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Ultrathin complex oxide nanomechanical resonators

Abstract

Complex oxide thin films and heterostructures exhibit a variety of electronic phases, often controlled by the mechanical coupling between film and substrate. Recently it has become possible to isolate epitaxially grown single-crystalline layers of these materials, enabling the study of their properties in the absence of interface effects. In this work, we use this technique to create nanomechanical resonators made out of SrTiO3 and SrRuO3. Using laser interferometry, we successfully actuate and measure the motion of the nanodrum resonators. By measuring the temperature-dependent mechanical response of the SrTiO3 resonators, we observe signatures of a structural phase transition, which affects both the strain and mechanical dissipation in the resonators. Here, we demonstrate the feasibility of integrating ultrathin complex oxide membranes for realizing nanoelectromechanical systems on arbitrary substrates and present a novel method of detecting structural phase transitions in these exotic materials.

Introduction

It is well established that the electronic and magnetic properties of complex oxides are extremely sensitive to mechanical strain due to the strong coupling between the lattice and the charge, spin, and orbital degrees of freedom1,2,3,4,5,6. This sensitivity stems from rotations and distortions of the corner-connected BO6 octahedra (where B is a transition metal ion situated in the centre of the octahedron formed by the oxygen atoms), which determine the overlap between orbitals on adjacent atomic sites7. The B–O bond lengths and rotation angles are routinely controlled by strain through heteroepitaxy, which forms a powerful tool to tune the properties of ultrathin films. The strong dependence of their electronic properties on mechanical strain has attracted a lot of attention towards their implementation in nanoelectromechanical sensors and actuators8, but exploiting this trait to the fullest has been limited by the requirement of a substrate for the epitaxial growth. This constrains the possibilities for their mechanical manipulation and integration with electronics and it could not be circumvented until recently, when single-crystal films of complex oxides were successfully released and transferred9,10. This sparked a new wave of interest in studying the properties of these materials, this time in their isolated, ultrathin form11.

On the other hand, a wide variety of mechanical manipulation techniques have been developed for van der Waals materials12, where weak interlayer bonding enables exfoliation of single- and few-layer films. Their ease of manipulation has enabled the top–down fabrication of nanomechanical elements, such as suspended membranes and ribbons. This, combined with their flexibility, low mass, and remarkable strength, has made them promising candidates for nanomechanical sensing applications13,14,15,16. Conversely, the well-developed field of nanomechanics has established a solid basis for characterizing the thermal and mechanical properties of van der Waals materials17,18,19.

In this work, we utilize the fabrication techniques for van der Waals materials to realize ultrathin nanomechanical resonators made out of epitaxially grown single-crystal complex oxide films. We show that these devices can be used to detect signatures of temperature-induced phase transitions of the material, which manifest themselves through changes of strain and, even more prominently, of mechanical dissipation in the resonators.

Results

Fabrication of complex oxide nanodrums

The fabrication of the complex oxide mechanical resonators is described in Fig. 1. To isolate the epitaxial SrTiO3 (STO) and SrRuO3 (SRO) thin films from the substrate, a water-soluble epitaxial Sr3Al2O6 (SAO) layer is first deposited by pulsed laser deposition on a TiO2-terminated STO(001) substrate (see ‘Methods’). Figure 1a shows the reflection high-energy electron diffraction (RHEED) intensity of the specular spot during the growth of SAO and STO. Oscillations are observed during the growth of both films, indicating that the growth occurs in layer-by-layer mode. Atomic force microscopy (AFM) topographic maps are shown in Fig. 1b, c, showing that the STO surface has a step-and-terrace structure, corroborating the growth mode. An X-ray diffraction (XRD) measurement of an SRO/SAO/STO heterostructure is shown in Supplementary Fig. 1 and discussed in Supplementary Note 1.

