_2,3 and Ca-L_2,3 EELS analyses, integrating the intensities for each constituting block (i.e. half uc of the A₂BO₄ structure), summing up the values of all the constituting blocks along the growth direction, and scaling the doping concentration profiles in order to preserve the global stoichiometry, we have obtained the dopant concentrations (x ) for each constituting block. Figure 4 a–c summarizes the dopant concentrations and gives quantitative information about the composition of each block. It is known from the electronic phase diagram of the hole-doped lanthanum cuprate system, that the superconducting phase in bulk systems occurs when the doping level of a La₂CuO₄ uc lies between 0.05 ≤ x ≤ 0.26 [38]. At lower doping levels an insulating phase is present (under-doped), whereas a metallic (over-doped) phase appears at x > 0.26. The measured interatomic distances vs. the number of CuO₂ planes (or LCO blocks) are displayed in Fig. 4d–f. The basal and apical O–O interatomic distances are plotted in green and in red, respectively. Each data point corresponds to one measured LCO block. The O–O interatomic distances were calibrated according to the distances measured in the LSAO substrate.
All measurements of the basal in-plane O–O distances for the three different bilayers exhibit the same value (i.e. ~ 3.75 Å), showing a perfect coherency with the LSAO substrate. These findings demonstrate that all films are under compressive in-plane strain [30]. Conversely, in the LBCO/LCO system, a drastic decrease of the apical oxygen distances with increasing Ba concentration is observed (Fig. 4d). In the first LCO block of the epitaxial layer, the measured spacing is 4.72 ± 0.03 Å, whereas it is 4.51 ± 0.04 Å in the 6th LCO block. In the following column (the one next to the nominal LBCO/LCO interface) the O–O apical distance is assessed as 4.69 ± 0.030 Å. Considering the dopant concentrations from the EELS analyses (Figs 2e, f and 4a), it is evident that the blocks mostly exhibit metallic and superconducting phases. This indicates that, due to ionic intermixing, i.e. to ionic doping, superconductivity in the LBCO/LCO bilayer should not be ascribed to effects arising at the M–I interface; rather it is a bulk phenomenon involving several unit blocks [29]. Moreover, the correlation between the gradient in the Ba distribution and the apical O–O distances on both sides of the M–I interface (e.g. the decrease of the apical O–O distance with increasing Ba doping vice versa) could be ascribed to the AJT effect causing AJT distortions [33], which results in a localization of holes in both d_{x2 – y2} and d_z2 orbitals [39]. Consequently, although a larger c -lattice parameter is obtained via Ba doping in both bulk [32] and epitaxially grown heterostructures including single phase films, significant AJT distortions cause shorter Cu–O distances and prevent a T_c enhancement.
In the highly doped region of the LSCO/LCO bilayer, the O–O interatomic distances remain constant (Fig. 4e), while a marked increase by 15 pm from the 8th (4.55 ± 0.03 Å) to the 9th atomic row (4.70 ± 0.05 Å) is detected. Given the homogeneous Sr distribution in the over-doped layer, the AJT effect for the Sr-doped sample is negligibly small, as the O–O distance variations are almost as small as our measurement precision (~ 4 pm) [37]. However, we do observe a considerable increase of the O–O apical distance starting from the 9^th block. Notably, such an "anomalous expansion" has been previously reported for similar systems [8,30], in which the relation with the occurrence of HT-IS as a consequence of interface effects (i.e. hole redistribution near the interface) was clearly demonstrated [6]. Therefore, the observed sharp increase of the apical O–O distance starting from the 9^th block (JT distortion indicating localized holes in d_{x2 – y2} orbitals) can be considered as a fingerprint for a superconducting transition induced by interface phenomena.
In the LCCO/LCO bilayer, large O–O distances were obtained for the first two uc, where the Ca concentration is less than the nominal doping level (Fig. 4f). The value measured for the 2^nd epitaxial block was 4.68 ± 0.04 Å and the lowest values of around 4.56 Å are obtained for the 5th and 6^th blocks representing a decrease of the O–O interatomic distance. For these samples, we face a combination of both an AJT (in the metallic phase) and a JT (starting from the interface) distortion. In the Ca-depleted region (i.e. 1st and 2nd blocks), an increase (~ 10 pm) of the apical O–O distances is followed by a decrease starting from block 3, in which a higher dopant concentration is present. This again represents an AJT effect similar to the over-doped layer of the Ba-doped sample. Finally, a gradual increase starting from the 6th block is observed and the difference between 6^th (4.56 ± 0.04 Å) and 10^th (4.71 ± 0.03 Å) blocks is determined as 15 pm. Remarkably, blocks 9 and 10 do not exhibit the presence of any Ca-dopant, thus we observe here a typical JT distortion which, unlike what was observed for the M phase, cannot be ascribed to the presence of the dopant. Rather, given the superconducting character of the interface, such a JT distortion may be related to 2D interfacial superconductivity in a similar way as discussed for the Sr case.
Our investigations of lattice and octahedral deformations suggest that a JT distortion is present only in the case of Sr- and Ca-doped M–I bilayers. In the case of the Ba-doped bilayer, AJT distortions characterize both sides of the nominal interface of LBCO/LCO. Such a relation between the dopant concentrations and the out-of-plane O–O distances points towards two different superconducting mechanisms, activated by the different dopant distributions leading to different JT distortions. In particular for bulk superconductivity (Ba-doped case) we face a typical AJT distortion (holes located in both d_{x2 – y2} and d_z2 orbitals with parallel spins, resulting in shorter O–O distances [40]), whereas for Sr- and Ca-doped bilayers we observe a combination of AJT and JT distortions (in which holes are located only in d_{x2 – y2} orbitals and the apical oxygens are shifted away from the La sites resulting in larger O–O (apical) interatomic distances). This may be related to the presence of interface effects characterized by an electronic redistribution.

