To elucidate the epitaxial strain effect over a wide range of lattice mismatch, we investigated the structures of 25 nm thick films grown on the pseudocubic (001) surfaces of three different substrates, namely, (LAO), (STO), and DyScO (DSO). Such structural information had been inferred from the intensities of a small number of Bragg reflections that relate to the octahedral tilting in previous studies. Here, we measured more than 100 reciprocal lattice points to derive reliable structural information. The procedure of ordinary crystal structure analysis is hampered by the multidomain structure and limited volume of measurable reciprocal space, both caused by a huge, highly symmetric substrate. To overcome this difficulty, we employed the Bayesian inference to obtain the detailed atomic positions in film samples. Octahedral tilting about the axis was dominant for the compressively strained film grown on LAO, whereas tilting about the and axes was dominant for the tensile strained films grown on STO and DSO. The film lattice parameters of the samples grown on STO and DSO were nearly identical, whereas additional twofold lattice modulation, including cation displacement, was only observed in the latter.
I. INTRODUCTION
Thin-film fabrication is a major technique for controlling the physical properties of oxides.1–3 Epitaxial strain alters the symmetry, lattice parameters, and internal atomic arrangement within the unit cell. The atomic arrangement determines the electronic band structure4,5 and lattice dynamics6 of the film, thereby modulating the film properties. Examples of such modulation include orbital ordering in Mn oxides,1 thermoelectric activity in ,7 and superconductivity in Ni oxides.4,8
Perovskite Ni oxide films are known to exhibit quantum critical point behavior9 and enhanced catalytic activity through the tunability of their electronic states.10,11 Through the tuning of the in-plane strain through the substrate, the control of the transport,12,13 magnetic,14 thermoelectric,12 and optical15 properties was reported. Most studies on thin films have, therefore, quantified the structural modulation induced by the substrate.
The simplest measure of epitaxial distortion in perovskite oxide films (where A and B denote cations) is the lattice mismatch , where and denote the pseudocubic lattice parameters of bulk and the substrate, respectively. Lattice mismatch just shows a relation of the lattice parameters between two bulk materials. The ratio of the out-of-plane and in-plane lattice parameters is used to quantify the degree of lattice distortion imposed by the epitaxial strain. As the parameter is easy to measure and convenient, the physical properties of perovskite oxide films have been organized using this parameter. However, the behavior of electrons in materials depends not only on the lattice parameters but also on the internal structure of the unit cell. For example, most of the first principle calculations studies on oxide films search for stable atomic arrangement prior to the examination of the electronic states.6,7,16–18 As film fabrication often introduces unexpected vacancies, strain relaxation, and domain formation, experimental investigation of the structural information, such as BO octahedral tilting and A-site displacement, is required. Oxide films thicker than 10 nm can be explored through x-ray crystal structure analysis,19–27 although this characterization technique is not widely adopted. Ordinary structure analyses of oxide films are rendered difficult by domain structures originating from the high symmetry of the substrate surface and the lack of information of large volumes in the reciprocal space, which makes it impossible to derive the space group from the reflection conditions. Some studies utilized an anomalous scattering factor19,28,29 to obtain additional information from the diffraction data in a limited reciprocal space.
Herein, octahedral tilting is represented using the Glazer notation,30,31 and the magnitudes of octahedral tilting about the pseudocubic , , and axes are expressed by the Glazer angles , , and , as shown in Fig. 1. The octahedral tilt angles of (LNO) films grown on SrTiO (STO) and LaAlO (LAO) substrates (with lattice mismatches of % and %, respectively) are reported in Refs. 20 and 27. These angles were obtained from the measurements of Bragg reflections characterized by the wavevector ( ) , where the subscript “pc” denotes the values for pseudocubic basis vectors. The authors reported that the films exhibit a tilt pattern of ( with alternating tilting), which resembles the tilt pattern of bulk LNO, .32 When the compressive (tensile) strain is applied, is the highest (lowest). Weber et al.6 examined LNO films on LAO and (LSAT, %) substrates by density functional theory calculations and Raman scattering. Their calculations derived a change in the stable tilt pattern from ( ), , and to with an increasing in-plane lattice parameter. Furthermore, their Raman scattering measurements revealed two Ni–O bond lengths in LNO on LAO and three Ni–O bond lengths in LNO on LSAT. These features were attributed to the change in the tilt pattern from to .