Fig. 1: Sample fabrication and basic characterization.
figure1

a Reflection high-energy electron diffraction (RHEED) intensity oscillations during the growth of Sr3Al2O6 (SAO)—red line—and SrTiO3 (STO)—blue line. Inset: RHEED diffraction pattern and atomic force microscopic (AFM) image of the SAO surface. The scale bar is 200 nm. b AFM images of the STO and c SrRuO3 (SRO) film surfaces grown on top of the SAO. The scale bars are 1 μm. d X-ray diffraction measurement of a 10 unit cell (u.c.) STO film transferred on a Si/SiO2 substrate. The expected peak positions are marked by the vertical dashed lines. e Rocking curve around the (002) reflection. f Schematics of the transfer of a thin SRO film onto a pre-patterned Si/SiO2 substrate. g Optical image of suspended 9 u.c. SRO drums with a diameter of 13 μm. The purple surface is the area covered by the SRO film, including the three suspended drums marked by the arrows. The scale bar is 10 μm. h Set-up for interferometric displacement detection (VNA vector network analyser, PD photodiode, LD laser diode, BE beam expander, PBS polarized beam splitter, CM cold mirror).

To dissolve the sacrificial layer and release the thin film from the substrate, a polydimethylsiloxane (PDMS) layer is attached to the surface before the entire stack is immersed in deionized water. After the dissolution of the SAO layer (approximately 1 h for a 5 × 5 mm2 50-nm-thick SAO film, see Supplementary Movie 1), the film can be transferred onto other substrates such as Si/SiO2 using a deterministic dry transfer technique20. An XRD measurement of a 10 unit cell (u.c.) STO flake on a Si/SiO2 substrate is shown in Fig. 1d. Laue oscillations are clearly visible, indicating that the films are of excellent crystalline quality after the release and transfer process. Since the film is no longer epitaxial on the substrate, the rocking curve (Fig. 1e) is a measure of the morphology of the STO film lying on the SiO2. The small full width at half maximum (0.95°) indicates that the film lies very flat on the Si/SiO2 substrate. To fabricate nanomechanical resonators, we transfer the STO and SRO films onto Si/SiO2 substrates pre-patterned with circular cavities (schematically shown in Fig. 1f), demonstrating the feasibility of creating suspended complex oxide membranes. An optical image of 9 u.c. (thickness: h = 3.6 nm) thick SRO drums (diameter: d = 13 μm) is shown in Fig. 1g. It is remarkable that these materials, much like their van der Waals counterparts, have the flexibility and tensile strength required to be suspended with aspect ratios exceeding d/h > 3600.

Mechanical characterization of the nanodrums

We characterize the high-frequency dynamics of the complex oxide nanodrums using the optical actuation and detection set-up shown in Fig. 1h. The drums are mounted in the vacuum chamber (10−6 mbar) of a closed-cycle cryostat with optical access. Their motion is read out using a red HeNe laser (λ = 632.8 nm). The complex oxide membrane and the silicon underneath form a Fabry–Pérot cavity, where the motion of the membrane modulates the intensity of the reflected light, which is measured by a photodiode. The resonators are actuated optothermally using a blue laser (λ = 405 nm) that is coupled into the optical path via a cold mirror21,22. Measurements are performed in a homodyne detection scheme using a vector network analyser (VNA), simultaneously sweeping the actuation and detection frequencies.

