title: Observation of ferrotoroidic domains.
abstract: 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 thermodynamics, 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 control and to other systems in which space and time asymmetry leads to possibilities for future applications.
authors.affiliation: Max-Born-Institut, Max-Born-Strasse 2A, 12489 Berlin, Germany.
authors.forename: Bas B
authors.initials: BB
authors.lastname: Van Aken
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Rivera
authors.forename: Hans
authors.initials: H
authors.lastname: Schmid
authors.forename: Manfred
authors.initials: M
authors.lastname: Fiebig