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Shear-strain-mediated magnetoelectric effects revealed by imaging


Large changes in the magnetization of ferromagnetic films can be electrically driven by non-180° ferroelectric domain switching in underlying substrates, but the shear components of the strains that mediate these magnetoelectric effects have not been considered so far. Here we reveal the presence of these shear strains in a polycrystalline film of Ni on a 0.68Pb(Mg1/3Nb2/3)O3–0.32PbTiO3 substrate in the pseudo-cubic (011)pc orientation. Although vibrating sample magnetometry records giant magnetoelectric effects that are consistent with the hitherto expected 90° rotations of a global magnetic easy axis, high-resolution vector maps of magnetization (constructed from photoemission electron microscopy data, with contrast from X-ray magnetic circular dichroism) reveal that the local magnetization typically rotates through smaller angles of 62–84°. This shortfall with respect to 90° is a consequence of the shear strain associated with ferroelectric domain switching. The non-orthogonality represents both a challenge and an opportunity for the development and miniaturization of magnetoelectric devices.

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Fig. 1: Cubic representation of the pseudocubic PMN–PT (011)pc unit cell.
Fig. 2: Macroscopic ME effects in Ni//PMN–PT (011)pc.
Fig. 3: Global and local magnetization for ME switching in Ni//PMN–PT (011)pc.
Fig. 4: Changes in the local magnetization for ME switching in Ni//PMN–PT (011)pc.
Fig. 5: Local magnetization and changes of local magnetization for ME switching in Ni//PMN–PT (011)pc.
Fig. 6: Predicted local ME switching for Ni//PMN–PT (011)pc.

Data availability

All relevant data are available from all corresponding authors on request.


  1. 1.

    Fiebig, M. Revival of the magnetoelectric effect. J. Phys. D 38, R123–R152 (2005).

    CAS  Google Scholar 

  2. 2.

    Eerenstein, W., Mathur, N. D. & Scott, J. F. Multiferroic and magnetoelectric materials. Nature 442, 759–765 (2006).

    CAS  Article  Google Scholar 

  3. 3.

    Ramesh, R. & Spaldin, N. A. Multiferroics: progress and prospects in thin films. Nat. Mater. 6, 21–29 (2007).

    CAS  Google Scholar 

  4. 4.

    Cheong, S.-W. & Mostovoy, M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater. 6, 13–20 (2007).

    CAS  Google Scholar 

  5. 5.

    Nan, C.-W., Bichurin, M. I., Dong, S., Viehland, D. & Srinivasan, G. Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103, 031101 (2008).

    Google Scholar 

  6. 6.

    Lebeugle, D. et al. Electric-field-induced spin flop in BiFeO3 single crystals at room temperature. Phys. Rev. Lett. 100, 227602 (2008).

    CAS  Google Scholar 

  7. 7.

    Choi, Y. J., Zhang, C. L., Lee, N. & Cheong, S.-W. Cross-control of magnetization and polarization by electric and magnetic fields with competing multiferroic and weak-ferromagnetic phases. Phys. Rev. Lett. 105, 097201 (2010).

    CAS  Google Scholar 

  8. 8.

    Tokunaga, Y., Taguchi, Y., Arima, T. H. & Tokura, Y. Electric-field-induced generation and reversal of ferromagnetic moment in ferrites. Nat. Phys. 8, 838–844 (2012).

    CAS  Google Scholar 

  9. 9.

    Chun, S. H. et al. Electric field control of nonvolatile four-state magnetization at room temperature. Phys. Rev. Lett. 108, 177201 (2012).

    Google Scholar 

  10. 10.

    Chai, Y.-S. et al. Electrical control of large magnetization reversal in a helimagnet. Nat. Commun. 5, 4208 (2014).

    CAS  Google Scholar 

  11. 11.

    Zavaliche, F. et al. Electrically assisted magnetic recording in multiferroic nanostructures. Nano Lett. 7, 1586–1590 (2007).

    CAS  Google Scholar 

  12. 12.

    Mundy, J. A. et al. Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic. Nature 537, 523–527 (2016).

    CAS  Google Scholar 

  13. 13.

