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ABSTRACT Advances in complex oxide heteroepitaxy have highlighted the enormous potential of utilizing strain engineering via lattice mismatch to control ferroelectricity in thin-film

heterostructures. This approach, however, lacks the ability to produce large and continuously variable strain states, thus limiting the potential for designing and tuning the desired

properties of ferroelectric films. Here, we observe and explore dynamic strain-induced ferroelectricity in SrTiO3 by laminating freestanding oxide films onto a stretchable polymer substrate.

Using a combination of scanning probe microscopy, optical second harmonic generation measurements, and atomistic modeling, we demonstrate robust room-temperature ferroelectricity in SrTiO3

with 2.0% uniaxial tensile strain, corroborated by the notable features of 180° ferroelectric domains and an extrapolated transition temperature of 400 K. Our work reveals the enormous

potential of employing oxide membranes to create and enhance ferroelectricity in environmentally benign lead-free oxides, which hold great promise for applications ranging from non-volatile

memories and microwave electronics. SIMILAR CONTENT BEING VIEWED BY OTHERS THE CLASSICAL-TO-QUANTUM CROSSOVER IN THE STRAIN-INDUCED FERROELECTRIC TRANSITION IN SRTIO3 MEMBRANES Article Open

access 13 May 2025 CLAMPING ENABLES ENHANCED ELECTROMECHANICAL RESPONSES IN ANTIFERROELECTRIC THIN FILMS Article 23 May 2024 THE ENHANCED FERROELECTRIC PROPERTIES OF FLEXIBLE HF0.85CE0.15O2

THIN FILMS BASED ON IN SITU STRESS REGULATION Article Open access 31 January 2025 INTRODUCTION Transition metal oxides exhibit a diverse set of electrical, magnetic, and thermal properties

and hold great promise for modern technological applications. Among these oxide materials, the perovskite SrTiO3 has stimulated considerable interest as it hosts a rich spectrum of physical

properties such as dilute superconductivity1, multiple structural instabilities2, and a variety of emergent phenomena arising from the interface of SrTiO3-based heterostructures3,4,5,6,7. In

addition, SrTiO3 is also one of the few known quantum paraelectric materials, in which quantum fluctuations and antiferrodistortive instabilities suppress ferroelectric polar order at low

temperature, thus resulting in a nonpolar paraelectric state8,9. Despite the intrinsic paraelectric nature of SrTiO3, it is possible to stabilize ferroelectric order via a variety of means

such as substrate-induced strain10,11,12,13,14, cation doping15, 18O isotope substitution16, and defect engineering17, etc. In particular, advances in thin-film epitaxy have highlighted the

role of substrate-induced strain in stabilizing ferroelectricity and enhancing the ferroelectric transition temperature _T_c in SrTiO3 thin-film heterostructures. This strategy of strain

engineering relies on the lattice mismatch between the film and the underlying substrate, and has been widely used in tuning the structure and properties of many oxide materials18,19,20,21.

However, due to the limited number of commercially available substrates and defect-induced strain relaxation during growth22, this approach is fundamentally limited in its lack of ability to

produce large and continuously tunable strain states. These constraints in turn limit the strain range that could be realized in practice, restricting the rational design, and control of

desired material properties via strain. The advent of freestanding crystalline oxide membrane films presents enticing possibilities to address these challenges and develop additional degrees

of freedom to manipulate material properties. In particular, the recently developed water-soluble pseudoperovskite Sr3Al2O6 has become widely used as a sacrificial buffer layer in the

fabrication of a variety of freestanding, crystalline oxide thin films23,24,25,26,27,28. These freestanding films, with millimeter-scale lateral dimensions and down to nanometer-scale

thickness, can accommodate much larger strains than their bulk counterparts29,30,31. Here, we integrate the freestanding SrTiO3 films onto a flexible polymer stretching platform to probe the

strain-tunable ferroelectric transition in SrTiO330. In this work, using a variety of characterization techniques we demonstrate robust room-temperature ferroelectricity in SrTiO3 with 2.0%

uniaxial tensile strain, which is corroborated by the notable features of 180° ferroelectric domains and an extrapolated transition temperature of 400 K. RESULTS FABRICATION OF SRTIO3

