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Order-by-disorder and spiral spin-liquid in frustrated diamond-lattice antiferromagnets


Frustration refers to competition between different interactions that cannot be simultaneously satisfied—a familiar feature in many magnetic solids. Strong frustration leads to highly degenerate ground states and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism include the characterization of the fluctuating spin-liquid regime and determination of the mechanism of eventual order at lower temperature. Here, we study a model of a diamond-lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration, a massive ground-state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional ‘spiral surface’ in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomenon called ‘order by disorder’. A broad spiral spin-liquid regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed through spin correlations. We discuss the agreement between these predictions and the well-characterized spinel MnSc2S4.

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Figure 1: Spin-spiral state on the diamond lattice.
Figure 2: Spiral surfaces.
Figure 3: Phase diagram.
Figure 4: Spiral surface measured from Monte Carlo simulation.
Figure 5: Correlation function of the spiral spin-liquid.
Figure 6: Powder-averaged structure factor.


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We would like to acknowledge R. Shindou, Z. Wang, C. Henley and M. P. A. Fisher for illuminating discussions, as well as T. Suzuki, M. Muecksch and A. Krimmel for sharing their unpublished results. This work was supported by the Packard Foundation (D.B. and L.B.) and the National Science Foundation through grants DMR-0529399 (J.A.) and DMR04-57440 (D.B. and L.B.).

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Correspondence to Doron Bergman.

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Bergman, D., Alicea, J., Gull, E. et al. Order-by-disorder and spiral spin-liquid in frustrated diamond-lattice antiferromagnets. Nature Phys 3, 487–491 (2007).

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