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Insect eyes have an anti-reflective coating, owing to nanostructures on the corneal surface creating a gradient of refractive index between that of air and that of the lens material 1,2 . These nanocoatings have also been shown to provide anti-adhesive functionality 3 . The morphology of corneal nanocoatings are very diverse in arthropods, with nipple-like structures that can be organized into arrays or fused into ridge-like structures 4 . This diversity can be attributed to a reaction-diffusion mechanism 4 and patterning principles developed by Alan Turing 5 , which have applications in numerous biological settings 6 . The nanocoatings on insect corneas are one example of such Turing patterns, and the first known example of nanoscale Turing patterns 4 . Here we demonstrate a clear link between the morphology and function of the nanocoatings on Drosophila corneas. We find that nanocoatings that consist of individual protrusions have better anti-reflective properties, whereas partially merged structures have better anti-adhesion properties. We use biochemical analysis and genetic modification techniques to reverse engineer the protein Retinin and corneal waxes as the building blocks of the nanostructures. In the context of Turing patterns, these building blocks fulfil the roles of activator and inhibitor, respectively. We then establish low-cost production of Retinin, and mix this synthetic protein with waxes to forward engineer various artificial nanocoatings with insect-like morphology and anti-adhesive or anti-reflective function. Our combined reverse- and forward-engineering approach thus provides a way to economically produce functional nanostructured coatings from biodegradable materials.

Four incorrect figure citations in this Letter have been corrected online.

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 emitter 1 , and inverting the evolution of a spin system by using a magnetic-field pulse enables magnetic resonance tomography 2 . 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 Co 3 TeO 6 and the multiferroic material Mn 2 GeO 4 , 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.

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.

The quest for higher data density in information storage is motivating investigations into approaches for manipulating magnetization by means other than magnetic fields. This is evidenced by the recent boom in magnetoelectronics and 'spintronics', where phenomena such as carrier effects in magnetic semiconductors and high-correlation effects in colossal magnetoresistive compounds are studied for their device potential. The linear magnetoelectric effect-the induction of polarization by a magnetic field and of magnetization by an electric field-provides another route for linking magnetic and electric properties. It was recently discovered that composite materials and magnetic ferroelectrics exhibit magnetoelectric effects that exceed previously known effects by orders of magnitude, with the potential to trigger magnetic or electric phase transitions. Here we report a system whose magnetic phase can be controlled by an external electric field: ferromagnetic ordering in hexagonal HoMnO3 is reversibly switched on and off by the applied field via magnetoelectric interactions. We monitor this process using magneto-optical techniques and reveal its microscopic origin by neutron and X-ray diffraction. From our results, we identify basic requirements for other candidate materials to exhibit magnetoelectric phase control.

Ferroelectromagnets are an interesting group of compounds that complement purely (anti-)ferroelectric or (anti-)ferromagnetic materials--they display simultaneous electric and magnetic order. With this coexistence they supplement materials in which magnetization can be induced by an electric field and electrical polarization by a magnetic field, a property which is termed the magnetoelectric effect. Aside from its fundamental importance, the mutual control of electric and magnetic properties is of significant interest for applications in magnetic storage media and 'spintronics'. The coupled electric and magnetic ordering in ferroelectromagnets is accompanied by the formation of domains and domain walls. However, such a cross-correlation between magnetic and electric domains has so far not been observed. Here we report spatial maps of coupled antiferromagnetic and ferroelectric domains in YMnO3, obtained by imaging with optical second harmonic generation. The coupling originates from an interaction between magnetic and electric domain walls, which leads to a configuration that is dominated by the ferroelectromagnetic product of the order parameters.