The two faces of a magnetic honeycomb

Quantum spin liquids are long-sought exotic states of matter that could transform quantum computing. Signatures of such a state have now been observed in a compound comprising iridium ions on a honeycomb lattice.
Martin Mourigal is in the School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

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Scientists are searching for elusive forms of magnetism in which spins — atomic-scale ‘compass needles’ associated with electrons — perpetually dance to an intrinsic quantum beat. In a paper published in Nature, Kitagawa et al.1 describe the synthesis and properties of a remarkable quantum magnet in which the ballet of spins persists down to a temperature of 0.05 kelvin. Such behaviour might be associated with exotic magnetic excitations that are of great fundamental interest and are sought for quantum-computing technologies.

Quantum magnets are often found in electrically insulating crystals. In such materials, unpaired electrons are arranged on a periodic lattice, which allows the spins of the electrons to interact with those of their neighbours. At low temperatures, these spins usually organize into symmetrical and regular patterns.

In rare cases, however, quantum fluctuations prevent the spins from becoming ordered. Instead, the spins enter a quantum superposition — a concerted and perpetual dance in which the spins are entangled, meaning that they are inseparable and share a common quantum state. Many flavours of such states, called quantum spin liquids, have been predicted2. At first sight, these states resemble paramagnetic materials, in which spins are disordered in the absence of an external magnetic field. However, whereas spins behave as independent entities in paramagnets, those in quantum spin liquids are entangled with one another, even if separated by long distances.

Experimental physicists have long pondered how to obtain and detect quantum spin liquids in real materials3. Much has been learnt from the study of one-dimensional quantum magnets — in particular, from chains of spins that exhibit antiferromagnetism4, whereby each spin is aligned in the opposite direction to that of its neighbours. For instance, a by-product of long-range entanglement is the presence of magnetic excitations that have fractional quantum numbers (fractions of quantities such as electric charge and spin). These excitations have been shown to leave distinct fingerprints in measurements of a material’s thermodynamic and magnetic properties. Furthermore, the presence or absence of an excitation gap (a lack of excitations that have particular energies) often reveals whether the underlying entanglement is short- or long-range, respectively.

However, in spite of these breakthroughs, finding two- and three-dimensional quantum spin liquids has been a daunting task5. One approach has been to use geometric frustration3, in which there is an incompatibility between the spatial arrangement of spins and their interactions. This causes many spin configurations to have the same energy, which jump-starts entanglement. Kitagawa and colleagues used a different materials-science strategy, and focused on a quantum spin liquid that was proposed by the theoretical physicist Alexei Kitaev6 in 2006.

In Kitaev’s model, spins on a honeycomb lattice are forced to interact in seemingly unnatural ways. The resulting quantum spin liquid has two types of exotic magnetic excitation: Majorana fermions, which have fractional quantum numbers, lack an excitation gap and can propagate on the lattice; and other excitations that have a small excitation gap and remain localized.

In a seminal paper7, it was demonstrated that the ingredients of Kitaev’s model might exist in real materials, accompanied by more-conventional spin interactions called Heisenberg interactions. It was later suggested8 that the model could be realized in materials that have two key properties. The first is a strong coupling between the motion of electrons and their spin — a feature present in the outer electron shells of some transition-metal ions. The second is a specific bonding geometry, which is achieved when octahedra formed from metal and oxygen ions share their edges to form a honeycomb lattice. Compounds such as lithium iridate9 (Li2IrO3), sodium iridate (Na2IrO3) and ruthenium chloride10 (RuCl3) fulfil these requirements. However, all of these compounds become magnetically ordered below a few kelvin, which excludes them as genuine realizations of Kitaev’s model.

Using an approach known as soft chemistry, in which materials are modified under mild temperature conditions (here, at 120 °C), Kitagawa et al. replaced inter-layer lithium ions of Li2IrO3 with hydrogen ions, while preserving the overall structure of the magnetic-honeycomb layers. The authors found that the resulting compound, H3LiIr2O6, has low-temperature properties that are spectacularly different from those of Li2IrO3. In particular, they observed no magnetic ordering in H3LiIr2O6 down to a temperature of 0.05 K, and used nuclear magnetic resonance to confirm these findings down to 1 K (see Figure 2 of the paper1). The complex interplay between Kitaev and Heisenberg interactions11 is probably key to stabilizing this quantum state (Fig. 1). The authors discovered that the compound’s thermodynamic and magnetic properties are highly unusual, and interpreted these measurements in terms of exotic magnetic excitations that lack an excitation gap and perhaps have fractional quantum numbers.

Figure 1 | The structure and spin interactions of H3LiIr2O6. a, Kitagawa et al.1 report that, unlike other magnetic materials, the compound H3LiIr2O6 does not show magnetic ordering at temperatures close to absolute zero (H, hydrogen; Li, lithium; Ir, iridium; O, oxygen). A single unit of a layer of the compound is shown here. Octahedra (purple) formed from iridium and oxygen ions cause the iridium ions to be arranged on a honeycomb lattice. b, The magnetic properties of H3LiIr2O6 suggest that at least two types of interaction are at play between the spins (magnetic moments) of neighbouring iridium ions. The first are Heisenberg interactions (black lines), which cause spins to align in the opposite direction to that of their neighbours. The second are Kitaev interactions (coloured lines), which predispose neighbouring spins to co-align in one of three possible orientations, depending on which bond of the lattice is considered. Each line colour corresponds to a different preferred orientation. Because each lattice site participates in three distinct bonds, a given spin receives contradictory requests from its neighbours, which prevents magnetic ordering.

H3LiIr2O6 is a remarkable compound: it is the first iridium-based honeycomb magnet that does not become magnetically ordered at temperatures below a few kelvin. However, its overall behaviour and unusual thermodynamic properties indicate that it is governed by microscopic ingredients that differ substantially from those of Kitaev’s model. This is not a curse, but a blessing: understanding exotic magnetic phases is often achieved by studying related materials and models12. Future experimental work in which, for example, large crystals of H3LiIr2O6 are grown, or particles such as neutrons or photons are scattered off H3LiIr2O6, could reveal whether the compound’s excitations have fractional quantum numbers — the ultimate experimental proof of a quantum spin liquid.

The soft-chemistry approach used by Kitagawa et al. offers great promise for controlling the properties of layered quantum magnets. However, with regard to oxide materials, there are challenges associated with the presence of chemical disorder and heterogeneities. For instance, the layered structure of H3LiIr2O6 is prone to faults associated with the stacking of the layers13. In the future, it will be exciting to see chemists and physicists join forces to develop a deeper understanding of how material defects influence, and potentially even favour, entangled magnetic matter.

Nature 554, 307-308 (2018)

doi: 10.1038/d41586-018-01747-2


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