MEMBRANES First, we prepared an epitaxial heterostructure of 14 nm SrTiO3 thin films with a 16 nm Sr2CaAl2O6 sacrificial buffer layer synthesized on single-crystalline SrTiO3 substrates via

reflection high-energy electron diffraction (RHEED)-assisted pulsed-laser deposition (Supplementary Fig. 1). We substituted Ca into Sr3Al2O6 to modify the lattice parameter of the

sacrificial layer to closely match the SrTiO3 lattice (the lattice constant of Sr2CaAl2O6 is 15.6 Å, which is close to four times the lattice constant of SrTiO3). Doing so can effectively

reduce the lattice mismatch between different layers and minimize the crack formation in released freestanding films27. After fully dissolving Sr2CaAl2O6 in deionized water, the SrTiO3 film

is released from the substrate and transferred onto a flexible polyimide sheet that can be stretched into various strain states (see “Methods” and Fig. 1a). The interface between the SrTiO3

membrane and the polyimide sheet provides strong interface adhesion, enabling the success of the strain experiment. Using both an optical microscope and atomic force microscopy, we

characterized the topography of the resulting freestanding membranes and noted that the millimeter-scale films (laterally) are free of cracks in their unstrained state (Fig. 1b–d). Since

strain relaxation occurs in the vicinity of cracks32, these crack-free SrTiO3 membranes are able to preserve homogeneous strain, presenting an ideal platform for our strain experiments. In

addition, a two-dimensional array of gold electrodes was evaporated on the membrane surface using electron-beam evaporation with a shadow mask. These electrodes serve as optical markers to

measure strain in the strain experiment (Fig. 1c). CHARACTERIZATION OF ROOM-TEMPERATURE FERROELECTRICITY Next, we conducted piezoresponse force microscopy (PFM) to explore how strain affects

ferroelectric order in SrTiO3 membranes. Here, the flexible polyimide sheet allows the strain state to be flexibly manipulated. In this work, we focus on the case of in-plane uniaxial

tensile strain by stretching the membrane along the [100] direction, while supplying a small amount of tensile stress to keep the membrane undeformed along the other orthogonal in-plane

direction. Note that it is usually difficult to create such a highly anisotropic strain geometry using commercially available substrates. The strain state was characterized optically by

measuring the change in spacing between gold markers (i.e. _ε_ = Δ_l_/_l_, Fig. 2a), and further microscopically confirmed by grazing incidence X-ray diffraction (GIXRD) measurements30 (see

“Methods” and Fig. 2b–d). Here, with increasing strain, the GIXRD peak measured along the [100] strain direction shifts towards lower angles, indicating the increase in the lattice parameter

upon stretching, whereas the peak position measured along the [010] direction remains almost unchanged. It is also noted that the uniaxial strain values measured by GIXRD closely match with

the optically measured strain values. In order to maintain the strain state of the film even after removing the external stress from membranes, the adhesive polycaprolactone was used in its

melted liquid form to bond the stretched membrane onto a rigid substrate at 110 °C, and then cooled to room temperature to lock-in the strain state (see “Methods”). Using this strain setup,

we characterize the ferroelectric properties of strained SrTiO3 via PFM at room temperature (see “Methods”). In a small strain state (_ε_ ≤ 1.25%), we measured very weak signals from the

membrane, indicating the absence of ferroelectricity at room temperature within this strain range (Fig. 2e–g and Supplementary Fig. 2). By contrast, for larger strain (_ε_ > 1.5%), we

observed strong lateral signals from membranes with notable stripe domain patterns, which indicates the emergence of room-temperature ferroelectricity (Fig. 2h, i and Supplementary Fig. 2).

The observed polydomain structures, which are only observable from lateral piezoresponse, are in-plane polarized due to the tensile strain. Since lateral PFM imaging is carried out via the

torsional movement of the PFM cantilever in response to shear deformation of in-plane polarized domains, in-plane piezoresponse signals will vanish when the cantilever is aligned along the

in-plane polarization direction. Therefore, by varying the relative orientation between the cantilever and the sample, we can determine the actual polarization direction (Supplementary Fig. 

3). Using this approach, we found that the ferroelectric polarization of SrTiO3 membranes is along [100]/[\(\bar 100\)] with the adjacent domains polarized at a 180° difference, which

coincides with the uniaxial tensile strain direction (Fig. 2j). These PFM results provide direct evidence of robust room-temperature ferroelectricity in strained SrTiO3 membranes,

corroborated by the notable 180° ferroelectric polydomain structures. Moreover, we find that the SrTiO3 membranes can sustain beyond 2.0% uniaxial tensile strain without fracture, which

exceeds the reported maximum substrate-induced tensile strain in SrTiO3 heterostructures10 (i.e., 1.0% for SrTiO3 films grown on DyScO3 (110)). Abrupt crack formation occurs typically above

2.5% strain in SrTiO3 membranes, giving rise to paraelectricity in SrTiO3 at room temperature due to strain relaxation (Supplementary Fig. 4). OPTICAL SECOND HARMONIC GENERATION MEASUREMENTS

We further performed temperature-dependent optical second harmonic generation (SHG) measurements to explore the strain-induced variation of _T_c in the SrTiO3 membranes. In our SHG

measurements, a 900 nm fundamental beam is used to excite the SHG signal from the membrane in a reflection geometry that can be probed at a wavelength of 450 nm (see “Methods” and Fig. 3a).

