Abstract
The inversion of inhomogeneous physical states has great technological importance; for example, active noise reduction relies on the emission of an inverted sound wave that interferes destructively with the noise of the emitter1, and inverting the evolution of a spin system by using a magnetic-field pulse enables magnetic resonance tomography2. In contrast to these examples, inversion of a distribution of ferromagnetic or ferroelectric domains within a material is surprisingly difficult: field poling creates a single-domain state, and piece-by-piece inversion using a scanning tip is impractical. Here we report inversion of entire ferromagnetic and ferroelectric domain patterns in the magnetoelectric material Co3TeO6 and the multiferroic material Mn2GeO4, respectively. In these materials, an applied magnetic field reverses the magnetization or polarization, respectively, of each domain, but leaves the domain pattern intact. Landau theory indicates that this type of magnetoelectric inversion is universal across materials that exhibit complex ordering, with one order parameter holding the memory of the domain structure and another setting its overall sign. Domain-pattern inversion is only one example of a previously unnoticed effect in systems such as multiferroics, in which several order parameters are available for combination. Exploring these effects could therefore advance multiferroics towards new levels of functionality.
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Change history
20 September 2018
Four incorrect figure citations in this Letter have been corrected online.
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Acknowledgements
J.S.W. thanks the SNSF for support via grant 200021_153451. M.K. acknowledges financial support by SNSF grant 200021_165855. S.A.I. acknowledges financial support from the Russian Foundation for Basic Research. M.F. is grateful for support by SNSF grant 200021_178825. We thank B. Harris for a discussion of the Landau theory for Mn2GeO4 in refs 14,15, prior to their publication.
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Nature thanks V. Gopalan and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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Contributions
All authors contributed to the discussion and interpretation of the experiment and to the completion of the manuscript. N.L. and V.C. performed the experiments. N.L., J.S.W. and M.K. interpreted the domain-pattern inversion on the basis of a previously published14,15 Landau-theoretical description of the order parameters. V.C., M.H. and P.T. performed the Landau-theoretical analysis of the Co3TeO6 experiments. M.W. grew single crystals of Co3TeO6 and S.A.I. analysed their stoichiometry and structure. T.H. and T.K. prepared single crystals of Mn2GeO4. Th.L. supervised the experiments on Co3TeO6. D.M. and M.F. initiated the experiment and supervised the work.
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Extended data figures and tables
Extended Data Fig. 1 Crystallographic structure, magnetic structure and optical excitation of Co3TeO6.
a, Three-dimensional view of the crystallographic unit cell along the x axis in relation to the magnetic propagation vectors k0 and k≠0. b, Section of the unit cell in the x–z plane showing the location of the paramagnetic Co2+ ions in five different positions. c, Magnetic moments of the Co2+ ions shown in b. d, Orientation of the spontaneous magnetization Mx,z and the electric polarization Py. The latter is symmetry-allowed as spontaneous polarization, yet observed only as a magnetic-field-induced contribution9,10,12. e, Geometry of the SHG transmission experiment with light at ω and 2ω propagating along the z axis, probing a z-cut Co3TeO6 platelet in perpendicular incidence. The sample is exposed to a magnetic field Hy.
Extended Data Fig. 2 Crystallographic structure, magnetic structure and optical excitation for Mn2GeO4.
a, Top, three-dimensional view of the crystallographic unit cell showing the location of the paramagnetic Mn2+ ions on the different positions ‘Mn1’ and ‘Mn2’. Bottom, orientation of the spontaneous magnetization Mz and spontaneous polarization Pz in relation to the magnetic propagation vectors k0 and k≠0. b, Conically modulated order of the magnetic Mn2+ moments on the Mn1 and Mn2 positions. Bold arrows show the resulting spontaneous magnetization Mz and spontaneous polarization Pz. c, As in b, but for reversed spontaneous magnetization. d, Geometry of the SHG transmission experiment with light incident onto a z-cut Mn2GeO4 platelet. The sample is exposed to a magnetic field Hz and it is rotated around the y axis so that the optical excitation does not occur in perpendicular geometry.
Extended Data Fig. 3 SHG coupling and interference.
a, Spatially resolved SHG image of a z-cut Co3TeO6 sample. At 5 K, a magnetization-induced SHG contribution from χxyy and a crystallographically induced SHG contribution from χyyy are present. The χxyy light waves from opposite domains differ by 180° because of proportionality to the spontaneous magnetization ±Mx,z. The phase of the χyyy wave is homogeneous across the sample because it is blind to the magnetic order. Constructive (+Mx,z) and destructive (−Mx,z) interference of the magnetic and crystallographic SHG contributions therefore yields the opposite magnetic domain states as regions of different brightness. b, Image of the same region as in a but at 30 K, at which Mx,z = 0 so that only the homogeneous crystallographic SHG contribution from χyyy remains. Scale bar, 500 μm.
Extended Data Fig. 4 Inversion of the ferroelectric domain pattern in an x-cut Mn2GeO4 sample.
Sequentially taken SHG images of ±Pz domains on an x-oriented Mn2GeO4 sample at the given magnetic fields Hz. The same domain-inversion behaviour as for the z-cut sample in Fig. 4 is observed. Because of the small SHG contrast, opposite polarization domain states are highlighted by colour shading. Darker or black areas are caused by cracks and pores in the Mn2GeO4 sample. Scale bar, 500 μm.
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Leo, N., Carolus, V., White, J.S. et al. Magnetoelectric inversion of domain patterns. Nature 560, 466–470 (2018). https://doi.org/10.1038/s41586-018-0432-4
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DOI: https://doi.org/10.1038/s41586-018-0432-4
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