Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet


The experimental realization of quantum spin liquids is a long-sought goal in physics, as they represent new states of matter. Quantum spin liquids cannot be described by the broken symmetries associated with conventional ground states. In fact, the interacting magnetic moments in these systems do not order, but are highly entangled with one another over long ranges1. Spin liquids have a prominent role in theories describing high-transition-temperature superconductors2,3, and the topological properties of these states may have applications in quantum information4. A key feature of spin liquids is that they support exotic spin excitations carrying fractional quantum numbers. However, detailed measurements of these ‘fractionalized excitations’ have been lacking. Here we report neutron scattering measurements on single-crystal samples of the spin-1/2 kagome-lattice antiferromagnet ZnCu3(OD)6Cl2 (also called herbertsmithite), which provide striking evidence for this characteristic feature of spin liquids. At low temperatures, we find that the spin excitations form a continuum, in contrast to the conventional spin waves expected in ordered antiferromagnets. The observation of such a continuum is noteworthy because, so far, this signature of fractional spin excitations has been observed only in one-dimensional systems. The results also serve as a hallmark of the quantum spin-liquid state in herbertsmithite.

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Figure 1: Inelastic neutron scattering from the spin excitations, plotted in reciprocal space.
Figure 2: Inelastic neutron scattering measured along symmetry directions and at high-symmetry locations.
Figure 3: The measured dynamic structure factor along specific directions in reciprocal space with comparison to the nearest-neighbour singlet model.
Figure 4: The measured dynamic structure factor along the K–Γ–K direction within the (1, 0, 0) Brillouin zone.


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We acknowledge T. Senthil, P. A. Lee, Z. Hao and O. Tchernyshyov for discussions, and J. Wen for assistance with data reduction. The work at MIT was supported by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences under grant no. DE-FG02-07ER46134. This work used facilities supported in part by the US National Science Foundation under agreement no. DMR-0944772. The work at IQM was supported by the DOE, Office of Basic Energy Sciences, Division of Material Sciences and Engineering under award DE-FG02-08ER46544.

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Y.S.L. supervised all aspects of the research. T.-H.H. synthesized and characterized the sample. T.-H.H., J.A.R.-R., J.S.H. and C.B. collected the neutron scattering data. T.-H.H. analysed the data with input from Y.S.L., C.B., J.S.H. and J.A.R.-R. S.C. and D.G.N. aided in the sample preparation process. T.-H.H. and Y.S.L. wrote the manuscript with comments from all others. The manuscript reflects the contributions of all authors.

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Correspondence to Tian-Heng Han or Young S. Lee.

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Han, T., Helton, J., Chu, S. et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406–410 (2012).

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