The mechanical resonances of several STO and SRO drums are shown in Fig. 2. Although STO is transparent in the visible range23, the motion of the drums can still be actuated and measured optically since the refractive index of the STO is different from that of vacuum and the absorption edge of strained STO can shift to higher wavelengths24. Figure 2a, b shows measurements of two STO drums and Fig. 2c, d of two SRO drums of different diameters. Measurements over a wider frequency range show that higher-order resonances of the drums can also be detected; two examples are shown in Fig. 2e, f, where up to four higher-order resonances are visible. By taking the ratio of the second harmonic (f1) to the fundamental mode (f0), we can estimate whether the mechanical properties are dictated by the pre-tension (theoretical ratio 1.59) or if they are dominantly determined by the bending rigidity (theoretical ratio 2.09), the latter being dependent on the Young’s modulus of the material (E). It can be seen from Fig. 2c that the STO drums are in a cross-over regime (ratio 1.72), similar to what has been observed in drums of similar dimensions made of MoS222 and TaSe225 (an AFM nanoindentation measurement of the sample characterized in Fig. 2c is shown in Supplementary Fig. 2 and the derivation of the extracted properties is outlined in Supplementary Note 2). On the other hand, the mechanical properties of the SRO drums are almost entirely determined by their pre-tension since f1/f0 = 1.47, which is close to the theoretical value of 1.59. Statistics on 18 STO drums are shown in Supplementary Fig. 3 and discussed in Supplementary Note 3.

Fig. 2: Mechanical characterization of SrTiO3 (STO) and SrRuO3 (SRO) nanodrums.
figure2

Resonance frequency measurements of 20-nm-thick STO and 10 nm-thick SRO nanodrums. a, b Frequency spectra of two STO drums with diameters of a 3 μm and b 4 μm. The red lines are linear harmonic oscillator fits. The extracted quality factors are shown in each of the panels. c, d Frequency spectra of two SRO drums with diameters of c 5 μm and d 13 μm. The red lines are linear harmonic oscillator fits. The extracted quality factors are shown in each of the panels. e A wide-range frequency spectrum of the drum shown in b. The positions of the fundamental resonance mode (f0) and the second resonance mode (f1) are marked with vertical dashed lines. f A wide-range frequency spectrum of the drum shown in c. The positions of the fundamental resonance mode (f0) and the second harmonic (f1) are marked with vertical dashed lines. The magnitude is a dimensionless number defined as the ratio of the input and output voltage of the vector network analyser.

Temperature-dependent mechanical properties

Having confirmed that the resonators can be mechanically characterized at room temperature, we now investigate how their mechanical properties change with temperature. The signal of the SRO drums <200 K was below the noise level of the measurement system, so systematic temperature-dependent measurements could only be performed on the STO drums. STO is known to undergo several phase transitions as a function of temperature. A phase transition is characterized by a discontinuity in specific heat26, which, depending on its magnitude, is expected to influence the mechanics of the membranes27, as it is closely related to the thermal expansion coefficient28. Figure 3 shows the mechanical properties of an STO nanodrum as a function of temperature. The temperature dependence of the resonance frequency (Fig. 3a) shows an evolution that is commonly observed in two-dimensional (2D) materials29,30,31. The monotonic increase of f0 with decreasing temperature is usually ascribed to a difference in the thermal expansion coefficients between the membrane and the substrate30,31, which results in thermally induced tensile stress. The fact that the resonance frequency increases with decreasing temperature despite the decrease of the Young’s modulus of bulk STO below the transition temperature32,33 indicates that the mechanical behaviour of the resonator is dominated by tension, rather than bending rigidity22. Since the resonance frequency f0 is related to the effective thermal expansion coefficient of the system αeff (\({f}_{0}^{2}\propto {\alpha }_{{\rm{eff}}}(T)\Delta T\)), an abrupt change in αeff will noticeably affect f0. Interestingly, a discontinuity is observed in f0 at around 30 K (Fig. 3a, dashed line), which coincides with the temperature at which the STO undergoes a structural phase transition, where the Sr ions disorder along [111] directions, rendering the structure locally triclinic34,35,36. This transition is accompanied by changes in mechanical properties32,33,37,38, as well as in the thermal expansion coefficient of STO39.

Fig. 3: Temperature dependence of the mechanical properties of a 4-μm SrTiO3 (STO) drum.
figure3

a Resonance frequency as a function of temperature (inset: temperature range 4–200 K). b Quality factor as a function of temperature. The red line is a guide to the eye (x-axis range goes to 200 K). c Inverse quality factor (Q−1) as a function of temperature in the region between 4 and 80 K. The fitting error for all graphs is within the size of the data points. For the Q factor, measurement-to-measurement fluctuations are observed with a standard deviation between 11% at 4 K and 4% at 200 K.

