Ordering of ferroelectric polarization1 and its trajectory in response to an electric field2 are essential for the operation of non-volatile memories3, transducers4 and electro-optic devices5. However, for voltage control of capacitance and frequency agility in telecommunication devices, domain walls have long been thought to be a hindrance because they lead to high dielectric loss and hysteresis in the device response to an applied electric field6. To avoid these effects, tunable dielectrics are often operated under piezoelectric resonance conditions, relying on operation well above the ferroelectric Curie temperature7, where tunability is compromised. Therefore, there is an unavoidable trade-off between the requirements of high tunability and low loss in tunable dielectric devices, which leads to severe limitations on their figure of merit. Here we show that domain structure can in fact be exploited to obtain ultralow loss and exceptional frequency selectivity without piezoelectric resonance. We use intrinsically tunable materials with properties that are defined not only by their chemical composition, but also by the proximity and accessibility of thermodynamically predicted strain-induced, ferroelectric domain-wall variants8. The resulting gigahertz microwave tunability and dielectric loss are better than those of the best film devices by one to two orders of magnitude and comparable to those of bulk single crystals. The measured quality factors exceed the theoretically predicted zero-field intrinsic limit owing to domain-wall fluctuations, rather than field-induced piezoelectric oscillations, which are usually associated with resonance. Resonant frequency tuning across the entire L, S and C microwave bands (1–8 gigahertz) is achieved in an individual device—a range about 100 times larger than that of the best intrinsically tunable material. These results point to a rich phase space of possible nanometre-scale domain structures that can be used to surmount current limitations, and demonstrate a promising strategy for obtaining ultrahigh frequency agility and low-loss microwave devices.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


  1. 1.

    Merz, W. J. Domain formation and domain wall motions in ferroelectric BaTiO3 single crystals. Phys. Rev. 95, 690–698 (1954).

  2. 2.

    Xu, R., Liu, S., Grinberg, I., Karthik, J., Damodaran, A. R., Rappe, A. M. & Martin, L. W. Ferroelectric polarization reversal via successive ferroelastic transitions. Nat. Mater. 14, 79–86 (2015).

  3. 3.

    Chanthbouala, A. et al. Solid-state memories based on ferroelectric tunnel junctions. Nat. Nanotechnol. 7, 101–104 (2012).

  4. 4.

    Muralt, P. Ferroelectric thin films for micro-sensors and actuators: a review. J. Micromech. Microeng. 10, 136–146 (2000).

  5. 5.

    Wessels, B. W. Ferroelectric epitaxial thin films for integrated optics. Annu. Rev. Mater. Res. 37, 659–679 (2007).

  6. 6.

    Arlt, G., Böttger, U. & Witte, S. Dielectric dispersion of ferroelectric ceramics and single crystals at microwave frequencies. Ann. Phys. 506, 578–588 (1994).

  7. 7.

    York, B. in Multifunctional Adaptive Microwave Circuits and Systems (eds Steer, M. & Palmer, W. D.) Ch. 6 (SciTech Publishing, Raleigh, 2006).

  8. 8.

    Pertsev, N. A., Zembilgotov, A. G. & Tagantsev, A. K. Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films. Phys. Rev. Lett. 80, 1988–1991 (1998).

  9. 9.

    Lee, C.-H. et al. Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics. Nature 502, 532–536 (2013).

  10. 10.

    Damodaran, A. R., Breckenfeld, E., Chen, Z., Lee, S. & Martin, L. W. Enhancement of ferroelectric Curie temperature in BaTiO3 films via strain-induced defect dipole alignment. Adv. Mater. 26, 6341–6347 (2014).

  11. 11.

    Damodaran, A. R. et al. Nanoscale structure and mechanism for enhanced electromechanical response of highly strained BiFeO3 thin films. Adv. Mater. 23, 3170–3175 (2011).

  12. 12.

    Prosandeev, S., Yang, Y., Paillard, C. & Bellaiche, L. Displacement current in domain walls of bismuth ferrite. npj Comput. Mater. 4, 8 (2018).

  13. 13.

    Wang, Y. L., Tagantsev, A. K., Damjanovic, D. & Setter, N. Giant domain wall contribution to the dielectric susceptibility in BaTiO3. Appl. Phys. Lett. 91, 062905 (2007).

  14. 14.

    Tagantsev, A. K., Sherman, V. O., Astafiev, K. F., Venkatesh, J. & Setter, N. Ferroelectric materials for microwave tunable applications. J. Electroceram. 11, 5–66 (2003).

  15. 15.

    Matzen, S. et al. Super switching and control of in-plane ferroelectric nanodomains in strained thin films. Nat. Commun. 5, 4415 (2014).

  16. 16.

    Griggio, F. et al. Composition dependence of local piezoelectric nonlinearity in (0.3)Pb(Ni0.33Nb0.67)O3-(0.7)Pb(ZrxTi1−x)O3 films. J. Appl. Phys. 110, 044109 (2011).

  17. 17.

    Meyers, C. J. G., Freeze, C. R., Stemmer, S. & York, R. A. (Ba, Sr)TiO3 tunable capacitors with RF commutation quality factors exceeding 6000. Appl. Phys. Lett. 109, 112902 (2016).

