Observing a previously hidden structural-phase transition onset through heteroepitaxial cap response

Significance

We provide an approach to study structural transitions by using appropriate heteroepitaxial caps. Previously unobservable phase transitions that involve small changes in lattice constants, but may have important impact on the physical properties of the material, can now be detected in real space. Using the coherent nanotwinning waves of epitaxial La_0.7Sr_0.3MnO₃/SrTiO₃ thin films as a sensitive detector, we are able to uncover the onset stage of the cubic-to-tetragonal structural-phase transition of SrTiO₃ in real space. Researchers involved in the study of material properties as well as technologists in a variety of industries, such as electronics, will greatly benefit from this approach.

Abstract

Characterization of the onset of a phase transition is often challenging due to the fluctuations of the correlation length scales of the order parameters. This is especially true for second-order structural-phase transition due to minute changes involved in the relevant lattice constants. A classic example is the cubic-to-tetragonal second-order phase transition in SrTiO₃ (STO), which is so subtle that it is still unresolved. Here, we demonstrate an approach to resolve this issue by epitaxially grown rhombohedral La_0.7Sr_0.3MnO₃ (LSMO) thin films on the cubic STO (100) substrate. The shear strain induced nanotwinning waves in the LSMO film are extremely sensitive to the cubic-to-tetragonal structural-phase transitions of the STO substrate. Upon cooling from room temperature, the development of the nanotwinning waves is spatially inhomogeneous. Untwinned, atomically flat domains, ranging in size from 100 to 300 nm, start to appear randomly in the twinned phase between 265 and 175 K. At ∼139 K, the untwinned, atomically flat domains start to grow rapidly into micrometer scale and finally become dominant at ∼108 K. These results indicate that the low-temperature tetragonal precursor phase of STO has already nucleated at 265 K, significantly higher than the critical temperature of STO (∼105 K). Our work paves a pathway to visualize the onset stages of structural-phase transitions that are too subtle to be observed using direct-imaging methods.

The onset stage of a phase transition can occur at temperatures well above its critical temperature (T_c) (1, 2). For second-order structural-phase transitions, determination of the onset requires resolution of subtle changes of lattice constants that are often spatially inhomogeneous. The antiferrodistortive structural-phase transition of SrTiO₃ (STO) at 105 K is a classic example, where adjacent TiO₆ octahedrals rotate and the crystal symmetry is lowered from cubic to tetragonal. The change of the lattice parameter is less than one thousandth of a percent upon the phase transition (3), which is beyond the sensitivity of current imaging techniques (4). Diffraction techniques, while showing evidences of fluctuations at temperatures above T_c (1, 2, 5, 6), generate controversial results regarding the correlation time and length scales (7–11) and fail to provide a microscopic picture of the onset of the phase transition as the temperature approaches T_c.

In this work, we are able to present a clear microscopic picture of the onset stages of the cubic-to-tetragonal structural-phase transition of STO by observing how an epitaxial La_0.7Sr_0.3MnO₃ (LSMO) thin film on the STO behaves. While the phase transition cannot be visualized by direct-imaging methods, in effect, we use a canary in a coalmine approach to recognize the onset of the extraordinarily subtle cubic-to-tetragonal phase transition in real space as temperature is lowered toward T_c. Specifically, we use the shear strain induced nanotwinning waves of LSMO thin films on STO (100) to probe the structural-phase transition of the STO underneath. Because the nanotwinning waves are generated by long-range elastic distortions of coherent growth of LSMO film on STO substrate (12), any slight changes of STO lattice constant will disturb the coherence yielding an amplified influence on the formation of the nanotwinning waves.