    Ohno, H. et al. Electric-field control of ferromagnetism. Nature 408, 944–946 (2000).

    CAS  Google Scholar 

  14. 14.

    Chiba, D., Yamanouchi, M., Matsukura, F. & Ohno, H. Electrical manipulation of magnetization reversal in a ferromagnetic semiconductor. Science 301, 943–945 (2003).

    CAS  Google Scholar 

  15. 15.

    Chiba, D. et al. Magnetization vector manipulation by electric fields. Nature 455, 515–518 (2008).

    CAS  Google Scholar 

  16. 16.

    Yamada, Y. et al. Electrically induced ferromagnetism at room temperature in cobalt-doped titanium dioxide. Science 332, 1065–1067 (2011).

    CAS  Google Scholar 

  17. 17.

    Maruyama, T. et al. Large voltage-induced magnetic anisotropy change in a few atomic layers of iron. Nat. Nanotech. 4, 158–161 (2009).

    CAS  Google Scholar 

  18. 18.

    Endo, M., Kanai, S., Ikeda, S., Matsukura, F. & Ohno, H. Electric-field effects on thickness dependent magnetic anisotropy of sputtered MgO/Co40Fe40B20/Ta structures. Appl. Phys. Lett. 96, 212503 (2010).

    Google Scholar 

  19. 19.

    Cuellar, F. A. et al. Reversible electric-field control of magnetization at oxide interfaces. Nat. Commun. 5, 4215–4222 (2014).

    CAS  Google Scholar 

  20. 20.

    Borisov, P., Hochstrat, A., Chen, X., Kleemann, W. & Binek, C. Magnetoelectric switching of exchange bias. Phys. Rev. Lett. 94, 117203 (2005).

    Google Scholar 

  21. 21.

    Eerenstein, W., Wiora, M., Prieto, J. L., Scott, J. F. & Mathur, N. D. Giant sharp and persistent converse magnetoelectric effects in multiferroic epitaxial heterostructures. Nat. Mater. 6, 348–351 (2007).

    CAS  Google Scholar 

  22. 22.

    Thiele, C., Dörr, K., Bilani, O., Rödel, J. & Schultz, L. Influence of strain on the magnetization and magnetoelectric effect in La0.7A0.3MnO3/PMN-PT(001) (A=Sr, Ca). Phys. Rev. B 75, 054408 (2007).

    Google Scholar 

  23. 23.

    Sahoo, S. et al. Ferroelectric control of magnetism in BaTiO3/Fe heterostructures via interface strain coupling. Phys. Rev. B 76, 092108 (2007).

    Google Scholar 

  24. 24.

    Geprägs, S., Brandlmaier, A., Opel, M., Gross, R. & Goennenwein, S. T. B. Electric field controlled manipulation of the magnetization in Ni/BaTiO3 hybrid structures. Appl. Phys. Lett. 96, 142509 (2010).

    Google Scholar 

  25. 25.

    Wu, T. et al. Giant electric-field-induced reversible and permanent magnetization reorientation on magnetoelectric Ni/(011)[PbMg1/3Nb2/3O3](1−x)–[PbTiO3]x. Appl. Phys. Lett. 98, 012504 (2011).

    Google Scholar 

  26. 26.

    Wu, T. et al. Electrical control of reversible and permanent magnetization reorientation for magnetoelectric memory devices. Appl. Phys. Lett. 98, 262504 (2011).

    Google Scholar 

  27. 27.

    Lahtinen, T. H. E., Franke, K. J. A. & van Dijken, S. Electric-field control of magnetic domain wall motion and local magnetization reversal. Sci. Rep. 2, 258–263 (2012).

    Google Scholar 

  28. 28.

    Zhang, S. et al. Electric-field control of nonvolatile magnetization in Co40Fe40B20/(PbMg1/3Nb2/3)0.7Ti0.3O3 structure at room temperature. Phys. Rev. Lett. 108, 137203 (2012).

    CAS  Google Scholar 

  29. 29.

    Buzzi, M. et al. Single domain spin manipulation by electric fields in strain coupled artificial multiferroic nanostructures. Phys. Rev. Lett. 111, 027204 (2013).

