From frustration to glassiness via quantum fluctuations and random tiling with exotic entropy

Abstract

When magnetic moments (spins) are regularly arranged in a geometry of a triangular motif, the spins may not satisfy simultaneously their interactions with their neighbors. This phenomenon, called frustration, leads to numerous energetically equivalent magnetic states (ground states), which results in exotic states such as spin liquid and spin ice. Here we report an alternative situation: a system that, classically, is to be a liquid in the clean limit freezes into a glassy state induced by quantum fluctuations. The case in point is a frustrated magnet in which spins are arranged in a triangular network of bi-pyramids. When taking into account quantum corrections, the classical degeneracy is broken into a set of local minima in a rugged energy landscape, which are separated by large energy barriers, over a finite number of degenerate, periodic, ground states. The appearance of large barriers is due to the absence of local zero-energy modes that are typical in spin-liquid candidate systems. We establish this by mapping the set of local energy minima states into a tiling with colored hexagonal tiles. We show that the system exhibits a large number of aperiodic tessellations. The configuration entropy of the local minima is extremely sensitive to boundary conditions, scaling with the boundary length rather than its volume. The low temperature thermodynamics is also discussed to compare it with other glassy materials.

paper+supplementary material 28 pages. too many figures

References in corpus (10)

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• Holographic rainbow networks for colorful Motzkin and Fredkin spin chains
• Non-monotonic residual entropy in diluted spin ice: a comparison between Monte Carlo simulations of diluted dipolar spin ice models and experimental results
• Exact holographic tensor networks for the Motzkin spin chain
• Freezing of a disorder induced quantum spin liquid
• Slow dynamics of the Fredkin spin chain
• Spin dynamics of the antiferromagnetic Heisenberg model on a kagome bilayer
• Neutron Scattering Study of Fluctuating and Static Spin Correlations in the Anisotropic Spin Glass Fe${}_2$TiO${}_5$
• Robust Topological Degeneracy of Classical Theories
• Interplay of disorder and geometrical frustration in doped Gadolinium Gallium Garnet
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• The nature of low-temperature spin-freezing in frustrated Kitaev magnets
• Zero-point entropies of spin-jam and spin-glass states in a frustrated magnet
• Survival of magnetic correlations above ordering temperature in a ferromagnetically ordered classical kagomé magnet: Li9Cr3(P2O7)3(PO4)2
• Frustrated magnets in the limit of infinite dimensions: dynamics and disorder-free glass transition
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