Skyrmion makeover


    Celebrating the treasures of topological twists.

    Sometimes a scientific idea falls into obscurity as researchers turn their attention elsewhere, yet contains such mathematical beauty that it is revived again and again. Such is the story of the skyrmion: a concept that has had several makeovers since it was first formulated in the late 1950s by the British physicist Tony Hilton Royle Skyrme.

    One way to visualize a skyrmion is to imagine a sphere studded with arrows pointing towards its centre. Then take away the sphere, project the arrows onto a plane while keeping their orientations fixed, and admire a twisting configuration.

    This texture is best defined mathematically as a 'topological' spatial feature that, like the twist in a Möbius strip, is preserved under continuous deformation. But the skyrmion turned out to be more than pure mathematics: in 1962, Skyrme found that it could explain how subatomic particles such as neutrons and protons exist as discrete entities emerging from a continuous nuclear field. This was a problem that had been worrying some of the highest-profile physicists of the day. In the Skyrme model it was intuitively explained by imagining such particles as stable geometric twists in an otherwise flat background, much like whirlpools in a mass of water.

    It was an imaginative and satisfying solution — and one that was overlooked for a decade or two. This was probably at least in part because of the advent of another big idea in particle physics in the 1960s: quarks. It may also have had something to do with Skyrme's modesty and lack of ambition to gain far-reaching acceptance for his ideas.

    The Skyrme model was finally embraced by particle physicists in the 1980s, only to be overshadowed a second time by an even bolder idea: string theory. In that same decade, however, an unexpected revival of skyrmions was already brewing, thanks to the discovery of a new kind of electronic system known as a quantum Hall device — the subject of two Nobel prizes, and the basis of a revolution in condensed-matter physics. Quantum Hall devices exhibit very unusual quantum effects, which show up as ultraprecise jumps in electronic current when a magnetic field is applied.

    Slowly, the understanding emerged that these quantum effects were best described in terms of topological features. This was a natural home for skyrmions and they were predicted and detected electronically in quantum Hall devices by the mid-1990s.

    A flurry of activity ensued in the field. As research topics do, the phenomenon eventually went out of fashion — again. But in recent years, skyrmions have made yet another comeback. The field of condensed-matter physics is abuzz with excitement about topological states of matter in a range of systems besides quantum Hall devices. Moreover, there is an ambitious agenda to exploit these topological features for practical applications: it is thought that they hold the key to a whole new range of robust electronic and magnetic functions and possibly also to quantum computation.

    In this issue, skyrmions are vividly brought to life in the stunning electron-microscope images of textures of swirling magnetization in a magnetic material (see Figures 1e and f on page 902). After re-emerging from the depths of obscurity several times over, the spotlight is back on skyrmions. And a reader can only wonder what other neglected gems of mathematical ideas are tucked away in the literature, awaiting a creative scientist to recognize their value to the physical world?

    Rights and permissions

    Reprints and Permissions

    About this article

    Cite this article

    Skyrmion makeover. Nature 465, 846 (2010).

    Download citation


    By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.