  18. 18.

    Vorobiev, A., Gevorgian, S., Löffler, M. & Olsson, E. Correlations between microstructure and Q-factor of tunable thin film bulk acoustic wave resonators. J. Appl. Phys. 110, 054102 (2011).

  19. 19.

    Budimir, M., Damjanovic, D. & Setter, N. Extension of the dielectric tunability range in ferroelectric materials by electric bias field antiparallel to polarization. Appl. Phys. Lett. 88, 082903 (2006).

  20. 20.

    Rojac, T., Bencan, A., Drazic, G., Kosec, M. & Damjanovic, D. Piezoelectric nonlinearity and frequency dispersion of the direct piezoelectric response of BiFeO3 ceramics. J. Appl. Phys. 112, 064114 (2012).

  21. 21.

    Zuo, C., Der Spiegel, J. V. & Piazza, G. 1.05-GHz cmos oscillator based on lateral- field-excited piezoelectric AlN contour-mode MEMS resonators. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 82–87 (2010).

  22. 22.

    Gong, S., Kuo, N. K. & Piazza, G. GHz high-Q lateral overmoded bulk acoustic-wave resonators using epitaxial SiC thin film. J. Microelectromech. Syst. 21, 253–255 (2012).

  23. 23.

    Rinaldi, M., Zuniga, C., Zuo, C. & Piazza, G. Super-high-frequency two-port AlN contour-mode resonators for RF applications. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 38–45 (2010).

  24. 24.

    Rinaldi, M., Zuniga, C. & Piazza, G. 5–10 GHz AlN contour-mode nanoelectromechanical resonators. In 2009 IEEE 22nd International Conference on Micro Electro Mechanical Systems 916–919 (IEEE, 2009).

  25. 25.

    Krupka, J., Tobar, M. E., Hartnett, J. G., Cros, D. & Le Floch, J. M. Extremely high-Q factor dielectric resonators for millimeter-wave applications. IEEE Trans. Microw. Theory Tech. 53, 702–712 (2005).

  26. 26.

    Hartnett, J. G., Tobar, M. E., Ivanov, E. N. & Krupka, J. Room temperature measurement of the anisotropic loss tangent of sapphire using the whispering gallery mode technique. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53, 34–38 (2006).

  27. 27.

    Magnusson, E. B. et al. Surface acoustic wave devices on bulk ZnO crystals at low temperature. Appl. Phys. Lett. 106, 063509 (2015).

  28. 28.

    Vendik, I. B., Vendik, O. G. & Kollberg, E. L. Commutation quality factor of two-state switchable devices. IEEE Trans. Microw. Theory Tech. 48, 802–808 (2000).

  29. 29.

    Berge, J. & Gevorgian, S. Tunable bulk acoustic wave resonators based on Ba0.25Sr0.75TiO3 thin films and a HfO2/SiO2 Bragg reflector. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2768–2771 (2011).

  30. 30.

    Gevorgian, S. S., Tagantsev, A. K. & Vorobiev, A. K. Tunable Film Bulk Acoustic Wave Resonators (Springer, New York, 2013).

  31. 31.

    Hoshina, T. et al. Domain size effect on dielectric properties of barium titanate ceramics. Jpn. J. Appl. Phys. 47, 7607–7611 (2008).

  32. 32.

    Gammaitoni, L., Hänggi, P., Jung, P. & Marchesoni, F. Stochastic resonance. Rev. Mod. Phys. 70, 223–287 (1998).

  33. 33.

    Akhiezer, A. On the absorption of sound in solids. J. Phys. USSR 1, 277 (1939).

  34. 34.

    Shirokov, V. B., Yuzkuk, Yu. I., Dkhil, B. & Lemanov, V. V. Phenomenological theory of phase transitions in epitaxial BaxSr1−xTiO3 thin films. Phys. Rev. B 79, 144118 (2009).

  35. 35.

    Qi, Y., Liu, S., Grinberg, I. & Rappe, A. M. Atomistic description for temperature-driven phase transitions in BaTiO3. Phys. Rev. B 94, 134308 (2016).

Download references


Work at Drexel University and the University of California at Berkeley was supported in part by the US National Science Foundation (NSF) and the Semiconductor Research Corporation under the ‘Nanoelectronics in 2020 and Beyond’ programme grant number DMR 1124696 and by the Materials Science Division of the US Army Research Office (ARO). Z.G. and G.X. acknowledge support from the ARO under grant number W911NF-14-1-0500. A.P. and A.A.P. acknowledge support from the NSF under grant number IIP 1549668. A.W.-C. acknowledges support from the NSF under grant number DMR 1608887. C.J.H. acknowledges support from the Office of Naval Research under grant number N00014-15-11-2170. J.E.S. acknowledges support from the Air Force Office of Scientific Research under grant number FA9550-13-1-012. I.G., A.S., H.B., J.E.S. and G.X. acknowledge support from the NSF–BSF (US–Israel Binational Science Foundation) joint programme under grant numbers BSF 2016637 and CBET 1705440. S.P. and A.R.D. acknowledge support from the ARO under grant number W911NF-14-1-0104. A.R.D. also acknowledges the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under award number DE-SC-0012375 for the development of the BST materials. A.D. acknowledges support from the NSF under grant number DMR 1708615. S.S. acknowledges support from the NSF under grant number DMR 1608938. L.W.M. acknowledges support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract number DE-AC02-05-CH11231: Materials Project programme KC23MP for the development of new functional materials. R.A.Y. and C.J.G.M. acknowledge support from ARO under grant number W911NF-14-1-0335. Numerical GLD and phase-field simulations were carried out on Proteus, a computer cluster supported by the Drexel University Research Computing Facility.