Schematics of the tilt angles , , and in the structure drawn in three different perspectives.
Schematics of the tilt angles , , and in the structure drawn in three different perspectives.
Here, we focused on LNO films, whose electric conductivity depends on epitaxial strain.12 The conductivity over a wide range of lattice mismatch from % to % is examined in Sec. III A. As a result, we found a sudden change in conductivity as a function of lattice mismatch. Therefore, we examined the structures of three LNO films with different electric conductivities. We studied the structures of LNO films grown on the pseudocubic (001) surfaces of LAO, STO, and (DSO). The corresponding films/substrates are referred to as LNO/LAO, LNO/STO, and LNO/DSO. Our synchrotron x-ray diffraction experiment revealed that the Bragg reflections of all film samples can be indexed by a unit cell with respect to the pseudocubic cell. Energy spectra of the Bragg reflections show cation displacement only in LNO/DSO but oxygen displacements in all samples. A Bayesian inference analysis of the atomic positions in the films revealed a loss of the fourfold symmetry in LNO/STO and cation displacement in LNO/DSO. The number of Bragg reflections used in our analysis (typically 100 reflections) was 10 times larger than those used in previous studies (typically 6–12 reflections), which provided us with highly reliable conclusions. The three samples with different transport properties show qualitatively different structures.
II. METHODS
LNO epitaxial films were grown on LAO, (NGO), LSAT, STO, DSO, and GdScO (GSO) substrates ( mm ) using pulsed laser deposition.33 The in-plane lattice mismatches of LNO on the LAO, NGO, LSAT, STO, DSO, and GSO substrates were , , , , , and %, respectively.34,35 A KrF excimer laser (wavelength of 248 nm) was used to ablate the target disk of polycrystalline bulk composed of and NiO phases, with a laser energy fluence and repetition rate of 0.5 J and 2 Hz, respectively. All LNO films were grown to a thickness of 25 nm at 700 C under high pressure (25 Pa). The electronic conductivities of the LaNiO films were measured using the direct-current four-probe method in the van der Pauw electrode configuration at room temperature.
For structural measurements, the LNO films were deposited on LAO (001) (rhombohedral, Å), STO (001) (cubic, Å), and DSO (orthorhombic, 5.54 Å, 5.71 Å, and 7.89 Å; is one of the planes with pseudocubic lattice parameters of Å35). In general, epitaxial films may have different symmetries from the substrate, which cause domain structures. In the present case, the surface symmetries of the substrates were as follows: (i) LAO: rhombohedral grains of sub-mm size having a mirror plane parallel to one of the {110} planes, and there are four types of domains related by the rotation about the axis; (ii) STO: ; and (iii) DSO: a mirror plane parallel to the -plane = -plane.
The Bragg reflection intensities were measured using four-circle diffractometers at beamlines 3A and 4C of the Photon Factory, KEK, Japan. Monochromatic 12 keV x rays scattered by the film sample placed in a vacuum chamber were detected by a two-dimensional pixel array detector or point detector. The integrated intensities were obtained by the -scan method with illuminated-area correction and ordinary Lorentz correction. The total number of measured reflections is summarized in Table I. Energy spectra of some of the Bragg reflections were measured with the same experimental setup.
Number of finite-intensity peaks/measured reciprocal lattice points of eee, ooo, eoe (oee), and other series in the three samples. The number of structural parameters is also listed.
