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Condensed-matter physics

Quantum mechanics in a spin

Nature volume 540, pages 534535 (22 December 2016) | Download Citation

Quantum spin liquids are exotic states of matter first predicted more than 40 years ago. An inorganic material has properties consistent with these predictions, revealing details about the nature of quantum matter. See Letter p.559

The phenomenon of magnetism, discovered thousands of years ago, arises from the alignment of electron magnetic moments known as spins. But if these spins do not align, they can form a truly quantum state called a quantum spin liquid (QSL). On page 559, Shen et al.1 report measurements of exotic spin excitations in an inorganic material (of ytterbium, magnesium, gallium and oxygen; YbMgGaO4). The authors' observations suggest that YbMgGaO4 forms a QSL that is closely analogous to a state of matter associated with electrons in a metal. The appearance of electron-like particles in such a material is surprising, and indicates extraordinary 'quantum entanglement' of the underlying spins.

The concept of a QSL was first introduced2 in 1973 by the physicist Philip Anderson, who described such a system as “resonating”, indicating the presence of quantum superposition — in quantum mechanics, reality is represented by a wavefunction in which physical states of a system can be added together like numbers in arithmetic. An extreme example of quantum superposition is Schrödinger's famous cat, whose wavefunction is the sum of the state of the living cat and that of the dead cat. The QSL is a close relative of Schrödinger's cat that incorporates long-range entanglement (a superposition involving many widely separated spins). According to modern quantum theory, this type of entanglement is so stable that a QSL constitutes a new phase of matter at zero kelvin3,4.

The pattern of entanglement in a QSL state can be disrupted locally to form objects called quasiparticles that behave like ordinary particles. Such objects can have substantially different properties from those of the underlying microscopic spins. A dramatic example is the appearance of electron-like particles called fermions in a QSL — these particles obey Pauli's exclusion principle (they cannot share a single quantum state), whereas spins do not. Such behaviour enables the formation of a spinon metal, a material that is a conductor of spin and heat, but an electrical insulator.

A spinon metal has been implicated in the organic crystals κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, which have been the most-studied QSLs experimentally for more than a decade5. Here, the presence of a spinon metal was deduced indirectly from thermodynamic and thermal-transport measurements. The spins in these crystals are arranged in an approximately triangular lattice — such a geometry prevents a simple alignment of spins that could disrupt QSL formation.

“YbMgGaO4 is a perfect candidate for neutron scattering, the gold standard of magnetic measurements.”

Shen and colleagues study the inorganic material YbMgGaO4, which, like the organic crystals, contains a triangular lattice of spins — in this case, Yb3+ ions separated by non-magnetic layers6 (see Figure 1 of the paper1). However, YbMgGaO4 is atomically dense (there is one spin per 5 square ångströms in each layer7; for comparison, the area per spin in κ-(BEDT-TTF)2Cu2(CN)3 is more than 100 Å2; ref. 8), and each spin carries a roughly 50% larger magnetic moment than its organic counterpart6. These distinctions, and the absence of hydrogen, make YbMgGaO4 a perfect candidate for neutron scattering, the gold standard of magnetic measurements.

In inelastic neutron scattering, a neutron transfers energy and momentum to a material, which manifests as an excitation of the electron spins. Using many neutrons, one can determine the number of such excitations that have a given energy and momentum. The form of this spectral density is very different in an ordinary magnet and a QSL (Fig. 1). In a magnet, the excitation, called a magnon, is simply a spin that is flipped with respect to the ordered pattern of the surrounding spins. Such an excitation behaves like a particle and therefore has a definite relationship between its energy and its momentum. As a result, the spectral density at fixed momentum is non-zero only at specific energies. By contrast, in a QSL, the excitation is two 'spinons', which share the energy and momentum that are imparted to the material. Consequently, the spectral density is non-zero for a large range of energies — a continuum.

Figure 1: Identifying a quantum spin liquid.
Figure 1

a, In a neutron-scattering experiment, an ordinary magnet can experience an excitation called a magnon (orange arrow) — a spin that is flipped with respect to the ordered pattern of the surrounding spins (blue arrows) in the lattice. For a fixed value of the momentum, such an excitation has a specific energy. b, Conversely, in a quantum spin liquid (QSL), neutron scattering can create two 'spinons' (red arrows); the surrounding spins are paired in 'valence' bonds. The two spinons give rise to a continuous energy spectrum: for a fixed momentum, the energy can take a wide range of values. Shen et al.1 report the observation of such a spectrum in the inorganic compound YbMgGaO4, suggesting that this material could be a QSL.

Shen and collaborators report the observation of such a continuum in YbMgGaO4. The spins in this material have been shown6 to remain unaligned at temperatures as low as 30 mK — strongly suggesting that this feature persists to 0 K — and thermodynamic quantities such as the specific heat and magnetic susceptibility have features quite similar to those of the organic crystals. The authors' data reveal a much more detailed view of this QSL state, showing a continuum spectrum that is devoid of any sharp excitation peaks; it has maxima in energy and an overall intensity that are momentum dependent. Shen et al. compare their material's spectral density at 70 mK with theoretical predictions for various QSL states, finding that the best agreement is with a spinon metal.

The authors determine the nature of YbMgGaO4 purely empirically — its QSL behaviour now needs to be understood theoretically. Microscopically, the forces between Yb3+ spins are direction dependent and somewhat complicated, and their effects have not been definitively determined. Moreover, the non-magnetic layers between the triangular planes in YbMgGaO4 have a random arrangement of Mg and Ga atoms — this must induce some disorder in the spins, but its role in QSL formation is unknown.

If the authors' interpretation is correct, their results constitute the first momentum- and energy-dependent spectroscopy of a spinon metal. Note that a simultaneously published study9 has reported consistent experimental results for YbMgGaO4, and that a possible spinon continuum has been observed in the mineral herbertsmithite10, which has been suggested to be a different type of QSL. Further exploration of spinon metals could reveal rich physics — for example, spinons are predicted to interact strongly through 'emergent gauge fields', whose effects on the spectral density are unknown. It is exciting to imagine these beautiful theoretical ideas realized in the laboratory.



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  1. Leon Balents is at the Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.

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Correspondence to Leon Balents.

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