Reviewer information

Nature thanks S. Prosandeev, A. Vorobiev and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information


  1. Department of Materials Science and Engineering, Drexel University, Philadelphia, PA, USA

    • Zongquan Gu
    • , Geoffrey Xiao
    • , Alessia Polemi
    • , Adrian A. Podpirka
    • , Alexandria Will-Cole
    • , Christopher J. Hawley
    •  & Jonathan E. Spanier
  2. Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA

    • Zongquan Gu
    •  & Jonathan E. Spanier
  3. Department of Materials Science and Engineering, University of California at Berkeley, Berkeley, CA, USA

    • Shishir Pandya
    • , Anoop R. Damodaran
    • , Arvind Dasgupta
    • , Sahar Saremi
    •  & Lane W. Martin
  4. Department of Chemistry, Bar-Ilan University, Ramat-Gan, Israel

    • Atanu Samanta
    • , Haim Barak
    •  & Ilya Grinberg
  5. Carnegie Institution for Science, Washington, DC, USA

    • Shi Liu
  6. Department of Electrical and Computer Engineering, University of California at Santa Barbara, Santa Barbara, CA, USA

    • Cedric J. G. Meyers
    •  & Robert A. York
  7. Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA, USA

    • Liyan Wu
    •  & Peter K. Davies
  8. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    • Lane W. Martin
  9. Department of Physics, Drexel University, Philadelphia, PA, USA

    • Jonathan E. Spanier


  1. Search for Zongquan Gu in:

  2. Search for Shishir Pandya in:

  3. Search for Atanu Samanta in:

  4. Search for Shi Liu in:

  5. Search for Geoffrey Xiao in:

  6. Search for Cedric J. G. Meyers in:

  7. Search for Anoop R. Damodaran in:

  8. Search for Haim Barak in:

  9. Search for Arvind Dasgupta in:

  10. Search for Sahar Saremi in:

  11. Search for Alessia Polemi in:

  12. Search for Liyan Wu in:

  13. Search for Adrian A. Podpirka in:

  14. Search for Alexandria Will-Cole in:

  15. Search for Christopher J. Hawley in:

  16. Search for Peter K. Davies in:

  17. Search for Robert A. York in:

  18. Search for Ilya Grinberg in:

  19. Search for Lane W. Martin in:

  20. Search for Jonathan E. Spanier in:


Z.G. and J.E.S. conceived the idea and, together with I.G., proposed the mechanism for high Q. Z.G. and J.E.S. developed and implemented the GLD model; G.X., Z.G. and J.E.S. implemented the phase-field model; and A.S., S.L. and I.G. carried out the molecular dynamics simulations and analysis of the molecular dynamics data. H.B. and I.G. developed the stochastic oscillator model. S.P., A.R.D., A.D., Z.G., L.W.M. and J.E.S. designed the growth experiments, and Z.G., I.G. and J.E.S. formulated the interpretation of the experimental data. A.D., A.R.D., S.P. and Z.G. carried out the film synthesis and its optimization. L.W. and P.K.D. produced the solid-state sources. S.P., A.D. and Z.G. carried out X-ray diffraction measurements, X-ray reflectivity analysis and reciprocal space mapping. Z.G., A.D. and S.P. carried out piezoresponse force microscopy analysis. C.J.G.M. designed the microwave devices, carried out film processing and device fabrication and performed microwave measurements and analysis, which were supervised by R.A.Y. Assistance in microwave device design, fabrication, measurements and analysis was provided by A.P., A.A.P. and A.W.-C. The theoretical, experimental and computational modeling aspects of the project were overseen together by I.G., R.A.Y., L.W.M. and J.E.S. All authors contributed to the data analysis. Z.G., I.G. and J.E.S. wrote the manuscript. Z.G., G.X., S.P., A.S., A.D., A.R.D., S.S., C.J.G.M., R.A.Y., I.G., L.W.M. and J.E.S. edited and commented on the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Jonathan E. Spanier.

Supplementary information

  1. Supplementary Information

    Ginzburg–Landau–Devonshire-based derivation of free energies and field-tuned dielectric susceptibility in domain wall variant phases, description of phase field model, table and illustrations of domain wall variants, X-ray diffraction and reciprocal space mapping data, additional microwave-band n, Q, and S parameter data; additional molecular dynamics calculation results and stochastic model calculations results.

About this article

Publication history




Issue Date




By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.