First, in order to understand the structural symmetry of the strain-induced ferroelectric phase, we carried out SHG measurements in strained membranes that exhibit room-temperature

ferroelectricity (_ε_ ≥ 1.5%) as a function of incident beam polarization (Supplementary Fig. 5). The intensity of the output SHG signals is detected at a polarizer angle which is either

parallel (_I__x_, Fig. 3b) or perpendicular (_I__y_, Fig. 3b) to the uniaxial strain direction in membranes. By analyzing these polar plots using the symmetry-based SHG tensor, we find that

the ferroelectric phase is in the orthorhombic _mm_2 point group symmetry with the polar axis aligned in-plane along the uniaxial strain direction33 (see “Methods”), which is consistent with

our PFM observations. Next, we measured the ferroelectric _T_c of strained membranes by probing SHG as a function of temperature. Since the adhesive used in our strain setup softens and

allows strain relaxation above 60 °C, our measurements were limited to temperatures below this scale. We probed the _T_c of membranes strained to _ε_ = 0.5%, 0.9%, and 1.25%, wherein the SHG

intensity decreases with temperature and gradually vanishes at a critical temperature which indicates the onset of the phase transition (Fig. 3c and Supplementary Fig. 6). Plotting the

integrated SHG peak intensity as a function of temperature for each strain state, we can extract _T_c using a temperature-dependent order parameter fit derived from the

Ginsburg–Landau–Devonshire (GLD) model (see “Methods” and Supplementary Fig. 7). Our results reveal that the measured _T_c increases linearly with strain, which agrees well with the

theoretical value predicted by the GLD model (see “Methods”, Fig. 3d and Supplementary Fig. 8). Following this theoretical trend, we can also estimate _T_c for membranes with a phase

transition far above room temperature (_ε_ ≥ 1.5%, Fig. 3d). Our results indicate that for 2.0%, _T_c extrapolates to 400 K, i.e. robust room-temperature ferroelectricity. In addition, these

results also indicate that it is possible to directly tune the transition temperature in a deterministic manner. FIRST-PRINCIPLES CALCULATIONS AND MD SIMULATIONS To understand the origin of

the strain-driven ferroelectric phase and the nature of the phase transition in strained SrTiO3 membranes, we performed first-principles density functional theory (DFT) calculations and

molecular dynamics (MD) simulations. We calculated the energy of the paraelectric and ferroelectric phase in SrTiO3 as a function of strain using DFT calculations with a 5-atom unit cell and

local density approximation (LDA) (see “Methods” and Fig. 4a). DFT calculations reveal that the ferroelectric phase is favored over the paraelectric phase by a small energy difference when

the applied strain is >0.25%. Also, consistent with our experimental observations, DFT calculations indicate that uniaxial tensile strain along the [100] direction induces polarization

along this direction, and the induced polarization is a result of the displacement of both the Sr and Ti atoms away from the center of the surrounding oxygen lattice (Supplementary Fig. 9,

Table 1, and Supplementary Data 1). Next, slab-model MD simulations were performed to understand the nature of temperature-driven phase transitions in 2.0% uniaxially strained SrTiO3

membranes. In order to obtain atomistic insights into the nature of the phase transition, we calculated the probability distribution of the unit cells adopting a [100]-component of local

polarization as a function of temperature (Fig. 4b). At low temperature, the distribution of local polarization in the ferroelectric phase is Gaussian-like with a single peak at ≈0.3 C m−2

(120 K, Fig. 4b). With increasing temperature, the peak shifts towards a lower polarization value, indicating the displacive character of the phase transition (e.g., 140 and 160 K, Fig. 4b).

At 180 K, another peak located near −0.18 C m−2 emerges, suggesting the onset of an order-disorder phase transition (180 K, Fig. 4b). In the high temperature paraelectric phase (240 and 300