By imaging the temperature-dependent evolution of the nanotwinning waves, we find that the disappearance of the nanotwinning waves upon cooling is spatially inhomogeneous. Specifically, untwinned and atomically flat domains with a length scale of ∼100–300 nm start to appear between 265 and 175 K and grow rapidly into micrometer scale at 139 K and finally become completely dominant around 108 K. This behavior of the LSMO film indicates that STO’s low-temperature tetragonal phase starts to nucleate at temperatures as high as 265 K, which is nearly 100 K higher than previously reported (13–15). Our data analysis indicates that the growth of the tetragonal-phase domains fits well with the proposed inhomogeneous microdomain model (15).

The LSMO thin films were grown on 0.1% Nb-doped STO (001) single-crystal substrates (CrysTec GmbH) using pulsed-laser deposition (PLD) (248 nm, 1 Hz, 1 J/cm² fluence). Undoped STO substrates were used for ex situ transport measurements. Before growth, the substrates were chemically etched by buffered HF, followed by ex situ annealing in furnace with 1-atm oxygen flow at 950 °C, and then in situ annealing at 820 °C in a flowing oxygen (8% ozone) environment under a pressure of 7 mtorr. To ensure an atomically flat surface and to minimize oxygen deficiencies, the films were in situ-annealed for 10 min after the completion of each unit cell (UC) layer. To prevent the surface reconstruction of oxygen overlayer, the annealing time after the completion of the final unit cell layer was limited to 2 min (16). After evacuating the oxygen from the growth chamber, the samples were transferred in situ to a STM chamber with a base pressure of 1 × 10⁻¹⁰ torr.

To understand the nature of the twinning domains in this system, one can view the rhombohedral structure of the LSMO as a compressed cubic unit cell along the <111> direction, as shown in Fig. 1A. In the cubic unit cell, the four <111> directions are equivalent, giving rise to four rhombohedral domain pairs when projecting to the (001) plane, which are (100)-r₁/r₂, (010)-r₂/r₃, (100)-r₃/r₄, and (010)-r₄/r₁ (Fig. 1B) (17). As sketched in Fig. 1C, neighboring twinning domains will have a small angle (θ) sheared both in the plane and out of the plane with opposite directions. Fig. 1 D–G shows the STM morphological appearance and corresponding line profiles of the nanotwinning patterns for a 43-UC and an 8-UC LSMO at 295 K. The cross-section of the nanotwinning patterns of the 43-UC LSMO is triangular in shape, with the up and down slopes corresponding to the two twin-related facets, as demonstrated schematically in Fig. 1C. The 31.4-nm lateral wave length and the 78.9-pm vertical peak-to-peak height gives rise to an out-of-plane tilting angle of 0.29°, which is close to the misfit angle 0.268° between rhombohedral LSMO and cubic STO (18). For the 8-UC film, a distinct appearance of the nanotwinning waves with periodicity of four atomic lattice spacing can be seen. The domain width is only 2 UC, and the tilting angle is 2.7°. The nanotwinning waves of the 8-UC film are not caused by an oxygen overlayer-induced surface reconstruction, because the height difference between the low and high atomic chains is only 0.3 Å (Fig. 1G), which is significantly smaller than the 1.3-Å height of an oxygen overlayer (16). The zoom-in image in Fig. 1H shows the in plane lattices of the two high-atomic chains and the two low-atomic chains with a shearing angle of 5° compared with the cubic unit cell. Note that the domain wall has a negligible in plane shearing angle compared with the cubic unit cell. This unusual strain relief behavior results in a monoclinic structure; thus it partially resembles the rhombohedral-like crystal structure of LSMO. Both (100) and (010) type domain walls coexist for these 2-UC-wide domains, limiting their length to several tens of nanometers. In contrast, the atomic resolved image of the 7-UC film (Fig. 1I) clearly shows a (1 × 1) square lattice, indicating that the 7-UC film is fully strained in tetragonal phase and is the critical thickness of nanotwinning formation.

Fig. 1.