Subst. . | eee . | ooo . | eoe . | Others . | Num. par. . |
---|---|---|---|---|---|
LAO | 40/40 | 42/45 | 18/67 | 0/12 | 10 |
STO | 37/37 | 49/54 | 9/51 | 0/133 | 13 |
DSO | 57/57 | 48/49 | 49/95 | 0/98 | 7 |
Subst. . | eee . | ooo . | eoe . | Others . | Num. par. . |
---|---|---|---|---|---|
LAO | 40/40 | 42/45 | 18/67 | 0/12 | 10 |
STO | 37/37 | 49/54 | 9/51 | 0/133 | 13 |
DSO | 57/57 | 48/49 | 49/95 | 0/98 | 7 |
Structural deformation was derived through Bayesian inference by employing the Monte Carlo (MC) method in a modified version of our software, the CTR-structure.36,37 The cost function ( ) was monitored throughout the MC calculations. In this expression, denotes the set of structure parameters , denotes the set of Bragg intensities measured at the scattering vector , and are the numbers of structural parameters and data points, respectively, and is the conditional probability of the structural parameters under the conditions of the measured intensity . Applying the uniform prior probability, we have . We also assumed that all measurements are independent, i.e., = . The conditional probability was assumed as a Gaussian distribution with a standard deviation of . This procedure is similar to that followed in Ref. 27; the procedure is sufficiently flexible to account for the desired types of multidomain structures.
The measurements, indexing, and analysis were performed using a unit cell. The Bragg reflections corresponding to the pseudocubic unit cell with lattice parameters of 3.9 Å were indexed to even–even–even and are called reflections. The rhombohedral symmetry of bulk LNO yielded odd–odd–odd ( ) and reflections. Other series in the cell ( , , , or ) are not on the reciprocal lattice points of the rhombohedral unit cell. We examined all series of the reciprocal lattice points in the cell. The structural model of LNO was constructed using the Glazer classification of octahedral tilting.30,31
III. RESULTS AND ANALYSES
A. Transport properties of LNO films on different substrates
Figure 2(a) shows the electrical conductivities ( ) of LNO films grown on various substrate materials at room temperature. The value of the bulk single crystal LNO34 is also presented by the open symbol. Comparing the of the films and the single crystal, we observe that on average, compressive and tensile strains increase and decrease the , respectively. However, the plot of vs mismatch can be classified into three regions: %, %, and with room-temperature conductivities of 10–40, 5, and 1 kS/cm, respectively. Given that epitaxial strain modifies the structure, these changes in transport properties are expected to originate from the structural changes in films. We, therefore, examined the structures of LNO films grown on LAO ( 40 kS/cm), STO ( 5 kS/cm), and DSO ( 1 kS/cm).
(a) Electrical conductivities of films grown on various substrates at room temperature. The open symbol indicates the conductivity of a single crystal.34 The red shaded bars are guides for the eye. (b) Temperature dependence of the conductivities of LNO/LAO, LNO/STO, and LNO/DSO.
(a) Electrical conductivities of films grown on various substrates at room temperature. The open symbol indicates the conductivity of a single crystal.34 The red shaded bars are guides for the eye. (b) Temperature dependence of the conductivities of LNO/LAO, LNO/STO, and LNO/DSO.
Figure 2(b) shows the temperature ( ) dependence of for LNO films on LAO, STO, and DSO substrates. The of the LNO/LAO substrate increased to 2 S/cm, which is two orders of magnitude higher than that of LNO/DSO at 10 K, S/cm. Note that the domain boundaries in LNO films may affect the under different epitaxial strain conditions. On the other hand, a previous study reported that the change originates from the large modulation of carrier concentration,12 suggesting that the crystal structure change modulates the electronic structure and of LNO films under different strain conditions.
B. Structure analysis of LNO/LAO
As mentioned above, the LAO substrate has a multidomain structure of rhombohedral crystallites. As the domain size was comparable to the x-ray beam footprint on the sample surface, the domain ratio had to be refined as a structural parameter.
Table I lists the number of measured reciprocal lattice points and the number of finite-intensity peaks of , , (and , which are overlapped to because of the substrate domain structure), and other series. The intensity distribution of each series of the peak is presented in Fig. 3. Clearly, there are reflections along with reflections. Only a few extremely weak reflections were observed. Furthermore, we do not discriminate from as they are overlapped because of the multidomain structure. In order to clarify the element involved in the structural modulation characterized by the and reflections, we measured the energy spectra of the , , and Bragg reflections. The results are shown in Fig. 4(a). The reflections having a finite contribution from La or Ni show a characteristic energy dependence of intensity at the corresponding absorption edge as shown in the spectra for the 222 Bragg reflection. The results show that the and reflections have no contribution from La or Ni, and, therefore, only oxygen atoms are displaced from the ideal perovskite structure.