 K, Fig. 4b), the distribution becomes a double-peaked curve (again an indicator of the order-disorder transition) but with a non-zero probability at _P_ = 0 (an indicator of the displacive

transition)34, indicating a notable mixture of displacive and order-disorder characteristics of the phase transition in SrTiO3 (Supplementary Fig. 10). Snapshots of the dipole configuration

from MD simulations further illustrate such mixed transition character (Fig. 4c). For instance, the snapshot obtained at 120 K shows a typical ferroelectric phase with the majority of unit

cells polarized along [100]. As the temperature increases, the orientation of the dipoles become more disordered but the long-range correlation still remains along [100]. At 300 K the

macroscopic paraelectricity arises as an ensemble-averaged result of randomly oriented local dipoles17, including both the nearly zero and non-zero dipoles, resulting in a zero-net

polarization. DISCUSSION We observe direct evidence of robust room-temperature ferroelectricity in strained SrTiO3 membranes, corroborated by 180° domain formation and the evolution of _T_c

with strain. Using SrTiO3 membranes as a promising example, our work demonstrates the significant potential of employing oxide membranes for enhanced ferroelectric properties in diverse

oxide materials. These significant enhancements in ferroelectric polarization and _T_c hold great promise for nonvolatile ferroelectric memory applications. The ability to obtain extreme and

continuously tunable strain states with freestanding membranes also provides broad opportunities for achieving high dielectric turnability at room temperature, which is important for

microwave electronics such as tunable capacitors and phase shifters, etc35. In addition, combining the nanoscale freestanding film with the flexible polymer substrate allows the strain state

to be manipulated to arbitrary geometries and anisotropies, providing additional degrees of freedom for creating unconventional polar structures and functional domain walls coupled with

potentially large dielectric, piezoelectric, and magnetic responses36,37. For instance, the observed in-plane polarized 180° domain structures in our work with only one in-plane polarization

variant (along the [100]/[\(\bar 1\)00] directions) is rather rare not just in SrTiO3 but also in other ferroelectric perovskites such as PbTiO3, BaTiO3, etc. Such in-plane polarized domain

structures could become potential candidates for device elements in next-generation nanoelectronics such as in-plane ferroelectric nonvolatile memories. Moreover, the polymer substrates

which are stretched in the elastic deformation regime allows the reversible control of the phase transition and their associated dielectric and piezoelectric responses, providing

possibilities for designing a variety of strain-tunable ferroelectric devices. METHODS THIN-FILM GROWTH The epitaxial heterostructure of 14 nm SrTiO3 films was synthesized with a 16 nm

Sr2CaAl2O6 sacrificial layer on (001)-oriented single-crystalline SrTiO3 substrates via RHEED-assisted pulsed-laser deposition. The growth of the Sr2CaAl2O6 layer was carried out in dynamic

argon pressure of 4 × 10−6 Torr, at a growth temperature of 710 °C, a laser fluence of 1.35 J cm−2, and a repetition rate of 1 Hz, using a 4.8 mm2 imaged laser spot. The growth of the SrTiO3

layer was conducted in dynamic oxygen pressure of 4 × 10−6 Torr, at a growth temperature of 710 °C, a laser fluence of 0.9 J cm−2, and a repetition rate of 1 Hz, using a 3.0 mm2 imaged

laser spot. SRTIO3 MEMBRANE FABRICATION The heterostructure was first attached to a polymer support of 100-μm-thick polypropylene carbonate (PPC) film and placed in deionized water at room

temperature until the sacrificial Sr2CaAl2O6 layer was fully dissolved. The PPC coated SrTiO3 film was then released from the substrate and transferred onto a polyimide sheet. Finally, the

PPC layer was removed from the membrane through thermal decomposition in O2 at 260 °C for 2 h. STRETCHING EXPERIMENT We applied uniaxial stress to SrTiO3 membranes along [100] directions via

micromanipulators to stretch the polyimide substrate, while keeping the membrane undeformed along the other orthogonal in-plane direction by applying a small amount of compensating stress

along [010]. The resultant strain was characterized using optical microscopy to measure the change in spacing between circular gold markers, which were evaporated with a shadow mask using

e-beam evaporation. In order to preserve the strain state in SrTiO3, polycaprolactone was used in its melted liquid form to bond the strained oxide/polymer bilayer to a ceramic chip carrier

at 110 °C. Polycaprolactone solidifies by cooling the strain setup to room temperature, which freezes the strain state of the SrTiO3 membranes, and is stable on the ~2 week time scale.

CRYSTAL STRUCTURE CHARACTERIZATION GIXRD measurements were performed using high-resolution X-ray diffractometer (PANalytical X’Pert Pro MRD). The measurement geometry was configured in the

in-plane diffraction mode to allow X-rays to probe the crystal lattice along the in-plane directions. DOMAIN STRUCTURE CHARACTERIZATION The PFM studies were carried out with a Cypher AFM

(Asylum Research) using Ir/Pt-coated conductive tips (Nanosensor, PPP-EFM, force constant ≈2.8 N m−1). The vector PFM mode was used to image both the out-of-plane and in-plane domain

structure simultaneously. OPTICAL SECOND HARMONIC GENERATION MEASUREMENTS In SHG measurements we illuminated the sample with a Coherent Chameleon Ultra II Ti: Sapphire laser tuned to 900 nm

wavelength and focused onto the sample with a 20 × NA = 0.45 ELWD Nikon objective. The temperature-dependent SHG measurements were performed using a modified Janus ST500 Optical Vacuum

Cryostat. Input polarization was controlled by the rotation of a half waveplate in the laser beam path. The generated SHG signals were collected on an Andor iXon CCD and Kymera Spectrometer.