(A) The rhombohedral structure of the LSMO can be obtained via compressed cubic unit cell along one of the four <111> directions. (B) The model of four rhombohedral domain pairs. (C) Schematics of nanotwinning patterns. (D and E) STM morphological image and line profile of 43-UC LSMO acquired at 295 K shows a periodic nanotwinning wave. (V_bias = 2.0 V; I = 30 pA) (F and G) STM image and line profile of 8-UC LSMO indicate the domain width is only 2 UC. (H) The zoom in image of 8-UC LSMO shows a typical (100)-r₃/r₄ twinning domain pair. The r₃ and r₄ domains have a 5° in plane shearing angle. (I) The 7-UC LSMO has an atomic flat surface, and there is no twinning wave formed.

LSMO is one of the rare colossal magnetoresistance manganites whose metal–insulator transition temperature is above room temperature. The high spin polarization makes it attractive for spintronic applications (19). In the ultrathin thickness regime, however, LSMO exhibits dramatically different physical properties compared with those of the bulk (20). Fig. 2 A and B shows resistivity and STM I–V curves (Inset) of 7- and 8-UC LSMO, respectively. The fully strained 7-UC film is an insulator with a gap of 0.25 V at 108 K (21). The tetragonal symmetry makes the MnO₆ octahedron deformed, which modifies the crystal field splitting of the d orbitals to favor $d_{3z^2-r^2}$ (20, 22), thereby suppressing the intralayer double-exchange (DE) interaction. As soon as the nanotwinning domains are formed at 8 UC with a partial relief of shear strain, the LSMO films become rhombohedral-like (23). This trigonal symmetry recovers the degeneracy of the e_g band and strengthens the intralayer DE interaction (24). The system correspondingly transits into the metallic state.

Fig. 2.

(A) The transport measurement and STM I–V curves of 7-UC LSMO indicate an insulator behavior. (B) The 8-UC LSMO recovers the metallicity. (C) Summarized thickness dependent domain width l and tilting angle θ of twin related facets with the blue line indicating the bulk value. Three regions can be recognized according to the tilting angle. (D) The thickness dependent magnetic Tc. The Inset is the FC curves along [100]. Except region I (4 and 7 UC), the FC curves of region II and III all show a dip at 105 K (marked by the black line).

The thickness dependent domain width and the out-of-plane tilting angle of the twinning domains in the LSMO films are shown in Fig. 2C. The blue line marks the distortion angle of the bulk LSMO as a reference (0.268°). The average domain width l increases with increasing thickness in agreement with theoretical predictions (12). We observe three thickness-dependent regimes. In region I (≤7 UC), the films are fully strained (tetragonal) with atomically flat surfaces. In region II (between 8 and 14 UC), the nanotwinning domains are formed, and the lattice relaxes to the rhombohedral-like symmetry, although the tilting angles are noticeably larger than the bulk value due to the epitaxial strain. In region III (>14 UC), the films are fully relaxed and the tilting angle of the twinning domains becomes bulk-like.

Fig. 2D shows T_c as a function of thickness derived from temperature-dependent magnetization measurements. With decreasing thickness, T_c first decreases slightly from 358 K at 80 UC to 324 K at 14 UC and then drops rapidly below 14 UC. The Inset of Fig. 2D shows normalized field cooling (FC) curves of several representative thicknesses measured in a magnetic field of 100 Oe along the [100] direction. Interestingly, the curvature continuity of the FC curves in region II and III breaks around 105 K (marked by the black line), while no such breaks are observed for the FC curves in region I (4 and 7 UC). This indicates that the twinned films are sensitive to the 105 K structural-phase transition of the STO substrate, while the untwinned films are not.

