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A novel route to quantum spin liquids


Bond-directional interactions provide a novel alternative to conventional Heisenberg interactions for designing and implementing quantum magnets. In particular, they serve as building blocks for the celebrated Kitaev model, which has a quantum spin liquid as its exact ground state. An international collaborative team led by B.J. Kim of the Max Planck Institute, Stuttgart, and including the ESRF has made a direct observation of this novel type of magnetic interaction for the first time in a real material. Using diffuse magnetic X-ray scattering, magnetic interactions in Na2IrO3, one of the candidate materials for realisation of the Kitaev quantum spin liquid, are shown to be extremely anisotropic in a spin-dependent way: each of the three spin components favours alignment along distinct crystallographic axes: the key feature of the model that leads to magnetic frustration. This work sets on solid ground the proposal to use bond-directional interactions for the realisation of quantum spin liquids.

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Quantum spin liquid is an elusive state of matter in which spins fluctuate in a liquid form without ever solidifying even at a temperature of absolute zero [1]. Observed only in the past decade [2], quantum spin liquids are currently the focus of intense research, with historical links to high temperature superconductivity and potential applications to quantum computation. The Kitaev model, based on the simplest form of bond-directional interactions, occupies a special position as a rare example of exactly solvable models with well-defined signatures of a quantum spin liquid [3,4]. This work takes a big experimental leap towards the realisation of a quantum spin liquid by unambiguous identification of such interactions leading to strong magnetic frustration in the 5d transition metal oxide Na2IrO3.

Na2IrO3 has a monoclinic stacking of two-dimensional honeycomb lattices that breaks the ideal three-fold rotational symmetry of the honeycomb lattice on which the Kitaev model is constructed. Structurally, it further deviates from the ideal model as the stacking compresses the IrO6 octahedra, which in turn distorts the Ir-O-Ir bonds – the main magnetic exchange pathway. Magnetically, Na2IrO3 orders at a finite temperature into the so-called zigzag pattern, rather than being the spin liquid predicted by the model. As the same spin pattern is found in other conventional magnets, the role, or even the presence of the bond-directional interactions has remained unknown.

Using the spectrometer designed for resonant inelastic X-ray scattering at ESRF beamline ID20 and beamlines at the Advanced Photon Source, we set out to look for the defining properties of the bond-directional interactions. Specifically, the magnetic interactions should differ on different bonds, particularly in the spin component that each bond couples. Our strategy was to measure the instantaneous correlation of spins, which amounts to taking a “snapshot” of spins in the Fourier-transformed (momentum) space. In this measurement a particular spin component was filtered out by orienting the sample with respect to the X-ray polarisation in such a way that by rotating the azimuth angle the spin channel being probed is continuously tuned.

Figure 1 shows a systematic evolution of the momentum-space spin-correlation map as one tunes the spin channel by rotating the azimuth angle. The location of the diffuse peaks provides information about the direction along which the spin correlations propagate, and their intensity is maximal when the azimuth angle is turned to the “right” spin component. This map provides evidence of the entanglement between the spin and the real space, a direct consequence of the bond-directional interactions.

 Diffuse magnetic X-ray scattering intensities above the ordering temperature

Figure 1. Diffuse magnetic X-ray scattering intensities above the ordering temperature, TN. Intensity plots in the HK-plane measured at T = 17 K (>TN = 12 K) for selected azimuth angles (Ψ) summing π-σ’ and π- π’ channels. The diffuse peaks are located at Q = ±(0,1), ±(0.5,0.5), and ±(0.5,-0.5) corresponding to three short-range ordered zigzag states. Ψ dependence of the intensities arises due to the distinct magnetic anisotropies of each state.

A theoretical calculation using the exact diagonalisation of a 24-site cluster indicates that the observed pattern is attributed to the bond-directional interactions overwhelming the conventional Heisenberg interactions, and thus the system should be on the verge of making a transition to the spin-liquid state. However, the transition can be hindered by other types of magnetic interactions not fully identified in this study. The full understanding of this material awaits further improvement of the spectrometers in terms of energy resolution, which would allow the full dynamics of the interacting spins to be resolved. In the mean time, these findings highlight the benefits of using the resonant inelastic X-ray scattering spectrometer at ID20 to probe the instantaneous spin correlations through diffuse magnetic X-ray scattering.


Principal publication and authors
Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3, S.H. Chun (a), J.-W. Kim (b), J. Kim (b), H. Zheng (a), C.C. Stoumpos (a), C.D. Malliakas (a), J.F. Mitchell (a), K. Mehlawat (c), Y. Singh (c), Y. Choi (b), T. Gog (b), A. Al-Zein (d), M. Moretti Sala (d), M. Krisch (d), J. Chaloupka (e), G. Jackeli (f,g), G. Khaliullin (f) and B.J. Kim (f), Nature Physics 11, 462 (2015).
(a) Materials Science Division, Argonne National Laboratory (USA)
(b) Advanced Photon Source, Argonne National Laboratory (USA)
(c) Indian Institute of Science Education and Research (IISER), Mohali (India)
(d) ESRF
(e) Central European Institute of Technology, Masaryk University (Czech Republic)
(f) Max Planck Institute for Solid State Research (Germany)
(g) Institute for Functional Matter and Quantum Technologies, University of Stuttgart (Germany)


[1] L. Balents, Nature 464, 199 (2010).
[2] T.-H. Han et al., Nature 492, 7429 (2012).
[3] A. Kitaev, Ann. Phys. (Amsterdam) 321, 2 (2006).
[4] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).


Top image: Diffuse magnetic X-ray scattering intensities arising from the short range magnetic zigzag states depicted by the atomic lattice in the centre.