The analysis of SHG intensity polar plots was performed using the symmetry-based SHG tensor. For the in-plane polarized domains, the fundamental beam produces electric field components

which can be described as _E_ω(_φ_) = (−_E_0s_inφ_, 0, _E_0_cosφ_), where _φ_ is the azimuthal angle of the fundamental light polarization shown in Fig. 3b. The light-induced non-linear

polarization of the in-plane polarized domains can be described using the _mm_2 point group-based SHG tensor: $$\left( {\begin{array}{*{20}{c}} {P_1} \\ {P_2} \\ {P_3} \end{array}}

\right)\,=\,\left( {\begin{array}{*{20}{c}} 0 & 0 & 0 & 0 & {d_{15}} & 0 \\ 0 & 0 & 0 & {d_{24}} & 0 & 0 \\ {d_{31}} & {d_{32}} & {d_{33}}

& 0 & 0 & 0 \end{array}} \right)\left( {\begin{array}{*{20}{c}} {E_1^2} \\ {E_2^2} \\ {E_3^2} \\ {2E_2E_3} \\ {2E_1E_3} \\ {2E_1E_2} \end{array}} \right),$$ (1) where _E_1 = 

−_E_0_sinφ_, _E_2 = 0, and _E_3 = _E_0_cosφ_. Since the output polarizer is placed either parallel (_I__x_, Fig. 3b) or perpendicular (_I__y_, Fig. 3b) to the in-plane uniaxial strain

direction (polarization direction) in the membrane, the output SHG signal can be described as \(I_x^{2{\upomega}}\left( \varphi \right)\) = \(I_3^{2{\upomega}} \propto \left(

{{\mathbf{P}}^{2{\upomega}} \cdot {\mathbf{A}}_x} \right)^2\) = \((d_{33}E_0^2{\mathrm{cos}}^2\varphi + d_{31}E_0^2{\mathrm{sin}}^2\varphi )^2\) and \(I_y^{2{\upomega}}\left( \varphi

\right)\) = \(I_1^{2{\upomega}} \propto \left( {{\mathbf{P}}^{2{\upomega}} \cdot {\mathbf{A}}_y} \right)^2\) = \((d_{15}E_0^2{\mathrm{sin}}2\varphi )^2\), where A_x_ = (0, 0, 1) and A_y_ = 

(1, 0, 0). The experimental polar plots can be well fitted using the derived \(I_x^{2{\upomega}}\left( \varphi \right)\) and \(I_y^{2{\upomega}}\left( \varphi \right)\), indicating the

strained SrTiO3 is in the orthorhombic _mm_2 point group symmetry. Detailed fitting analysis can be found in ref. 33. Note that the tetragonal 4_mm_ point group-based SHG tensor also

generates similar fitting results. But given the experimental strain geometry where the membrane elongates along only one in-plane direction while compresses along the out-of-plane direction

due to the Poisson effect (we keep the membrane undeformed along the other orthogonal in-plane direction), the possibility of the tetragonal 4_mm_ point group symmetry is thus ruled out

from our analysis. GINSBURG–LANDAU–DEVONSHIRE CALCULATIONS In this model, we used the power-series expansion of the Helmholtz free energy _F_ in terms of polarization components _P__i_ and

structural order parameters _Q__i_ (_i_ = 1, 2, 3), which is expressed as follows38: $$F\,= \, \alpha _1\left( {P_1^2\,+\,P_2^2\,+\,P_3^2} \right)\,+\,\alpha _{11}\left(

{P_1^4\,+\,P_2^4\,+\,P_3^4} \right)\\ +\,\alpha _{12}\left( {P_1^2P_2^2\,+\,P_1^2P_3^2\,+\,P_2^2P_3^2} \right)\,+\,\beta _1\left( {Q_1^2\,+\,Q_2^2\,+\,Q_3^2} \right)\\ +\,\beta _{11}\left(

{Q_1^4\,+\,Q_2^4\,+\,Q_3^4} \right)\,+\,\beta _{12}\left( {Q_1^2Q_2^2\,+\,Q_1^2Q_3^2\,+\,Q_2^2Q_3^2} \right)\\ +\,1{\mathrm{/}}2c_{11}\left( {S_1^2\,+\,S_2^2\,+\,S_3^2}