Fig. 3

The ABF images show coherent interfaces and all atomic column positions including the O positions for the (a) Ba-, (b) Sr-, and (c) Ca-doped bilayers. The yellow arrows indicate the nominal interface positions. (d) Illustration of the measurement of the apical and basal O-O distances on a magnified (and colored) section obtained from panel (a). Figures reproduced with permission from Ref. [36].

Fig. 4

Dopant concentration per CuO₂ block for the (a) Ba-, (b) Sr-, and (c) Ca-doped bilayers. The horizontal dashed lines delimitate the region corresponding to the superconducting phase. (d–f) The O-O atomic-column spacing along the apical (red) and basal (green) directions for the LBCO/LCO, LSCO/LCO, and LCCO/LCO bilayers, respectively. The yellow arrows and vertical lines indicate the nominal interface positions. The error bars represent the 95% confidence interval (corresponding to two times the standard error) of the average of 14 uc of LCO along the basal direction. Figures reproduced with permission from Ref. [36].

Dopant – hole decoupling

The structural and chemical investigations performed via comprehensive STEM techniques at the interfaces are compiled in Fig. 5. The high-angle annular dark-field (HAADF) micrograph (Fig. 5a, e) demonstrates perfect epitaxy. In the intensity profile obtained from the HAADF image (averaged perpendicularly to the growth direction), the intensity drop is connected with the Sr-containing layers, which involves more than a single atomic plane, indicating a certain Sr redistribution into the La₂CuO₄ matrix. Spectroscopic analyses (Figs 5c, d) reveal a pronouncedly asymmetric character of the Sr profile: Virtually abrupt at the side facing the substrate (downward side) with an extent of 0.9 ± 0.2 nm and redistributed over 2.3 ± 0.4 nm at the upward side. STEM-EELS (Fig. 5d) provides further robust evidence of the asymmetric Sr distribution, ensuring single atomic layer resolution (step size ≈ 2 Å) [51]. By averaging the different EELS Sr-L_2,3 intensity profiles from several Sr-containing atomic slabs, one can accurately define the Sr level (x ) that can be assigned to each ‘constituting block’ (namely a single CuO₂ plane and the two surrounding (La, Sr)O layers) in proximity of the layer where Sr was initially inserted (Fig. 5f). Obviously, we have realized an abrupt profile, but only at the downward side, while at the other side (upward) there is a pronounced redistribution of the aliovalent cation.
In these 2D-doped La₂CuO₄ multilayers, by appropriately choosing the spacing between the dopant planes, the resulting electrical properties of such heterostructures exhibit HTSC up to ~35 K [31] and is a consequence of the local charge accumulation occurring on both sides of the doped planes as a consequence of different mechanisms of doping: (i) heterogeneous doping at the downward side and (ii) "classical" homogeneous doping at the upward side of the interface. Here "heterogeneous doping" means that hole accumulation occurs to compensate for the spatially confined ionic negative charge stemming from the SrO layer, i.e. a space-charge region is formed as a consequence of 2D doping. In this case, the electronic and dopant distributions are decoupled. "Homogeneous doping" refers to the local compensation of Sr (zero-dimensional) point defects by electron holes. This situation, which is triggered by the highly asymmetric Sr distribution resulting from the growth kinetics, is therefore characterized by the presence of two spatially separated doping modes [31]. (iii) In addition, as highlighted by complimentary Zn-tomography [6] at the downward side, HT-IS is confined in a single CuO₂ plane, namely the second plane far from the interface, while the very first layer is not superconducting [31]. This "overdoping" is most probably due to a high oxygen vacancy concentration, which has to steeply increase in the space-charge electric field created by the SrO layer, owing to a double charge.