Another, more often discussed phase transition occurs in this material at 105 K, a temperature at which the cubic structure of bulk STO is known to break up into locally ordered tetragonal domains joined by ferroelastic domain walls40,41. Signatures of this transition are absent from the resonance frequency as a function of temperature (inset of Fig. 3a). A possible reason may be that STO undergoes no substantial changes of the specific heat at this transition42, hence there is no significant influence on the mechanics. It is important to note that optical second-harmonic generation (SHG) measurements, sensitive to structural distortions, performed on this sample still show a prominent feature at around 105 K, as shown in Supplementary Fig. 4 and discussed in Supplementary Note 4.

While the shift in the resonance frequency (Fig. 3a) at 27 K is relatively small, we observe more pronounced features in the mechanical dissipation. To characterize dissipation, we use the quality factor Q of the resonator (shown in Fig. 3b), which is extracted from the frequency domain measurements as Q = f0ff is the full width at half maximum of the resonance peak). The overall monotonic decrease of dissipation (increase in Q) at lower temperatures is often observed in 2D materials29,31,43 and in microelectromechanical systems in general44 and is a subject of ongoing discussion. A proposed explanation for this effect is the increased in-plane tension, which is known to lower dissipation in nanomechanical structures25,45,46,47. Nevertheless, at the temperature of the phase transition we observe an evident change of trend.

Whereas f0 is influenced by the pre-tension of the membrane and the Young’s modulus of the STO, the quality factor is also dependent on the intrinsic losses in the material46, which at low temperatures are expected to be dominated by thermoelastic damping. Zener48 defines a proportionality between the thermoelastic damping term and the specific heat in the following way: \({Q}^{-1}(T)\propto \frac{{\alpha }^{2}(T)T}{{c}_{{\rm{v}}}(T)}\), where α and cv are the thermal expansion coefficient and the specific heat of the material, respectively. Taking αcv49, we get a direct relationship between the damping and the specific heat Q−1(T) cv(T)T. The inverse of the quality factor for the same resonator is plotted in Fig. 3c, which shows an evident peak in the dissipation at around 30 K. Interestingly, the position and the width of the peak are in accordance to the peak in specific heat of STO measured by Durán et al.50. In Supplementary Note 5, we discuss similar trends in f0 and Q as a function of temperature that were observed in two other drums from the same STO flake (see Supplementary Figs. 5 and 6). For another STO sample (h = 16 nm), the transition was not observed under intrinsic thermally accumulated strain but did reappear with added strain by means of electrostatic gating (Supplementary Fig. 7), suggesting that strain can play a role in stabilization of the anomaly, similar to the proposed effect of defects51.

Discussion

We demonstrated the fabrication of ultrathin mechanical resonators made of epitaxially grown STO and SRO films. Using laser interferometry, we mechanically characterized the nanodrums and showed that they can be used as nanomechanical devices, much like drums made of van der Waals materials21,22,25,31,52,53. We show that phase transitions affect the temperature-dependent dynamics of the resonators and that their mechanical dissipation can shed light on the microscopic loss mechanisms, which are often coupled to electronic and magnetic degrees of freedom. This work connects and presents advances in two fields: (i) the field of complex oxides will benefit from a method for probing the mechanical properties of these strongly correlated electron materials in suspended form; (ii) the field of nanomechanics will now have access to a class of atomically engineerable materials and heterostructures with exotic properties that can be used as functional elements in nanoelectromechanical systems (NEMS). Such nanomechanical resonators can be used in self-transducing mechanical devices, suspended Bragg reflectors, bimorphic actuators, and novel thermomechanical and piezoelectric sensors. Furthermore, by decoupling the high-temperature growth of the materials from the device fabrication flow, the presented complex oxide NEMS resonators can be easily integrated into fully functional complementary metal oxide semiconductor devices that cannot tolerate temperatures >400 °C.