\right)\,+\,c_{12}\left( {S_1S_2\,+\,S_1S_3\,+\,S_2S_3} \right)\\ +\,{\mathrm{1/}}2c_{44}\left( {S_4^2\,+\,S_5^2\,+\,S_6^2} \right)\,-\,g_{11}\left( {S_1P_1^2\,+\,S_2P_2^2\,+\,S_3P_3^2}

\right)\\ -\,g_{12}\left[ {S_1\left( {P_2^2\,+\,P_3^2} \right)\,+\,S_2\left( {P_1^2\,+\,P_3^2} \right)\,+\,S_3\left( {P_1^2\,+\,P_2^2} \right)} \right]\\ -\,g_{44}\left(

{S_4P_2P_3\,+\,S_5P_1P_3\,+\,S_6P_1P_2} \right)\,-\,\lambda _{11}\left( {S_1Q_1^2\,+\,S_2Q_2^2\,+\,S_3Q_3^2} \right)\\ - \,\lambda _{12}\left[ {S_1\left( {Q_2^2\,+\,Q_3^2}

\right)\,+\,S_2\left( {Q_1^2\,+\,Q_3^2} \right)\,+\,S_3\left( {Q_1^2\,+\,Q_2^2} \right)} \right]\\ -\,\lambda _{44}\left( {S_4Q_2Q_3\,+\,S_5Q_1Q_3\,+\,S_6Q_1Q_2} \right)\,-\,t_{11}\left(

{P_1^2Q_1^2\,+\,P_2^2Q_2^2\,+\,P_3^2Q_3^2} \right)\\ -\,t_{12}\left[ {P_1^2\left( {Q_2^2\,+\, Q_3^2} \right)\,+\,P_2^2\left( {Q_1^2\,+\,Q_3^2} \right)\,+\,P_3^2\left( {Q_1^2\,+\,Q_2^2}

\right)} \right]\\ -\,t_{44}\left( {P_1P_2Q_1Q_2\,+\,P_1P_3Q_1Q_3\,+\,P_2P_3Q_2Q_3} \right),$$ (2) where _S__n_ (_n_ = 1, 2, 3, 4, 5, 6) are lattice strains, _c__nl_ are the elastic

stiffnesses, _g__nl_ are the electrostrictive constants, _λ__nl_ are the linear-quadratic coupling coefficients between the strain and structural order parameters, and _t__nl_ are the

coupling coefficients between the polarization and structural order parameters. In order to simplify the analysis, we considered the scenario where there is no antiferrodistortive structural

transition, i.e., _Q__i_ = 0 (_i_ = 1, 2, 3). In that care Eq. (2) can be written in the following format: $$F\,= \, \alpha _1\left( {P_1^2\,+\,P_2^2\,+\,P_3^2} \right)\,+\,\alpha

_{11}\left( {P_1^4\,+\,P_2^4\,+\,P_3^4} \right)\\ +\,\alpha _{12}\left( {P_1^2P_2^2\,+\,P_1^2P_3^2\,+\,P_2^2P_3^2} \right)\,+\,1{\mathrm{/}}2c_{11}\left( {S_1^2\,+\,S_2^2\,+\,S_3^2}

\right)\\ +\,c_{12}\left( {S_1S_2\,+\,S_1S_3\,+\,S_2S_3} \right)\,+\,1{\mathrm{/}}2c_{44}\left( {S_4^2\,+\,S_5^2\,+\,S_6^2} \right)\\ -\,g_{11}\left( {S_1P_1^2\,+\,S_2P_2^2\,+\,S_3P_3^2}

\right)\\ -\,g_{12}\left[ {S_1\left( {P_2^2\,+\,P_3^2} \right)\,+\,S_2\left( {P_1^2\,+\,P_3^2} \right)\,+\,S_3\left( {P_1^2\,+\,P_2^2} \right)} \right]\\ -\,g_{44}\left(

{S_4P_2P_3\,+\,S_5P_1P_3\,+\,S_6P_1P_2} \right).$$ (3) Given the experimentally used in-plane uniaxial strain geometry, we considered the case of _S_1 ≠ 0, _S_2 = 0, and _S_3 ≠ 0. In

addition, in this case the shear strain _S_6 is zero38. For the experimentally observed 180° ferroelectric domains, we can simplify the problem with the consideration of only one

polarization component along the uniaxial strain direction, i.e., _P_1 ≠ 0, _P_2 = _P_3 = 0. Therefore, the Eq. (3) can be further simplified as: $$F\,= \, \alpha _1P_1^2\,+\,\alpha

_{11}P_1^4\,+\,1/2c_{11}\left( {S_1^2\,+\,S_3^2} \right)\\ +\,c_{12}S_1S_3\,+\,1/2c_{44}\left( {S_4^2\,+\,S_5^2} \right)\\ -\,(g_{11}S_1\,+\,g_{12}S_3)P_1^2.$$ (4) Next, using the relation