Peak intensity distribution for the , , and / reflections of the three samples.
Peak intensity distribution for the , , and / reflections of the three samples.
Energy spectra of some Bragg reflections for (a) LNO/LAO, (b) LNO/STO, and (c) LNO/DSO. Left and right hand side panels show the spectra around the La -edge and the Ni -edge, respectively.
Energy spectra of some Bragg reflections for (a) LNO/LAO, (b) LNO/STO, and (c) LNO/DSO. Left and right hand side panels show the spectra around the La -edge and the Ni -edge, respectively.
The reflections are caused by the octahedral tilt, which yields no or reflections. The existence of weak reflections indicates that the structure breaks the symmetry of the previously reported structure.20,27 We need to take into account the series reflections to clarify the structural deformation from the Glazer model. However, the peaks are too weak and the number of observed reflections was insufficient to derive reliable results. For this reason, we analyzed only and reflections to derive the fundamental structure. The refinement was performed by adjusting the octahedral tilt angles , isotropic atomic displacement parameters of each element (La, Ni, O), and scale factors of the four domains assuming the tilt pattern; note that we have examined other tilt patterns such as and found that other patterns produce strong intensity at the position, where we did not observe any Bragg reflections.
Figure 5(a) shows the measured Bragg intensities vs the calculated intensities on a log–log scale. The minimum intensity observed was 10 on the scale of this graph. The for series reflections is 0, and in this figure, the for this series is plotted at position for presentation.
Observed intensity vs calculated intensity based on the resulting structure models of the (a) LNO/LAO, (b) LNO/STO, and (c) LNO/DSO samples. Blue and red symbols show the and reflections, respectively, and black symbols show the of the and reflections. Many of the and reflections have zero intensity (see Table I). The for ( ) series is zero for the tilt pattern, and the for reflections in panels (a) and (b) are plotted against for presentation. for LNO/DSO is based on the structure model provided in Sec. III D.
Observed intensity vs calculated intensity based on the resulting structure models of the (a) LNO/LAO, (b) LNO/STO, and (c) LNO/DSO samples. Blue and red symbols show the and reflections, respectively, and black symbols show the of the and reflections. Many of the and reflections have zero intensity (see Table I). The for ( ) series is zero for the tilt pattern, and the for reflections in panels (a) and (b) are plotted against for presentation. for LNO/DSO is based on the structure model provided in Sec. III D.
The structural parameters were derived by the MC method. Figure 6(a) shows the frequency distributions (probability densities) of the octahedral tilt angles , , and obtained in the MC analyses. As the signs of the angles have no meaning, two peaks at the same absolute value appeared in the histograms for the three parameters. The peak positions and widths show the most probable value and uncertainty, respectively, of the derived parameters. The derived parameters are summarized in Table II.
Frequency distributions of MC analysis for the octahedral tilt angles , , and in the (a) LNO/LAO, (b) LNO/STO, and (c) LNO/DSO samples.
Frequency distributions of MC analysis for the octahedral tilt angles , , and in the (a) LNO/LAO, (b) LNO/STO, and (c) LNO/DSO samples.
Pseudocubic lattice parameters apc, bpc, and cpc and the obtained structural parameters of the a−b−c− structure. φa, φb, and φc are the octahedral tilt angles about the apc, bpc, and cpc directions, respectively. da,b,c and θa,b,c denote the Ni–O bond length and the Ni–O–Ni angle along the a, b,a and c directions, respectively.