Temperature-dependent STM studies reveal that the nanotwinning domains depend sensitively on temperature. Fig. 3 shows the surface morphology of a 50-UC LSMO film acquired at 295 and 108 K, respectively. While the nanotwinning domains are clearly visible at 295 K, they disappear at 108 K. Note that direct STM imaging of the STO (001) substrate reveals no differences between 295 and 108 K (SI Appendix, Fig. S1), indicating that the structural transition of STO is indeed too subtle to be visualized directly. We argue that the disappearance of the nanotwinning domains is caused by the phonon softening and structural transition of the STO substrate. For the displacive phase transition of STO, the frequency of R₂₅ phonon will completely go to zero around T_c, and the restoring force of the lattice goes to zero accordingly. The phonon softening makes the LSMO/STO interface become less rigidly confined, resulting in the disappearance of the nanotwinning domains of the LSMO films. Since the nanotwinning patterns originate from the relaxation of the shear strain between the rhombohedral LSMO thin film and the cubic STO substrate, their existence requires long-range coherence of the LSMO and the STO lattices, similar to the Moiré pattern. In addition, there exist lots of nanometer scale random anti-phase domain boundary in the low-temperature tetragonal STO because the neighboring TiO₆ octahedron can rotate in the same or the opposite directions along the rotation axis (25). Any local lattice decoherence between the LSMO and the STO will affect the existence of the nanotwinning patterns, which can thus serve as an ultrasensitive local probe of the structural-phase transition of the STO substrate underneath. To further prove this point, we grew 50-UC LSMO on (LaAlO₃)_0.3(Sr₂AlTaO₆)_0.7(001) substrate (LSAT), another system showing nanotwinning wave (26). Because the LSAT maintains its cubic structure over a wide temperature range, one would not expect changes of nanotwinning patterns. Indeed, as shown in the SI Appendix, Fig. S2, the satellite peaks of nanotwinning waves at 100 K are almost identical to those at room temperature (295 K). We thus conclude that the nanotwinning wave of LSMO can indeed unveil the long range coherence of substrate underneath. Using this ultrasensitive method, we can study the kinetics of STO’s structural-phase transition in real space.

Fig. 3.

STM images of 50-UC LSMO acquired at 295 K (A) and 108 K (B), which are fully twinned and untwined, respectively.

Surprisingly, untwinned, atomically flat regions start to appear (indicated by the blue dotted lines) at temperatures as high as 265 K for the 50-UC film upon cooling, as shown in Fig. 4A. The initial untwinned regions are between 100 and 300 nm in size and distributed randomly in the twinned phase. The nucleation sites are not associated with edge or screw dislocations. Upon further cooling to 240 K (Fig. 4B), 209 K (Fig. 4C), and 175 K (Fig. 4D), the untwinned regions increase slightly in number without noticeable change in size. Further cooling results in a rapid growth of the untwinned regions. At 139 K, the untwinned regions become dominant with some remaining nanotwinning domains scattered inside (marked by red dotted lines in Fig. 4E). The line profile in Fig. 4G indicates that the remaining nanotwinning domains at 139 K have the same periodicity but much smaller corrugation compared with those at 295 K. When the film is further cooled to 108 K, the nanotwinning domains largely disappear (Figs. 3B and 4F). We note that when the film is warmed back to room temperature, the nanotwinning patterns recover fully to their original appearance as shown in Fig. 3A.

Fig. 4.

STM images of a 50-UC LSMO recorded at T = 265 K (A), 240 K (B), 209 K (C), 175 K (D), 139 K (E), and 108 K (F), respectively. The untwinned, atomic flat domains nucleate between 265 and 175 K as marked by the blue dotted lines. The residual nanotwinning domains at 139 and 108 K are marked by the red dotted lines. The nanotwinning domains largely disappear upon cooling. (G) Line profiles of 50-UC LSMO at 295 and 139 K indicate the cooling would not change the periodicity, but the corrugation. (H) Summarized temperature dependent area percentage of the twinned regions with the red circle and line showing the average value.