\(\frac{{\partial F}}{{\partial S_3}}\,=\,\frac{{\partial F}}{{\partial S_4}}\,=\,\frac{{\partial F}}{{\partial S_5}}\,=\,0\), which is derived from the mechanical boundary condition

\(\sigma _3\,=\,\sigma _4\,=\,\sigma _5\,=\,0\), we can derive the following relations: $$c_{11}S_3\,+\,c_{12}S_1\,-\,g_{12}P_1^2\,=\,0;$$ (5) $$c_{44}S_4\,=\,0;$$ (6) $$c_{44}S_5\,=\,0.$$

(7) From these relations, we can further derive \(S_4\,=\,S_5\,=\,0\) and \(S_3\,=\,\frac{{g_{12}P_1^2\,-\,c_{12}S_1}}{{c_{11}}}\). Using these values in Eq. (4), we can rewrite the free

energy in the following form with renormalized expansion coefficients: $$F\,=\,\alpha _{11}^\prime P_1^4\,+\,\alpha _1^\prime P_1^2\,+\,C,$$ (8) where \(\alpha _{11}^\prime\,=\,\alpha

_{11}\,-\,\frac{{g_{12}^2}}{{2c_{11}}}\), \(\alpha _1^\prime\,=\,\alpha _1\,-\,g_{11}S_1\,+\,\frac{{g_{12}c_{12}S_1}}{{c_{11}}}\),

\(C\,=\,\frac{1}{2}c_{11}s_1^2\,-\,\frac{{c_{12}^2S_1^2}}{{2c_{11}}}\). For the in-plane uniaxial strain geometry used in our experiment, _S_1 = _S_u where _S_u is the uniaxial strain state.

Using the thermodynamic parameters38 (Supplementary Table 2) in Eq. (8), _F_ becomes a function of _P_1, _S_u, and temperature _T_ (since _α_1 relates to temperature). By calculating the

minima of _F_ with respect to _P_1, we can find the relation between _P_1 and _T_ at a given _S_u: $$P_1^2\,=\,\frac{{\left( {g_{11}\,-\,\frac{{g_{12}c_{12}}}{{c_{11}}}}

\right)S_{\mathrm{u}}\,-\, \alpha _1}}{{2\alpha _{11}\,-\,\frac{{g_{12}^2}}{{c_{11}}}}},$$ (9) where \(\alpha _1\,=\,4.5[\coth \left( {\frac{{54}}{T}}

\right)\,-\,{\mathrm{coth}}(\frac{{54}}{{30}})]\,\times\,10^{ - 3}\). Such a relation is plotted in Supplementary Fig. 8, which allows us to extract _T_c at _P_1 = 0 as a function of _S_u

(Fig. 3d). FIRST-PRINCIPLES DENSITY FUNCTIONAL THEORY CALCULATIONS First-principles DFT calculations were performed with QUANTUM-ESPRESSO39 package using the LDA40 and ultrasoft

pseudopotentials from the Garrity, Bennet, Rabe, Vanderbilt high-throughput pseudopotential set41. We used an 8 × 8 × 8 Monkhorst-Pack _k_-point mesh42 for Brillouin-zone sampling and a

plane-wave cutoff of 50 Ry and a charge density cutoff of 250 Ry. A force convergence threshold of 1.0 × 10−4 y Bohr−1, a pressure convergence threshold of 0.5 kbar, and Marzari–Vanderbilt

smearing43 of 1 mRy were used to optimize the atomic positions and lattice constants. In order to simplify the analysis, we use a 5-atom unit cell model, which rules out the possible effects

of oxygen octahedral rotation, a known antiferroelectric mode in SrTiO3. Our simplification is justified as the unstrained structure of interest in the experiment is cubic SrTiO3 in which

the oxygen octahedral rotation is zero above 105 K. The LDA lattice constant of cubic SrTiO3 is 3.857 Å, which is consistent with previous theoretical results44 and close to the experimental

value of 3.905 Å. Following the experimental setup, the uniaxial strain state is induced by fixing the lattice constant _b_ along [010] to its ground-state value while fixing the lattice

constant _a_ along [100] to a uniformly spaced grid sampled between 3.838 and 3.934 Å (corresponding to a strain range from −0.5% to 2.0% in reference to the DFT ground-state cubic

structure) with a step size of 0.002 Å. For a given combination of (_a_, _b_), the perpendicular lattice constant _c_ and internal coordinates are fully relaxed to obtain the most stable

structure under the given strain condition. The polarization is then estimated using the Born effective charges and the atomic positions. The detailed structural information can be found in

