Physical chemistry

Model's reputation restored

The structure of a mineral has been validated, ending the controversy about its potential usefulness as a model of an unusual magnetic lattice. This model might provide insight into superconductivity.

The mineral herbertsmithite has been hailed as a rare model of an unconventional type of magnetism thought to have a key role in the mechanism of high-temperature superconductivity (a form of superconductivity that occurs above 30 kelvin). But concerns have been raised that chemical disorder in this material could produce defects in the array of magnetic atoms, disturbing or even destroying the properties that make it a useful model. In the Journal of the American Chemical Society, Daniel Nocera and his group1 now report that they have clearly identified the type of disorder present, and have found it to have little influence on the magnetic lattice of the mineral. This represents a crucial step in establishing a simple, clean system to provide unambiguous insight into this important form of magnetism.

A material's magnetism is ultimately derived from unpaired electrons, each of which has a property called spin (S), with a value of ½, that bestows on each of them a magnetic moment. In insulators, such moments or spins are localized on atoms, and commonly interact with their closest neighbours so that specific spin orientations are preferred. In most cases, an antiparallel (antiferromagnetic) configuration of nearest-neighbour spins is favoured so that, when a lattice of such atoms is cooled, their spins usually freeze to form an ordered array (Fig. 1a). However, under certain circumstances — for some magnetic lattices, for instance — quite different behaviour can ensue. One such case is the kagome antiferromagnet, which is formed from corner-sharing triangles (Fig. 1b). In these systems, it is impossible to arrange each near-neighbour pair of spins so that they are all antiparallel, and the system is said to be geometrically frustrated.

Figure 1: Spin arrangements in crystal lattices.

Unpaired electrons on atoms have a magnetic moment, or spin. These spins adopt preferred alignments (indicated by red arrows) in crystal lattices. a, Antiferromagnetic alignments, in which all neighbouring spins are antiparallel (as in this square lattice) are often favoured. b, In kagome lattices, triangles of atoms are joined at their corners, making a completely antiparallel spin arrangement impossible. c, This can lead to a compromise arrangement in which the spins are oriented at 120° to each other. d, Alternatively, a quantum spin liquid might form as a combination of many states (one of which is depicted here) in which spins pair up, analogous to the pairing of electrons in chemical bonds. e, The mineral herbertsmithite (ZnCu3(OH)6Cl2) contains kagome layers of Cu2+ ions (blue) linked by O2− ions (red), separated by layers of Zn2+ (grey) and Cl ions (not shown). Defects occur in the lattice when Cu2+ ions occupy Zn2+ sites and vice versa (indicated by the double-headed arrow between atoms marked 'X' and 'Y'). Nocera and colleagues1 find that the number of defects in herbertsmithite is smaller than had been thought. This makes the mineral an ideal model for studying spin-liquid states, which have been implicated in high-temperature superconductivity.

The lowest-energy arrangement of a kagome antiferromagnet might be expected to be one in which neighbouring spins are oriented 120° to each other (Fig. 1c). However, the physicist Philip Anderson pointed out that, for several lattices composed of triangles2 in which there is just one electron per atom (that is, when S = ½), it is more favourable for neighbouring spins to pair up in a manner analogous to that of the electron spins in chemical bonds. Quantum mechanics allows the spins in 'valence' bonds to be simultaneously up–down and down–up (where 'up' and 'down' are the two possible alignments of the spins), thus relieving geometric frustration by effectively allowing pairs of local moments to cancel out.

Because such coupling may occur between all pairs of spins, the overall picture is that of a 'liquid' of valence bonds, a state that resonates between all possible ways of making such bonds (Fig. 1d). This state is called a quantum spin liquid, or a resonating valence bond (RVB) liquid (by analogy with Linus Pauling's model3 of chemical bonding in organic molecules such as benzene, in which the chemical structure can also be described as a hybrid of different valence-bond arrangements). It was proposed4 — again by Anderson — that in the cuprate class of high-temperature superconductors, the RVB state enables the formation of superconducting charge carriers.

Among lattices of triangles, kagome lattices that have antiferromagnetically coupled spins of S = ½ have been regarded for some time as prime candidates for a RVB state. But an undistorted realization of this highly prized system — herbertsmithite, which has the nominal formula ZnCu3(OH)6Cl2 — was only recently reported5 by Nocera's group. To be precise, it is the array of spins on the copper ions (Cu2+) in herbertsmithite that could form an RVB magnetic state (Fig. 1e).

It was soon demonstrated6 that, although there is a very strong antiferromagnetic coupling between spins in the mineral, no spin freezing could be observed, even at temperatures as low as 50 millikelvin. This is consistent with the existence of some form of RVB state in herbertsmithite. But evidence was also found for disorder in the compound's structure, raising concerns that it was not as clean a model system as had been hoped. Neutron-diffraction data, combined with elemental analysis using inductively coupled plasma Auger electron spectroscopy (ICP-AES) on herbertsmithite indicated that about one-quarter of the sites expected to be occupied by zinc ions (Zn2+) are actually occupied by Cu2+ (Fig. 1e), and that one-twelfth of the Cu2+ sites on the kagome lattice are occupied by Zn2+. The actual level of disorder was estimated to be slightly lower, however, on the basis of analyses of the compound's magnetic susceptibility7 and heat capacity8. Both of these properties contain a contribution from nearly free spins (which interact only very weakly with other spins in the material). This contribution can be attributed to the S = ½ spins of Cu2+ ions occupying one-fifth of the Zn2+ sites.

Nocera and colleagues appreciated that the uncertainty about the disorder was unsatisfactory — they felt that rigorous determination of the exact level of disorder should depend on structural and chemical methods alone. They therefore performed1 new measurements on herbertsmithite, using a suite of techniques: X-ray absorption spectroscopy and advanced X-ray- and neutron-diffraction methods. Taken together, their results show that about 15% of the Zn2+ sites are occupied by a Cu2+ ion, thus confirming the earlier interpretations of the magnetic susceptibility7 and heat capacity8 of herbertsmithite, and convincingly dispelling the last doubts about the concentration of Cu2+ ions (and so of S = ½ spins) on the Zn2+ sites. These defect spins will interact only weakly with other spins, and thus will have very little influence on the behaviour of the spins on the kagome lattice.

What comes as a surprise in Nocera and colleagues' results1 is that the concentration of Zn2+ ions in the kagome Cu2+ sites was found to be only about 1 ± 3%. This is good news for those investigating quantum magnetism — it means that there are very few vacancies in the periodic array of spins forming the kagome lattice, allowing for a reliable comparison between theory and experiment in herbertsmithite. The lower than expected chemical disorder implies that the chemical formula of herbertsmithite is probably closer to Zn0.85Cu3.15(OH)6Cl2, rather than ZnCu3(OH)6Cl2, as was thought previously. This revised formula will doubtless be checked in other laboratories using the ICP-AES method of chemical analysis.

As the first RVB system in which spin correlations and dynamics can readily be measured, herbertsmithite has great potential to reveal the character of spin liquids. More broadly, it should also allow an exploration of the relationship between antiferromagnetism and superconductivity in layered transition-metal compounds.


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de Vries, M., Harrison, A. Model's reputation restored. Nature 468, 908–909 (2010).

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