Fig. 5

(a) HAADF–STEM image of two-dimensionally doped La₂CuO₄ showing the microstructure of a superlattice (R=8, N= 7) grown on a LaSrAlO₄ (001) substrate. The alternation of brighter and darker areas reflects the superlattice structure, in which Sr-doped regions (dark) are separated by undoped La₂CuO₄ (bright). This is demonstrated by the maxima envelope of the image-intensity profile, integrated perpendicular to the growth direction (b, dark blue line). Scale bar, 2 nm. (b) The intensity oscillations of the intensity profile due to the different contrast of each atomic layer (green line). A magnified image of the region highlighted in red in (a) is shown in (e), in which the dotted yellow line corresponds to the layer having maximum Sr content. Scale bar, 1 nm.(c) [Sr]/[La] ratio, extracted from an EDX line scan across the region shown in (a). An asymmetric Sr distribution, extended in growth direction, is detected. Sr-L and La-L lines were used for quantification of the Sr concentration, and the integrated signals of Sr and La were calibrated using the substrate region where concentration ratio [La]/[Sr] is equal to unity. The error bars are the square root of the intensity. A similar Sr asymmetric profile results from the integration of the Sr-L_2,3 EELS line profiles, as shown in (d), which has been acquired across four Sr-containing layers (blue line in (a)). Here, the error bars (square root of the intensity) are smaller than the symbols. From the EELS analysis, the average Sr number per formula unit (FU, x in La2_-xSrxCuO₄), for each (La,Sr)O-CuO₂-(La,Sr)O ‘constituting block’ in proximity of the Sr-containing layers, as depicted in (f), was obtained (the standard deviation is represented by the error bars). Figures reproduced with permission from Ref. [31].

Probing octahedral distortions

Now, we turn our attention to the hole distribution across the doped interfaces. The pre-edge feature of the O−K edge is very sensitive to the hole concentration [52,53], enabling the local determination of the hole concentration in the superconducting phase [54]. As shown in Fig. 6a, typical O-K edge spectra recorded in the Sr-doped region (red) and in the LCO region (black) can be readily distinguished: a pre-edge feature at around 528 eV (in yellow), which is attributed to transitions from the O 1s core level to hole states with p symmetry in the valence band [55], is clearly seen in the former. The black curve shows no detectable O-K edge prepeak. The intensity of the pre-edge peak has been quantified by multi-Gaussian peak fitting using a nonlinear least-squares (NLLS) routine for all spectra in the line-scan profile across several interfaces (Fig. 6a). To quantify the hole and Sr concentrations per building block of La_2–x Sr_xO₄, we averaged the EELS intensity profiles for line scans over different Sr-doped regions. Subsequently, the amplitude of the hole profile was scaled to satisfy the charge neutrality condition and we obtained the Sr and hole concentrations as functions of the distance from the nominal SrO plane position shown in Fig. 6b (red and blue curves for holes and Sr, respectively). In the two profiles one can again observe the pronounced asymmetry of the Sr concentration whereas, most interestingly, the hole profile is symmetric around the nominal position (x = 0) of the SrO layer. Such a finding indicates that the distribution of the holes is remarkably different from the distribution of the Sr dopant atoms. This highlights that the region with CuO₂ atomic plane numbers P = –4, –3, and –2 is doped via a "nonconventional" mode, i. e., by heterogeneous (2D) doping [31]. The highly confined Sr dopant layer acts as a negatively charged region, which is electrically compensated via the formation of a hole accumulation layer (space-charge effect) on the downward side of the interface. On the upward side of the interface, the formation of a space-charge region is hindered by the broad Sr profile. In this case, the hole concentration follows the Sr²⁺ ion concentration as in conventional homogeneous (one-dimensional) doping.
To evaluate the local atomic distances across the Sr-doped interfaces, we again used simultaneously acquired HAADF and ABF images. Figure 7a presents the atomically resolved overlay of HAADF (blue) and ABF (red) images of an area covering four unit cells around the doped plane. The position of the nominal Sr-doped plane (marked by the yellow arrows in Fig. 7a) was obtained from the HAADF intensity profile. Subsequently, the interatomic apical (out-of-plane) and basal (in-plane) oxygen-to-oxygen (O–O) distances were measured by using the O–O picker software [37]. Figure 7 shows the variations of the La–La spacing (b) and the O–O spacing (c) for each LCO perovskite block as a function of the distance from