Par. . | LNO/LAO . | LNO/STO . | LNO/DSO . |
---|---|---|---|
apc (Å) | 3.789 | 3.905 | 3.888 |
bpc (Å) | 3.788 | 3.905 | 3.904 |
cpc (Å) | 3.896 | 3.781 | 3.782 |
φa ( ) | 2.8(3) | 5.8(6) | 7.2(5) |
φb ( ) | 3.0(3) | 5.7(6) | 7.6(4) |
φc ( ) | 10.1(3) | 2.0(4) | 0.8(4) |
Uiso(La) (Å2) | 0.0152(13) | 0.045(8) | 0.038(5) |
U11 (Å2) | … | 0.005(2) | … |
U22 (Å2) | … | 0.12(2) | … |
U33 (Å2) | … | 0.010(2) | … |
Uiso(Ni) (Å2) | 0.018(5) | 0.030(14) | 0.036(5) |
U11 (Å2) | … | 0.012(8) | … |
U22 (Å2) | … | 0.06(3) | … |
U33 (Å2) | … | 0.019(5) | … |
Uiso(O) (Å2) | 0.017(4) | 0.037(5) | 0.050(5) |
U11 (Å2) | … | 0.013(2) | … |
U22 (Å2) | … | 0.09(1) | … |
U33 (Å2) | … | 0.009(5) | … |
da (Å) | 1.927(3) | 1.946(2) | 1.961(2) |
db (Å) | 1.926(2) | 1.959(2) | 1.967(2) |
dc (Å) | 1.953(1) | 1.911(3) | 1.925(4) |
158.8(8) | 167.4(8) | 165.0(8) | |
158.9(8) | 168.8(10) | 165.7(12) | |
172.0(9) | 163.1(10) | 158.4(13) |
Par. . | LNO/LAO . | LNO/STO . | LNO/DSO . |
---|---|---|---|
apc (Å) | 3.789 | 3.905 | 3.888 |
bpc (Å) | 3.788 | 3.905 | 3.904 |
cpc (Å) | 3.896 | 3.781 | 3.782 |
φa ( ) | 2.8(3) | 5.8(6) | 7.2(5) |
φb ( ) | 3.0(3) | 5.7(6) | 7.6(4) |
φc ( ) | 10.1(3) | 2.0(4) | 0.8(4) |
Uiso(La) (Å2) | 0.0152(13) | 0.045(8) | 0.038(5) |
U11 (Å2) | … | 0.005(2) | … |
U22 (Å2) | … | 0.12(2) | … |
U33 (Å2) | … | 0.010(2) | … |
Uiso(Ni) (Å2) | 0.018(5) | 0.030(14) | 0.036(5) |
U11 (Å2) | … | 0.012(8) | … |
U22 (Å2) | … | 0.06(3) | … |
U33 (Å2) | … | 0.019(5) | … |
Uiso(O) (Å2) | 0.017(4) | 0.037(5) | 0.050(5) |
U11 (Å2) | … | 0.013(2) | … |
U22 (Å2) | … | 0.09(1) | … |
U33 (Å2) | … | 0.009(5) | … |
da (Å) | 1.927(3) | 1.946(2) | 1.961(2) |
db (Å) | 1.926(2) | 1.959(2) | 1.967(2) |
dc (Å) | 1.953(1) | 1.911(3) | 1.925(4) |
158.8(8) | 167.4(8) | 165.0(8) | |
158.9(8) | 168.8(10) | 165.7(12) | |
172.0(9) | 163.1(10) | 158.4(13) |
The present analysis is based on the fact that only the and series are strong. Thus, the analysis procedure is similar to previous reports,20,27 which utilize only the series. In these studies, the tilt pattern was and the tilt angles were , 20 or , .27 In our result, , , and , showing equals within the experimental uncertainty, thus supporting the tilt pattern. It should be noted that there is some deviation from such a simple Glazer model, as exhibited by the weak reflections. The information we derived from the intensity of reflections is the atomic displacement parameters for La, Ni, and O atoms. The parameter ( 0.016 Å ) is common to the three elements and exceeds the typical values of ordinary single crystals of oxide materials ( 0.005 Å ). This tendency implies that the main source of positional fluctuations is not thermal vibration but static lattice distortion imposed by the substrate. In other words, the film lattices have a larger amount of faults. Even in a few unit cell thick ultrathin films, large parameters are often detected,38 suggesting that film growth processes often involve dislocation formations. The inhomogeneity exhibited by the enhanced parameters can be the Ruddlesden–Popper faults, which are often observed in perovskite films39,40 and superlattices.41
C. Structure analysis of LNO/STO
Table I summarizes the number of measured and observed peaks. Similar to LNO/LAO, LNO/STO exhibited clear and reflections, while only a few reflections were observed. The intensities are consistent with the substrate-surface symmetry, indicating that either (i) the film structure has the symmetry or (ii) the film has a lower symmetry and a much smaller structural domain size than the beam footprint. As shown in Fig. 3, the observed peaks of LNO/STO were weak. The energy spectra of , , and reflections are summarized in Fig. 4(b). The spectra are similar to LNO/LAO, meaning that the and reflections are provided only by the oxygen atoms. When this structure was further analyzed with an octahedral tilt, we did not obtain a sufficient fit by adjusting the tilt angles and the isotropic atomic displacement parameters (La), (Ni), and (O). A reasonable fit was obtained only after assuming anisotropic atomic displacement parameters.