the provided crystallographic information files (Supplementary Data 1). MOLECULAR DYNAMICS SIMULATIONS MD simulations of SrTiO3 were performed using a bond-valence-based atomistic potential

parameterized from first-principles calculations34,45. This force field was able to reproduce both composition- and temperature-driven phase transitions of the BaxSr1−xTiO3 solid solution46

and has been successfully used to describe the THz-driven transient ferroelectric phase in SrTiO347. In order to model SrTiO3 thin films without periodicity in the direction perpendicular to

the surface, we constructed a supercell containing a SrTiO3 slab of 90,000 atoms (30 × 20 × 30 cells) adjacent to a vacuum region. The SrTiO3 slab, which is 20 unit cells in thickness, has

the surface normal along the [010] direction. The vacuum along the surface normal is 85.4 Å thick, which is sufficiently large to prevent spurious interactions between neighboring periodic

images. To stabilize the thin film in vacuum, the bond-valence charges of the surface layers were reduced by a factor of two, following a similar protocol developed in ref. 48. In order to

investigate the nature of temperature-driven phase transitions in strained SrTiO3 membranes, we first equilibrated the slab model by running NVT (constant-volume constant-temperature)

simulation using a time-step of 1 fs with a 2.0% tensile strain along the [100] direction. The temperature was controlled via the Nosé–Hoover thermostat49 implemented in Large-scale

Atomic/Molecular Massively Parallel Simulator50. To facilitate the equilibrium process, a small bias field was applied along the [100] direction for 50 ps after which another equilibrium run

of 50 ps was performed with the bias field turned off. The final equilibrium structure is a single domain with the polarization along the [100] direction. Then we increased temperature

gradually to explore the temperature-driven ferroelectric phase transition in strained SrTiO3 membranes. DATA AVAILABILITY Crystallographic data in this study are provided in Supplementary

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discussions with Ian R. Fisher during the course of this work. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences (DOE-BES), Division of Materials

Sciences and Engineering, under contract no. DE-AC02-76SF00515. S.C. and D.L. were supported by the Gordon and Betty Moore Foundation’s Emergent Phenomena in Quantum Systems Initiative

through grant no. GBMF4415. V.H. was supported by the Air Force Office of Scientific Research (AFOSR) Hybrid Materials MURI under award no. FA9550-18-1-0480. R.X. also acknowledges partial

support from Stanford Geballe Laboratory for Advanced Materials (GLAM) Postdoctoral Fellowship program. S. L. acknowledges support from the Westlake Foundation. Work at the Molecular Foundry

was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Part of this work was performed at the

Stanford Nano Shared Facilities (SNSF), supported by the National Science Foundation under award ECCS-1542152. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Applied Physics,

Stanford University, Stanford, CA, 94305, USA Ruijuan Xu, Seung Sae Hong, Prastuti Singh, Thies Jansen, Sam Crossley & Harold Y. Hwang * Stanford Institute for Materials and Energy

Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA Ruijuan Xu, Seung Sae Hong, Prastuti Singh, Varun Harbola, Jun Xiao, Bai Yang Wang, Sam Crossley & Harold Y.

Hwang * School of Science, Westlake University, Hangzhou, 310012, Zhejiang, China Jiawei Huang & Shi Liu * The Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road,

Berkeley, CA, 94720, USA Edward S. Barnard & Ed K. Wong * Department of Physics, Stanford University, Stanford, CA, 94305, USA Varun Harbola, Bai Yang Wang & Di Lu * Department of

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R.X., H.Y.H., and D.L. conceived of the study. R.X., S.S.H., and S.C. designed the experiments. R.X. carried out the film synthesis, PFM characterization, and GLD calculations. J.H. and S.L.

performed the DFT and MD simulations. R.X., E.S.B., E.K.W., and J.X. conducted the SHG measurements and analysis. R.X., T.J., V.H., and B.Y.W. performed the membrane fabrication. P.S.,

R.X., and S.S.H. carried out the GIXRD measurements. R.X., S.L., P.S., and H.Y.H. wrote the paper, with contributions from all authors. CORRESPONDING AUTHORS Correspondence to Ruijuan Xu or

Harold Y. Hwang. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PEER REVIEW INFORMATION _Nature Communications_ thanks Jiandong

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THIS ARTICLE CITE THIS ARTICLE Xu, R., Huang, J., Barnard, E.S. _et al._ Strain-induced room-temperature ferroelectricity in SrTiO3 membranes. _Nat Commun_ 11, 3141 (2020).

https://doi.org/10.1038/s41467-020-16912-3 Download citation * Received: 28 February 2020 * Accepted: 30 May 2020 * Published: 19 June 2020 * DOI: https://doi.org/10.1038/s41467-020-16912-3

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