    CAS  Google Scholar 

  30. 30.

    Cherifi, R. O. et al. Electric-field control of magnetic order above room temperature. Nat. Mater. 13, 345–351 (2014).

    CAS  Google Scholar 

  31. 31.

    Ghidini, M. et al. Perpendicular local magnetization under voltage control in Ni films on ferroelectric BaTiO3 substrates. Adv. Mater. 27, 1460–1465 (2015).

    CAS  Google Scholar 

  32. 32.

    Chopdekar, R. V. et al. Giant reversible anisotropy changes at room temperature in a (La,Sr)MnO3/Pb(Mg,Nb,Ti)O3 magneto-electric heterostructure. Sci. Rep. 6, 27501 (2016).

    CAS  Google Scholar 

  33. 33.

    Gao, Y. et al. Dynamic in situ observation of voltage-driven repeatable magnetization reversal at room temperature. Sci. Rep. 6, 23696 (2016).

    CAS  Google Scholar 

  34. 34.

    Li, P. et al. Spatially resolved ferroelectric domain-switching-controlled magnetism in Co40Fe40B20/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 multiferroic heterostructure. ACS Appl. Mater. Interfaces 9, 2642–2649 (2017).

    CAS  Google Scholar 

  35. 35.

    Lo Conte, R. et al. Influence of nonuniform micron-scale strain distributions on the electrical reorientation of magnetic microstructures in a composite multiferroic heterostructure. Nano Lett. 18, 1952–1961 (2018).

    CAS  Google Scholar 

  36. 36.

    Molegraaf, H. J. A. et al. Magnetoelectric effects in complex oxides with competing ground states. Adv. Mater. 21, 3470–3474 (2009).

    CAS  Google Scholar 

  37. 37.

    Skumryev, V. et al. Magnetization reversal by electric-field decoupling of magnetic and ferroelectric domain walls in multiferroic-based heterostructures. Phys. Rev. Lett. 106, 057206 (2011).

    CAS  Google Scholar 

  38. 38.

    Heron, J. T. et al. Deterministic switching of ferromagnetism at room temperature using an electric field. Nature 516, 370–373 (2014).

    CAS  Google Scholar 

  39. 39.

    Saenrang, W. et al. Deterministic and robust room-temperature exchange coupling in monodomain multiferroic BiFeO3 heterostructures. Nat. Commun. 8, 1583–1590 (2017).

    CAS  Google Scholar 

  40. 40.

    Bibes, M. & Barthelemy, A. Towards a magnetoelectric memory. Nat. Mater. 7, 425–426 (2008).

    CAS  Google Scholar 

  41. 41.

    Hu, J. M., Li, Z., Chen, L. Q. & Nan, C. W. High-density magnetoresistive random access memory operating at ultralow voltage at room temperature. Nat. Commun. 2, 553–560 (2011).

    Google Scholar 

  42. 42.

    Heron, J. T., Schlom, D. G. & Ramesh, R. Electric field control of magnetism using BiFeO3-based heterostructures. Appl. Phys. Rev. 1, 021303 (2014).

    Google Scholar 

  43. 43.

    Fang, F., Yang, W., Zhang, F. C. & Luo, H. S. Fatigue crack growth for BaTiO3 ferroelectric single crystals under cyclic electric loading. J. Am. Ceram. Soc. 88, 2491–2497 (2005).

    CAS  Google Scholar 

  44. 44.

    Park, S. E. & Shrout, T. R. Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals. J. Appl. Phys. 82, 1804–1811 (1997).

    CAS  Google Scholar 

  45. 45.

    Viehland, D. & Salje, E. K. H. Domain boundary-dominated systems: adaptive structures and functional twin boundaries. Adv. Phys. 63, 267–326 (2014).

    CAS  Google Scholar 

  46. 46.

    Wu, T. et al. Domain engineered switchable strain states in ferroelectric (011) [Pb(Mg1/3Nb2/3)O3](1-x)-[PbTiO3]x(PMN-PT, x≈0.32) single crystals. J. Appl. Phys. 109, 124101 (2011).

