Domains are of unparalleled technological importance as they are used for information storage and for electronic, magnetic and optical switches. They are an essential property of any ferroic material. Three forms of ferroic order are widely known: ferromagnetism, a spontaneous magnetization; ferroelectricity, a spontaneous polarization; and ferroelasticity, a spontaneous strain. It is currently debated whether to include an ordered arrangement of magnetic vortices as a fourth form of ferroic order, termed ferrotoroidicity. Although there are reasons to expect this form of order from the point of view of thermodynamics1, a crucial hallmark of the ferroic state—that is, ferrotoroidic domains—has not hitherto been observed. Here ferrotoroidic domains are spatially resolved by optical second harmonic generation in LiCoPO4, where they coexist with independent antiferromagnetic domains. Their space- and time-asymmetric nature relates ferrotoroidics to multiferroics with magnetoelectric phase control2,3,4,5 and to other systems in which space and time asymmetry leads to possibilities for future applications.
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We thank the Collaborative Research Center (SFB) 608 and the Priority Program (SPP) 1133 of the DFG and the Swiss NSF for subsidy, and R. Boutellier and S. Gentil for help with growing the crystals. We further thank C. Ederer and N. A. Spaldin for many discussions. M.F. thanks T. Elsässer for continuous support. H.S. is indebted to E. Ascher for initiating him into the realm of symmetries and into the importance of the time-odd polar vector.
The authors declare no competing financial interests.
The file contains Supplementary Notes consisting of two parts: (1) Supplement 1: Absence of ferroelectricity and ferroelasticity in LiCoPO4. In this text the possibility of ferroelectricity and ferroelasticity in LiCoPO4 is discussed. It is shown that neither form of ordering can be applied as alternative explanation for the domain structures denoted as ferrotoroidic. In addition, experimental data confirming the absence of ferroelectricity and ferroelasticity in LiCoPO4 are reported. (2) Supplement 2: Derivation of 2’ symmetry from SHG data. In this text it is shown that the 2’ symmetry of LiCoPO4 in the spin-ordered phase can be derived from the set of polarization contributions to the SHG signal alone if only the crystal structure and the presence of a weak magnetization is taken into account. (PDF 108 kb)
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Van Aken, B., Rivera, JP., Schmid, H. et al. Observation of ferrotoroidic domains. Nature 449, 702–705 (2007). https://doi.org/10.1038/nature06139
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