Fig. 4H shows the temperature dependence of the area fraction of the twinned regions in the 50-UC LSMO film based on statistical analysis of STM images acquired at different positions. With decreasing temperature, the area fraction of the nanotwinned regions gradually decreases between 265 and 175 K (stage I, nucleation stage) and drops rapidly between 175 and 105 K (stage II, growth stage), until the surface is completely dominated by the atomically flat, untwinned phase. The low-temperature tetragonal precursor phase of the STO starts to nucleate at 265 K and then develops rapidly at 139 K. We note here that the high temperature of the onset of structural-phase transition of STO is not influenced by the epitaxial stress from LSMO film. As shown in the SI Appendix, Fig. S3, the nonuniform nanotwinning patterns start to appear around 270 K in the case of 11-UC LSMO film. Considering the fact that the stress applied from the 11- and 50-UC LSMO film is quite different, and yet the onset of transition temperature is similar, we conclude that the observed high T_c indeed represents the intrinsic transition temperature of STO substrate.

The evolution of the nanotwinning patterns has strong influence on the physical properties of the LSMO films. As shown in the Inset of Fig. 5A, STM I–V curves measured from the twinned and untwinned regions exhibit distinctly different line shapes. At 108 K, although both regions are metallic, the conductivity of the untwinned regions (black) is lower than that of the twinned regions (red). The transport data in Fig. 5A also shows a bump around 105 K. With the vanishing of the nanotwinning domain walls upon cooling, the nanotwinning patterns of the LSMO films will transform into a monodomain with one of the four possible variants. The hysteresis loops in Fig. 5B show that the magnetic easy axis is along the [110] direction with a saturation field around 250 Oe. As shown in Fig. 5C, if the external field is smaller than the saturation field, the FC curve exhibits a curvature break around 105 K when the field is applied along the hard axis ([100] direction) and remains smooth when field is applied along the easy axis ([110] direction). By increasing the magnetic field to 1,000 Oe, the FC curves in [100] and [110] directions are almost identical without breaks at 105 K (Fig. 5D). Our results indicate that the curvature breaks of the FC curves at 105 K reflect the temperature-induced spin reorientation transition due to the vanishing of nanotwinning domains.

Fig. 5.

(A) The resistivity of 50-UC LSMO shows a bump around 105 K. (A, Inset) STM I–V curves obtained at set point of (−0.5 V, 0.3 nA) on the surface of untwined and residual twinned regions at 108 K show different conductivity. (B) The hysteresis loops show the magnetic easy axis to be along [110] direction with a saturation field of 250 Oe. C and D are FC curves measured under 100- and 1,000-Oe external magnetic field, which indicates a spin reorientation due to the vanishing of nanotwinning patterns. Only when the field is smaller than 250 Oe and along a hard axis, the FC curve will have a dip around 105 K.

The observation that STO begins to undergo a structural-phase transition at 265 K is important. Previous studies could only observe the onset stage of the transition below 150 K, when the tetragonal phase starts to form rapidly (13–15). Without the help of direct-imaging methods, it remains a matter of dispute whether the onset of transition is caused by high surface T_c (27) or early formation of microdomains of tetragonal phase (15). Our results not only confirm the existence of the microdomains above bulk T_c but also reveal that the nucleation of the low-temperature tetragonal precursor phase occurs at 265 K. The fact that we can catch the nucleation process during the onset stage of the STO structural-phase transition demonstrates that our approach is ultrasensitive to very early stages of structural-phase transitions.

In conclusion, we have used the nanotwinning patterns in the LSMO films as a sensitive probe to study the structural-phase transition of the STO underneath in real space. Our results reveal that the low-temperature tetragonal precursor phase of STO nucleates at 265 K, and the low-temperature tetragonal phase and high-temperature cubic phase coexist in a relatively large temperature range. Recognizing that STO begins to undergo structural-phase transition at such a high temperature is also extremely important to the larger oxide community as STO is one of the most widely used substrate. A coherently strained epitaxial film can be influenced by the minute changes of the STO’s lattice parameters, which in turn may affect the physical properties of the epitaxial films. Moreover, our approach paves a way to study the onset stage of second-order structural-phase transition in real space, which is very challenging for direct-imaging methods.