Physicists have puzzled over a hidden electronic order in a uranium-based material for decades. A new theory attributes it to not just a single but a double breaking of time-reversal symmetry. See Article p.621
A magnet sticks to a fridge door, but an aluminium spoon does not. This distinction is well understood in terms of the different ways in which the many billions of billions of electrons are collectively organized inside these materials. In a magnet, the electrons form an order: their tiny spins line up along a particular direction, producing an aggregate magnetic moment, whereas in aluminium these spins are randomly oriented. On page 621 of this issue, Chandra et al.1 propose a different kind of electronic order, which could resolve a riddle that has confounded physicists for more than a quarter of a century.
Much of the fascination and challenge of condensed-matter physics lies in figuring out how the electrons are organized in their microscopic world to produce the macroscopic properties observed in the laboratory. The tendency of the electrons in a magnet to develop order is analogous to that of water molecules to form a rigid spatial pattern as the liquid freezes into ice. This electronic order, called ferromagnetism, breaks time-reversal symmetry: if the time direction were reversed, so would be the direction of the magnetic moment.
The condensed-matter system studied by Chandra and colleagues is URu2Si2. This uranium-based compound is a member of a broad class of materials called strongly correlated electron systems, in which a large Coulomb repulsion between the electrons tends to produce spectacular physical phenomena — such as the high-temperature superconductivity observed in copper-based ceramics. This large repulsion in strongly correlated electron systems contrasts with the weak interactions found in many of the materials used in technology, such as silicon, aluminium or even ordinary magnets.
In the mid-1980s, researchers discovered2,3,4 clear signatures of an electronic order in URu2Si2 when the material was cooled below 17.5 kelvin. But the order was mysterious: it was different from ferromagnetism, antiferromagnetism (Fig. 1) or any other order known in the magnetic world. Since then, more than two dozen theoretical ideas5 have been put forward as candidate orders for URu2Si2. Some have been invalidated by experiments, whereas others remain a matter of contention. Condensed-matter physicists, in frustration, have referred to the phenomenon as a hidden order.
To make progress, Chandra et al. went back to basics. The spin of an electron has its origin in quantum mechanics, which divides subatomic particles into two categories: bosons and fermions. Electrons are fermions and, unlike bosons, cannot share the same quantum state. Nonetheless, they can quantum-mechanically entangle with each other. This entanglement is deeply ingrained in our understanding of heavy-fermion metals6, which make up a prominent family of materials within the strongly correlated electron systems to which URu2Si2 belongs.
The entanglement of itinerant (mobile) electrons with strongly correlated electrons that are localized on the uranium ions of URu2Si2 inhibits the motion of the itinerant electrons, and effectively enhances their mass by a huge factor — typically in the hundreds — compared with the bare-electron mass. The entanglement also mixes up the identities of the itinerant and localized electrons, a process called hybridization. The spins of the electrons in such a hybridized state can point in any direction, and no symmetry is broken.
Chandra and colleagues examined the details of this hybridization in URu2Si2, a crystal comprising layers of atomic planes. The process involves quantum tunnelling of itinerant electrons into or out of the compound's uranium ions, resulting in an odd number of electrons in the ion's 5f orbitals and two excited electronic states of opposite spin orientation on each ion. The two states, known as a Kramers doublet, are connected to each other by a time-reversal transformation.
On theoretical grounds, Chandra et al. have proposed that lowering the temperature of the material induces an order in the hybridization that breaks the time-reversal symmetry. More precisely, unlike in ordinary magnets — in which the elementary unit of the order is a spin carrying an angular momentum that is an integer amount of Planck's reduced constant (ħ) — in the proposed order, the elementary unit has an angular momentum of one-half of ħ. Consequently, when a time-reversal operation is applied twice to the system, symmetry is not restored. In other words, the order breaks symmetry not only in a single time reversal, but also in a double time reversal. The elementary unit of the proposed order forms a mathematical object known as a spinor (Fig. 1).
On the basis of this theoretical proposal, Chandra et al. have provided an explanation for several of the intriguing properties observed in URu2Si2, including a striking magnetic anisotropy7 — a large difference between the system's responses to a magnetic field that is applied parallel to the atomic planes, and to one that is applied perpendicular to the planes. The theory also includes an earlier-derived feature that connects the hidden-order state with a pressure-induced antiferromagnetic state8. These results make the proposed order a leading contender for the hidden order in URu2Si2. However, the theory rests on specific assumptions about the electronic configurations of the 5f orbitals in the uranium ions that should be tested experimentally. The evolution of the hybridization process as the temperature is lowered, from one that preserves all symmetries to one that breaks time-reversal invariance, should also be investigated by measuring the momentum dependence of the electronic states using photoemission spectroscopy9 and electronic tunnelling spectroscopy10,11,12.
From a theoretical perspective, the proposed spinor order is a refreshing idea. Ordinarily, whereas the onset of hybridization at absolute-zero temperature represents a sharp phase transition6, its thermally induced counterpart is only a gradual crossover phenomenon. Because the proposed spinor order breaks time-reversal symmetry, it turns the hybridization onset into a sharp phase transition even at a non-zero temperature. However, a spinor is usually a fermionic object and therefore is not allowed to order. Chandra et al. introduced an approximate treatment of the strong electron-correlation effects that made the spinor order possible, but this theoretical procedure requires further elucidation.
Regardless of what future investigations may uncover, Chandra and colleagues' study opens up a new dimension in the ongoing debate about the nature of the hidden order in URu2Si2, and enriches our exploration of strongly correlated matter that breaks time-reversal symmetry. More generally, strong correlations often produce competing tendencies for electronic order, which, in turn, foster the emergence of electronic phenomena such as superconductivity. Hence, the spinor order proposed here, as well as other exotic orders in related strongly correlated materials, will offer insight into collective electronic organization that may lead us to understand pressing issues such as high-temperature superconductivity.
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