Methods

Pulsed laser deposition of epitaxial films

SAO, STO, and SRO films were grown by pulsed laser deposition on TiO2-terminated STO(001) substrates. The pulses were supplied by a KrF excimer laser and the substrate was mounted using two clamps and heated by an infrared laser. SAO and STO were deposited using a laser fluence of 1.2 J/cm2, a substrate temperature of 850 °C, and an oxygen pressure of 10−6 mbar. SRO was deposited at 600 °C, with a fluence of 1.1 J/cm2 and an oxygen pressure of 0.1 mbar. The growth occurred in layer-by-layer mode for SAO and STO, while SRO was grown in step-flow mode. After the deposition, the heterostructures were annealed for 1 h at 600 °C in 300 mbar O2 and cooled down in the same atmosphere.

Release and transfer

The thin films were released by adhering a PDMS layer to the film surface and immersing the stack in water. Dissolution of a 50-nm SAO layer was found to take approximately 60 min, without stirring or heating the water. After releasing the substrate, the PDMS layer with the thin film was dried using dry N2. The STO and SRO films were transferred onto pre-patterned Si/285 nm SiO2 substrates using an all-dry deterministic transfer technique20. The crystallinity of the thin films before and after their release was investigated by XRD (see Fig. 1b).

Mechanical characterization

The mechanical characterization of the resonators (Figs. 2 and 3) was performed with an active position feedback and variable frequency range to ensure that the laser spot is always centred and focussed on the drum. The resonance peaks are recorded with high accuracy (5000 points per measurement) to rule out any measurement artefacts in the interpretation of the data. In order to eliminate potential artefacts stemming from variations in the adhesion between the membranes and the substrate, the samples are thermally cycled prior to the measurement.

Second harmonic generation

The optical SHG measurement was performed in a reflection geometry to further confirm the presence of the structural transition seen in the mechanical experiments. The sample was excited by a 100-fs laser pulse at a central wavelength of 800 nm from a regenerative Ti:Sapphire amplified laser system operating at a 1-kHz repetition rate. The fluence of the laser radiation used in the experiment was in the order of 10 mJ/cm2. The nonlinear optical response at the central wavelength of 400 nm was detected using a photomultiplier tube.

Data availability

The manuscript has associated data in a data repository. The numerical data shown in figures of the manuscript can be downloaded from the Zenodo online repository at https://doi.org/10.5281/zenodo.3978636.

References

  1. 1.

    Dagotto, E. Complexity in strongly correlated electronic systems. Science 309, 257–262 (2005).

    ADS  Google Scholar 

  2. 2.

    Reyren, N. et al. Superconducting interfaces between insulating oxides. Science 317, 1196–1199 (2007).

    ADS  Google Scholar 

  3. 3.

    Farokhipoor, S. et al. Artificial chemical and magnetic structure at the domain walls of an epitaxial oxide. Nature 515, 379–383 (2014).

    ADS  Google Scholar 

  4. 4.

    Holsteen, A., Kim, I. S. & Lauhon, L. J. Extraordinary dynamic mechanical response of vanadium dioxide nanowires around the insulator to metal phase transition. Nano Lett. 14, 1898–1902 (2014).

    ADS  Google Scholar 

  5. 5.

    Zubko, P. et al. Negative capacitance in multidomain ferroelectric superlattices. Nature 534, 524–528 (2016).

    ADS  Google Scholar 

  6. 6.

    Manca, N. et al. Selective high-frequency mechanical actuation driven by the VO2 electronic instability. Adv. Mater. 29, 1701618 (2017).

    Google Scholar 

  7. 7.

