One of the fundamental ideas in physics is the existence of broken symmetries. One famous broken symmetry is the Higgs mechanism, which leads to the prediction of one or more Higgs bosons. In materials, broken symmetries of different sorts lead to magnetism, superconductivity—and a bit of strange behavior that has puzzled physicists for three decades. In one particular material, electrons behave as though they are much more massive than usual, and respond very differently to magnetic fields.

A new model may help resolve the confusion by proposing a different form of symmetry breaking. Ordinarily, if you reverse the direction of time (akin to running a movie backward), then reverse it again, everything comes back to normal. For the particular uranium-rubidium-silicon compound at issue, Premala Chandra, Piers Coleman, and Rebecca Flint argued that symmetry is broken: it will not behave normally even under double time reversal. While a literal double reversing of time isn't possible in the lab, the broken symmetry has a measurable consequence in the distortion of electron orbits in the uranium. If confirmed, this hypothesis could resolve a thirty-year-old mystery.

To understand broken symmetries as they apply to materials, consider an ordinary, non-magnetic solid. The spins of the electrons inside are randomly oriented, meaning that whichever way you look at the material, it appears the same, at least in terms of magnetic properties. That implies it has maximum symmetry.

In a magnet, on the other hand, the electron spins have a preferred direction, which is what produces the magnetic field. The maximum symmetry of an unmagnetized material has been broken, yielding a material that looks different depending on which way you look at it. In this way, broken symmetries lead to materials with special properties.

Another symmetry that's less obvious involves the reversal of time. If you think of electrons as little spinning spheres (a useful metaphor, but one we shouldn't take literally!), then reversing the direction of time effectively turns the spheres upside-down, swapping north and south poles. That means if you reverse the direction of time in a magnet, you also reverse the direction of the magnetic field, swapping the polarity. This is what physicists mean when we say that magnets break time-reversal symmetry.

A weird material

The uranium compound URu 2 Si 2 has a number of strange properties. Due to interactions between the particles in the material, electrons behave as though their masses are 12.5 times greater than the free electron mass. Below 17.5 Kelvins (17.5 degrees above absolute zero), the material exhibits a strange kind of behavior that isn't like an ordinary magnet: it responds differently depending on whether the magnetic field is applied parallel or perpendicular to planar structures in the crystal. Over the last three decades, a number of explanations for this behavior have been mooted, of which the current study is the latest.



There are many types of symmetries, and many ways to break them. The proposed hidden broken symmetry in the uranium-rubidium-silicon compound URu 2 Si 2 involved double time reversal. While most things are restored to their original configuration upon reversing the direction of time, then reversing it again, that symmetry is broken in the authors' model.

This type of transformation is known as a spinor, which, as the name suggests, relates mathematically to the spins of some particles. A simple spinor is illustrated in with coins above and in the animation below: it takes two revolutions of the quarter to return to the original configuration. Double time-reversal isn't quite the same, since it's a double reflection rather than a double rotation, but the idea is similar enough for the purposes of this article.

The proposed broken symmetry in URu 2 Si 2 was a mixture of time-reversal and double time-reversal. The authors called this a "hastatic" order (pretentiously using the Latin word for "spear", which is hasta). Since URu 2 Si 2 defies conventional magnetic description, the hastatic order could help explain many of the material's unusual properties.

According to the model, the single and double time-reversal symmetries exist above a critical temperature, then break when the material is cooled. Additionally, the researchers proposed that there is a testable consequence of the hastatic order, in terms of the shapes of the electron orbits in the uranium atoms.

An intriguing question is whether hastatic order could explain other unusual materials—assuming its existence is confirmed in URu 2 Si 2 , of course. Given that other systems have strong interactions between their constituent electrons that give rise to currently puzzling phenomena, it's possible that the hastatic symmetry idea will bear fruit elsewhere.

Nature, 2013. DOI: 10.1038/nature11820 (About DOIs).