For this refinement, we used a scale factor, and anisotropic atomic displacement parameters ( ) for La, Ni, and O. The fitting result is presented in Fig. 5(b) and the obtained parameters are listed in Table II. For all three elements, the and values were approximately 0.01 Å and was approximately 0.1 Å . Note that the typical value for LNO/LAO (0.016 Å ) is similar to the and values for LNO/STO. The large indicates the loss of the fourfold symmetry and a large fluctuation in atomic positions in the -direction. The symmetry of the Bragg intensity results from the multidomain structure.
Figure 7(a) shows the line profiles along ( ) with and . Two series of peaks are observed: sharp peaks at , which are independent of , and broad weak peaks at . The latter series is one order of magnitude weaker than the former. If we interpret them as the Bragg reflections, the reciprocal lattice is monoclinic [Fig. 7(b)] and the angle between and is . In two of the domains, the film axis is parallel to the substrate axis and the film axis is inclined by 0.7 from the substrate axis as shown in panels (c) (black and red dashed domains) and (d) (wide area view of the black domain). As shown in panel (d), the atomic positions of the film deviate from those in the substrate lattice along the -direction. This feature results in an inhomogeneous strain being imposed by the substrate lattice, thereby increasing the parameter value for all the ions.
(a) ( ) profiles measured on and . The Bragg reflections of the film are accompanied by peaks at finite positions (indicated by the gray bars). The dashed lines exhibit the dependence of the peak positions. (b) Schematic of the reciprocal lattice on a constant plane. Gray horizontal lines correspond to the measured lines in panel (a). Black, red, blue, and sky-blue symbols show the reciprocal lattice points in the four possible domains having monoclinic distortion. (c) Real-space images of the unit cells in the four domains. (d) Lattice matching of the black domains in panels (b) and (c) with the STO substrate (thin dashed lattice).
(a) ( ) profiles measured on and . The Bragg reflections of the film are accompanied by peaks at finite positions (indicated by the gray bars). The dashed lines exhibit the dependence of the peak positions. (b) Schematic of the reciprocal lattice on a constant plane. Gray horizontal lines correspond to the measured lines in panel (a). Black, red, blue, and sky-blue symbols show the reciprocal lattice points in the four possible domains having monoclinic distortion. (c) Real-space images of the unit cells in the four domains. (d) Lattice matching of the black domains in panels (b) and (c) with the STO substrate (thin dashed lattice).
Similar to the LNO/LAO case, the LNO/STO system was refined using only the and reflections. Previous reports,20,27 which analyzed only a few reflections, yielded , ,20 and , .27 Previous studies reported the tilt pattern, but our result ( , , and ) supports the tilting pattern. Again, the weak reflections show the symmetry breaking, while the corresponding structural modulation is minor.
D. Structure analysis of LNO/DSO
The DSO substrate has orthorhombic symmetry, and the surface is (110) in the lattice. The orientation is illustrated in Fig. 8(a). The octahedral tilt of the substrate is . Based on our measurements, the lattice parameters of the substrate and the film in the notation are (DSO) Å, Å, Å, and (LNO) Å, Å, Å, , , and , where the superscripts s and f denote the substrate and the film, respectively. The in-plane directions and are chosen to be parallel to and , respectively. In the pseudocubic setting, the lattice parameters are Å, Å, , and for DSO and Å, Å, Å, and within the experimental uncertainty ( ) for the LNO film (see Table II). Note that and , indicating that the stress is partially relaxed. The reciprocal lattice of this sample is illustrated in Fig. 8(b). The tilt in causes a tilt of the axis of the substrate; consequently, the Bragg reflections of the substrate overlap with those of the film over a wide range in the positive -side. For quantitative analysis, reflections having no substrate contribution were selected based on the peak width, intensity, and position.