    Rondinelli, J. M., May, S. J. & Freeland, J. W. Control of octahedral connectivity in perovskite oxide heterostructures: An emerging route to multifunctional materials discovery. MRS Bull. 37, 261–270 (2012).

    Google Scholar 

  8. 8.

    Bhaskar, U. K. et al. A flexoelectric microelectromechanical system on silicon. Nat. Nanotechnol. 11, 263 (2016).

    ADS  Google Scholar 

  9. 9.

    Paskiewicz, D. M., Sichel-Tissot, R., Karapetrova, E., Stan, L. & Fong, D. D. Single-crystalline SrRuO3 nanomembranes: a platform for flexible oxide electronics. Nano Lett. 16, 534–542 (2015).

    ADS  Google Scholar 

  10. 10.

    Lu, D. et al. Synthesis of freestanding single-crystal perovskite films and heterostructures by etching of sacrificial water-soluble layers. Nat. Mater. 15, 1255–1260 (2016).

    ADS  Google Scholar 

  11. 11.

    Ji, D. et al. Freestanding crystalline oxide perovskites down to the monolayer limit. Nature 570, 87 (2019).

    ADS  Google Scholar 

  12. 12.

    Novoselov, K., Mishchenko, A., Carvalho, A. & Neto, A. C. 2D materials and van der waals heterostructures. Science 353, aac9439 (2016).

    Google Scholar 

  13. 13.

    Atalaya, J., Kinaret, J. M. & Isacsson, A. Nanomechanical mass measurement using nonlinear response of a graphene membrane. EPL 91, 48001 (2010).

    ADS  Google Scholar 

  14. 14.

    Koenig, S. P., Wang, L., Pellegrino, J. & Bunch, J. S. Selective molecular sieving through porous graphene. Nat. Nanotechnol. 7, 728–732 (2012).

    ADS  Google Scholar 

  15. 15.

    Smith, A. D. et al. Electromechanical piezoresistive sensing in suspended graphene membranes. Nano Lett. 13, 3237–3242 (2013).

    ADS  Google Scholar 

  16. 16.

    Dolleman, R. J., Davidovikj, D., Cartamil-Bueno, S. J., van der Zant, H. S. J. & Steeneken, P. G. Graphene squeeze-film pressure sensors. Nano Lett. 16, 568–571 (2016).

    ADS  Google Scholar 

  17. 17.

    Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).

    ADS  Google Scholar 

  18. 18.

    Dolleman, R. J. et al. Optomechanics for thermal characterization of suspended graphene. Phys. Rev. B 96, 165421 (2017).

    ADS  Google Scholar 

  19. 19.

    Davidovikj, D. et al. Nonlinear dynamic characterization of two-dimensional materials. Nat. Commun. 8, 1253 (2017).

    ADS  Google Scholar 

  20. 20.

    Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).

    Google Scholar 

  21. 21.

    Bunch, J. S. et al. Electromechanical resonators from graphene sheets. Science 315, 490–493 (2007).

    ADS  Google Scholar 

  22. 22.

    Castellanos-Gomez, A. et al. Single-layer MoS2 mechanical resonators. Adv. Mater. 25, 6719–6723 (2013).

    Google Scholar 

  23. 23.

    Cardona, M. Optical properties and band structure of SrTiO3 and BaTiO3. Phys. Rev. 140, A651–A655 (1965).

    ADS  Google Scholar 

  24. 24.

    Tang, Y., Zhu, Y., Liu, Y., Wang, Y. & Ma, X. Giant linear strain gradient with extremely low elastic energy in a perovskite nanostructure array. Nat. Commun. 8, 1–8 (2017).

    Google Scholar 

  25. 25.

    Cartamil-Bueno, S. J. et al. High-quality-factor tantalum oxide nanomechanical resonators by laser oxidation of TaSe2. Nano Res. 8, 2842–2849 (2015)

  26. 26.

    Landau, L. D., Pitaevskii, L. P. & Lifshitz, E. M. Electrodynamics of Continuous Media. (Butterworth-Heinemann, Oxford, 1984).