    Google Scholar 

  47. 47.

    Wang, Z., Wang, Y., Ge, W., Li, J. & Viehland, D. Volatile and nonvolatile magnetic easy-axis rotation in epitaxial ferromagnetic thin films on ferroelectric single crystal substrates. Appl. Phys. Lett. 103, 132909 (2013).

    Google Scholar 

  48. 48.

    Liu, M. et al. Voltage-impulse-induced non-volatile ferroelastic switching of ferromagnetic resonance for reconfigurable magnetoelectric microwave devices. Adv. Mater. 25, 4886–4892 (2013).

    CAS  Google Scholar 

  49. 49.

    Zhang, S. et al. Giant electrical modulation of magnetization in Co40Fe40B20/Pb(Mg1/3Nb2/3)0.7Ti0.3O3(011) heterostructure. Sci. Rep. 4, 3727 (2014).

    Google Scholar 

  50. 50.

    Heidler, J. et al. Manipulating magnetism in La0.7Sr0.3MnO3 via piezostrain. Phys. Rev. B 91, 024406 (2015).

    Google Scholar 

  51. 51.

    Zhou, C., Wang, F., Dunzhu, G., Yao, J. & Jiang, C. Piezostrain tuning non-volatile 90° magnetic easy axis rotation in Co2FeAl Heusler alloy film grown on Pb(Mg1/3Nb2/3)O3-PbTiO3 heterostructures. J. Phys. D 49, 455001 (2016).

    Google Scholar 

  52. 52.

    Noheda, B., Cox, D. E., Shirane, G., Gao, J. & Ye, Z.-G. Phase diagram of the ferroelectric relaxor (1–x)PbMg1/3Nb2/3O3xPbTiO3. Phys. Rev. B 66, 054104 (2002).

    Google Scholar 

  53. 53.

    Peng, J. et al. Shear-mode piezoelectric properties of 0.69Pb(Mg1/3Nb2/3)O3-0.31PbTiO3 single crystals. Solid State Commun. 130, 53–57 (2004).

    CAS  Google Scholar 

  54. 54.

    Pertsev, N. A. Giant magnetoelectric effect via strain-induced spin reorientation transitions in ferromagnetic films. Phys. Rev. B 78, 212102 (2008).

    Google Scholar 

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This work was funded by Isaac Newton Trust grants 10.26(u) and 11.35(u), UK EPSRC grant EP/G031509/1, the Royal Society (X.M.) and a start-up fund from the University of Wisconsin-Madison (J.-M.H.). D.P. acknowledges funding from the Agència de Gestió d’Ajuts Universitaris i de Recerca – Generalitat de Catalunya (grant 2014 BP-A 00079). We thank Diamond Light Source for time on beamline I06 (proposal SI-8876), and we thank S. Zhang for discussions.

Author information




M.G. initiated the study. M.G. and N.D.M. led the project with S.S.D. R.M., R.P.C. and C.H.W.B. were responsible for the growth of thin-film Ni. The collection and preliminary analysis of PEEM data were performed by M.G., with assistance from X.M., L.C.P and W.Y. All other experimental work was performed by M.G. F.M. and S.S.D. were responsible for constructing PEEM vector maps, and the subsequent pixel-by-pixel analysis. D.P. performed image and data processing. N.D.M. proposed the pixel-by-pixel analysis of PEEM vector maps that led to the key finding of sub-90° magnetization rotation. J.-M.H. identified and calculated the shear strain that accompanies ferroelectric domain switching in PMN–PT. M.G. identified the resulting principal axes of strain and hence magnetic easy axes. M.G. and N.D.M. interpreted the observed ME effects. N.D.M. wrote the manuscript with M.G., using substantive feedback from S.S.D. and J.-M.H. and additional feedback from R.M.

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Correspondence to M. Ghidini or S. S. Dhesi or N. D. Mathur.

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Supplementary Notes 1–6, Figs. 1–7 and Table 1.

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Ghidini, M., Mansell, R., Maccherozzi, F. et al. Shear-strain-mediated magnetoelectric effects revealed by imaging. Nat. Mater. 18, 840–845 (2019).

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