(a) (black arrows) and pseudocubic (red arrows) settings of the DSO substrate lattice and the pseudocubic lattice of the LNO film. (b) Schematic of the reciprocal lattices of the DSO substrate (black) and the LNO film (red dashed lines). The tilted axis of DSO causes the inclination of the axis. (c) -axis view, and (d) -axis view of the LNO/DSO structure obtained in Sec. III D. The large, middle, and small circles denote La, Ni, and O, respectively. The color of the symbols exhibits the atomic position perpendicular to the page.
(a) (black arrows) and pseudocubic (red arrows) settings of the DSO substrate lattice and the pseudocubic lattice of the LNO film. (b) Schematic of the reciprocal lattices of the DSO substrate (black) and the LNO film (red dashed lines). The tilted axis of DSO causes the inclination of the axis. (c) -axis view, and (d) -axis view of the LNO/DSO structure obtained in Sec. III D. The large, middle, and small circles denote La, Ni, and O, respectively. The color of the symbols exhibits the atomic position perpendicular to the page.
The number of measured and observed peaks are summarized in Table I. Again, and reflections were clearly observed. In addition, reflections are stronger than those in the other two samples as shown in Fig. 3. The energy spectra shown in Fig. 4(c) indicate that there is a cation displacement characterized by reflections, i.e., a twofold structure along the direction. Based on the relative intensity between and reflections, the amplitude of the cation displacement was estimated to be as large as 0.03 Å. The spectra for reflections were measured at the 302 or 102 positions. There is no cation contribution, which indicates that these reflections are caused by the oxygen displacement.
The octahedral tilt angles were examined with the Glazer model by assuming all eight combinations of the tilt modes ( ) with all the measured reflections, and we found that with was the most probable. The obtained structural parameters are listed in Table II. Note that the series reflections, which are provided from the oxygen displacement, were not reproduced by this model. They show noticeable intensity, meaning that the amplitude of the twofold oxygen displacement is comparable with the displacement caused by the octahedral tilting. The structure we obtained for LNO/DSO differs from the previously reported theoretical expectation.6,20
In order to derive the modulated structure characterized by the additional and reflections, we tried to find the atomic positions based on all the measured intensities for LNO/DSO. The cation structure provides finite scattering amplitudes at and , meaning that the cation structure has a periodicity of ; thus, there are only two crystallographically unique La (Ni) atoms. We made an assumption that each oxygen octahedra keeps inversion symmetry with respect to the undistorted Ni position. As a result, the number of unique oxygen atoms is reduced to 12, and the number of parameters is 52 ( , , and for 2 La, 2 Ni, and 12 O atoms, for the three elements, and the scale factor). It is also important to find the multidomain structure. The DSO substrate has a mirror plane parallel to the -plane. In addition, the shape of the film unit cell is the orthorhombic cell, which also has a mirror plane parallel to the -plane. When we assume only the domains connected by the -mirror plane, the derived structure was highly distorted and we did not obtain a physically reasonable solution. Therefore, we assumed that there are four kinds of domains connected by the - and -mirror planes. The result of the fit is presented in Fig. 5(c). The -axis view and the -axis view of the resultant structure are presented in Figs. 8(c) and 8(d). The volume of the octahedra is uneven, which suggests a nonuniform Ni valence state. This may cause the suppressed electric conductivity found in the films having a large lattice mismatch . The resulting atomic positions are summarized in the supplementary material.
IV. DISCUSSION
We examined the structures of LNO films grown on three different substrates; they have distinct electric conductivity. Compressively strained films exhibit higher electric conductivity, which has been explained by the increased carrier density, as determined from Hall measurements and band calculations.12 According to the band calculation on a compressively strained structure, the increased carrier density (and, hence, conductivity) is caused by a self-doping effect from the O -band to the Ni -band. In a tensile strained film, the O -band is fully occupied and the self-doping effect is quenched, resulting in a constant carrier density.12 This mechanism explains the results of our transport measurements in the range of (Fig. 2). However, our transport measurements revealed strongly suppressed conductivity in those films whose were larger than , which require another mechanism for conductivity reduction. The observed strong reflections and cation displacements suggested a charge disproportionation mechanism. Here, we examine the results again to discuss other possible causes.