    Google Scholar 

  27. 27.

    Šiškins, M. et al. Magnetic and electronic phase transitions probed by nanomechanical resonators. Nat. Commun. 11, 1–7 (2020).

    Google Scholar 

  28. 28.

    Sanditov, D. & Belomestnykh, V. Relation between the parameters of the elasticity theory and averaged bulk modulus of solids. Tech. Phys. Lett. 56, 1619–1623 (2011).

    Google Scholar 

  29. 29.

    Chen, C. et al. Performance of monolayer graphene nanomechanical resonators with electrical readout. Nat. Nanotechnol. 4, 861–867 (2009).

    ADS  Google Scholar 

  30. 30.

    Singh, V. et al. Probing thermal expansion of graphene and modal dispersion at low-temperature usinggraphene nanoelectromechanical systems resonators. Nanotechnology 21, 165204 (2010).

    ADS  Google Scholar 

  31. 31.

    Morell, N. et al. High quality factor mechanical resonators based on WSe2 monolayers. Nano Lett. 16, 5102–5108 (2016).

    ADS  Google Scholar 

  32. 32.

    Scott, J. & Ledbetter, H. Interpretation of elastic anomalies in SrTiO3 at 37 K. Z. Phys. B Condens. Matter 104, 635–639 (1997).

    ADS  Google Scholar 

  33. 33.

    Kityk, A. et al. Nonlinear elastic behaviour of SrTiO3 crystals in the quantum paraelectric regime. EPL 50, 41 (2000).

    ADS  Google Scholar 

  34. 34.

    Zalar, B. et al. NMR study of disorder in BaTiO3 and SrTiO3. Phys. Rev. B 71, 064107 (2005).

    ADS  Google Scholar 

  35. 35.

    Scott, J. F., Salje, E. K. H. & Carpenter, M. A. Domain wall damping and elastic softening in SrTiO3: evidence for polar twin walls. Phys. Rev. Lett. 109, 187601 (2012).

    ADS  Google Scholar 

  36. 36.

    Salje, E. K. H., Aktas, O., Carpenter, M. A., Laguta, V. V. & Scott, J. F. Domains within domains and walls within walls: evidence for polar domains in cryogenic SrTiO3. Phys. Rev. Lett. 111, 247603 (2013).

    ADS  Google Scholar 

  37. 37.

    Ledbetter, H., Lei, M. & Kim, S. Elastic constants, debye temperatures, and electron-phonon parameters of superconducting cuprates and related oxides. Phase Transit. 23, 61–70 (1990).

    Google Scholar 

  38. 38.

    Ang, C., Scott, J. F., Yu, Z., Ledbetter, H. & Baptista, J. L. Dielectric and ultrasonic anomalies at 16, 37, and 65 K in SrTiO3. Phys. Rev. B 59, 6661–6664 (1999).

    ADS  Google Scholar 

  39. 39.

    Tsunekawa, S., Watanabe, H. & Takei, H. Linear thermal expansion of SrTiO3. Phys. Status Solidi A 83, 467–472 (1984).

    ADS  Google Scholar 

  40. 40.

    Lytle, F. W. X-ray diffractometry of low-temperature phase transformations in strontium titanate. J. Appl. Phys. 35, 2212–2215 (1964).

    ADS  Google Scholar 

  41. 41.

    Unoki, H. & Sakudo, T. Electron spin resonance of Fe3+ in SrTiO3 with special reference to the 110 K phase transition. J. Phys. Soc. 23, 546–552 (1967).

    ADS  Google Scholar 

  42. 42.

    Garnier, P. Specific heat of srtio3 near the structural transition. Phys. Lett. A 35, 413–414 (1971).

    ADS  Google Scholar 

  43. 43.

    Will, M. et al. High quality factor graphene-based two-dimensional heterostructure mechanical resonator. Nano Lett. 17, 5950–5955 (2017).