From the microscopic point of view, the structural features that dominantly affect the conductivity are Ni–O distance , Ni–O–Ni bond angle , and the volume of octahedra. The parameters and control the transfer integral, and the octahedral volume relates to the energy level of the Ni site, i.e., the valence of the site, in the localized picture. The values of them for LNO/LAO and LNO/STO are shown in Table II. They are derived by the Glazer model, which involves a small number of structural parameters. For the structure of LNO/DSO, the structure model we finally used involves 52 parameters, which is comparable to the number of observed Bragg reflections. The number of reflection limits the reliability of our result. We examined the values of and for LNO/DSO. They show a wide distribution within the range of 1.7–2.2 Å and – , respectively, which should have a large uncertainty. In addition, the Ni position in the LNO/DSO structure model is displaced from the center of symmetry. It is desired to examine if the inversion symmetry is actually broken from other experimental techniques, such as second harmonic generation measurements.
Although the quantitative analysis contains a large uncertainty, our result clearly shows that LNO/DSO involves cation displacement and twofold oxygen displacement along the direction. The magnitude of the cation displacement is estimated to be 0.03 Å. The intensity of reflections is nearly as strong as that of reflections, showing that the oxygen displacement characterized by the reflections should be much larger, which suggests strong deformation of the octahedra.
Another possible source of suppressed conductivity is the large atomic positional fluctuation. The parameters for La, Ni, and O in LNO/DSO are 0.0439(9), 0.0244(13), and 0.0433(10) Å , respectively, as provided in the supplementary material. These values are larger than those in LNO/LAO by a factor of 2. A large atomic positional fluctuation makes carriers localized, which can result in suppressed conductivity.
V. CONCLUDING REMARK
A detailed structural investigation was performed for LNO/LAO, LNO/STO, and LNO/DSO to elucidate the effect of epitaxial strain on the average structures of rather thick ( 25 nm) films. The octahedral tilt patterns of LNO/LAO, LNO/STO, and LNO/DSO were , , and with noticeable octahedral deformation. The positional fluctuations of atoms in the film samples are significantly larger than those in the bulk crystals, showing that the main source of positional fluctuations is not thermal vibration but static lattice distortion imposed by the substrate. Larger parameters are found in films whose in-plane lattice parameters differ from those of the substrate. In the case of LNO/STO, the positional fluctuations of atoms were highly anisotropic within the plane, which are related to the deformation of the film lattice characterized by the lattice parameter . The atomic displacement in LNO/DSO indicates the existence of crystallographically independent Ni sites, allowing the charge disproportionation. Further theoretical investigation is required to examine the energetic stability and effect on the conductivity of the charge disproportionation.
SUPPLEMENTARY MATERIAL
The derived atomic positions in the 2 × 2 × 2 unit cells are provided as cif files in the supplementary material.
ACKNOWLEDGMENTS
This work was supported by a Grant-in-Aid for Scientific Research [Japan Society for the Promotion of Science (JSPS) KAKENHI, Grant Nos. JP22H02024 and JP23K23292] and by the MEXT program: Element Strategy Initiative to Form Core Research Center (Grant No. JPMXP0112101001) and Data Creation and Utilization Type Material Research and Development Project (Grant No. JPMXP1122683430). The synchrotron radiation experiments at the Photon Factory were performed with the approval of the Photon Factory Program Advisory Committee (Proposal Nos. 2018G533, 2019V003, 2020V001, 2020G526 and 2022G016).
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Fumiya Izumisawa: Investigation (lead); Software (lead); Writing – original draft (equal). Yuta Ishii: Investigation (equal). Masatoshi Kimura: Investigation (equal). Takayoshi Katase: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). Toshio Kamiya: Supervision (equal); Writing – review & editing (equal). Jun-ichi Yamaura: Investigation (supporting); Writing – review & editing (equal). Yusuke Wakabayashi: Conceptualization (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.