    ADS  Google Scholar 

  44. 44.

    Kim, B. et al. Temperature dependence of quality factor in MEMS resonators. J. Microelectromech. Syst. 17, 755–766 (2008).

    Google Scholar 

  45. 45.

    Verbridge, S. S., Parpia, J. M., Reichenbach, R. B., Bellan, L. M. & Craighead, H. High quality factor resonance at room temperature with nanostrings under high tensile stress. J. Appl. Phys. 99, 124304 (2006).

    ADS  Google Scholar 

  46. 46.

    Unterreithmeier, Q. P., Faust, T. & Kotthaus, J. P. Damping of nanomechanical resonators. Phys. Rev. Lett. 105, 027205 (2010).

    ADS  Google Scholar 

  47. 47.

    Norte, R. A., Moura, J. P. & Gröblacher, S. Mechanical resonators for quantum optomechanics experiments at room temperature. Phys. Rev. Lett. 116, 147202 (2016).

    ADS  Google Scholar 

  48. 48.

    Zener, C. Internal friction in solids. I. Theory of internal friction in reeds. Phys. Rev. 52, 230 (1937).

    ADS  MATH  Google Scholar 

  49. 49.

    Garai, J. Correlation between thermal expansion and heat capacity. Calphad 30, 354–356 (2006).

    Google Scholar 

  50. 50.

    Durán, A., Morales, F., Fuentes, L. & Siqueiros, J. Specific heat anomalies at 37, 105 and 455 K in SrTiO3 :Pr. J. Condens. Matter Phys. 20, 085219 (2008).

    ADS  Google Scholar 

  51. 51.

    Arzel, L. et al. Observation of a sample-dependent 37 K anomaly on the lattice parameters of strontium titanate. EPL 61, 653 (2003).

    ADS  Google Scholar 

  52. 52.

    Wang, Z. et al. Black phosphorus nanoelectromechanical resonators vibrating at very high frequencies. Nanoscale 7, 877–884 (2015).

    ADS  Google Scholar 

  53. 53.

    Cartamil-Bueno, S. J. et al. Mechanical characterization and cleaning of CVD single-layer h-BN resonators. npj 2D Mater. Appl. 1, 16 (2017).

    Google Scholar 

Download references

Acknowledgements

The authors thank Pavlo Zubko and Gustau Catalan for the fruitful discussions and extensive feedback. This work was supported by the Dutch Research Council (NWO/OCW), as part of the Frontiers of Nanoscience (NanoFront) program, by the Dutch Foundation for Fundamental Research on Matter (FOM), by the European Research Council under the European Union’s H2020 programme/ERC Grant Agreement No. [677458], by the European Union Seventh Framework Programme under grant agreement no. 604391 Graphene Flagship, and by the European Union’s Horizon 2020 research and innovation programme under grant agreement nos. 785219 and 881603.

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D.J.G., A.M.V.R.L.M., and A.D. deposited and characterized the epitaxial heterostructures and prepared the suspended films. D.D. and D.J.G. performed the measurements and analysed the data. M.Š. and M.L. performed the measurements on the additional samples. D.D., D.J.G., A.M.V.R.L.M., M.Š., M.L., H.S.J.v.d.Z., A.D.C., and P.G.S. interpreted the data. D.A. performed the second-harmonic generation measurements. Y.H. and E.v.H. synthesized the SAO target for pulsed laser deposition. P.G.S. and A.D.C. supervised the overall project. D.D., D.J.G., A.D.C., and P.G.S. wrote the manuscript with input from all authors.

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Correspondence to A. D. Caviglia or P. G. Steeneken.

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Davidovikj, D., Groenendijk, D.J., Monteiro, A.M.R.V.L. et al. Ultrathin complex oxide nanomechanical resonators. Commun Phys 3, 163 (2020). https://doi.org/10.1038/s42005-020-00433-y

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