npj Quantum Materials · 2018 · 211 citations · 74 references
Natural SciencesPhysicsCondensed Matter PhysicsQuantum MechanicsSolid State PhysicsLow-dimensional SolidsMagnetic OxidesMagnetic Properties Of SolidsMagnetism In SolidsPhase TransitionsSuperconducting MaterialsFrustrated MagnetismLow-dimensional MagnetismLow-dimensional Quantum SystemsOrbital OrderingQuantum MagnetismSpin ChainsSpin FrustrationTransition Metal Magnetism
Low‑dimensional magnetism theory, developed by Ising, Heisenberg, and Bethe, remained experimentally unverified for decades until the discovery of high‑Tc cuprate superconductivity sparked a surge of new phenomena. Researchers test two‑dimensional magnetic concepts on a variety of lattice geometries—including square, triangular, kagome, honeycomb, Shastry–Sutherland, and Nersesyan–Tsvelik patterns—to explore resonating valence bond states, Berezinskii–Kosterlitz–Thouless transitions, and the Kitaev model. Compounds that reach quantum ground states—either gradually or via instabilities—display gapless or gapped spin excitations in half‑integer or integer spin chains, odd or even leg ladders, and complex oxides that achieve gapped states through spin‑Peierls, charge, or orbital ordering, while most low‑dimensional systems ultimately form exotic long‑range ordered states, including field‑induced multipolar or spin‑nematic phases.
Abstract There is a long time gap between the formulation of the basic theory of low-dimensional (low-D) magnetism as advanced by Ising, Heisenberg and Bethe and its experimental verification. The latter started not long before the discovery of high- T C superconductivity in cuprates and has been boosted by this discovery result in an impressive succession of newly observed physical phenomena. Milestones on this road were the compounds which reached their quantum ground states upon lowering the temperature either gradually or through different instabilities. The gapless and gapped ground states for spin excitations in these compounds are inherent for isolated half-integer spin and integer spin chains, respectively. The same is true for the compounds hosting odd and even leg spin ladders. Some complex oxides of transition metals reach gapped ground state by means of spin-Peierls transition, charge ordering or orbital ordering mechanisms. However, the overwhelming majority of low-dimensional systems arrive to a long-range ordered magnetic state, albeit quite exotic realizations. Under a magnetic field some frustrated magnets stabilize multipolar order, e.g., showing a spin-nematic state in the simplest quadropolar case. Finally, numerous square, triangular, kagome and honeycomb layered lattices, along with Shastry–Sutherland and Nersesyan–Tsvelik patterns constitute the playground to check the basic concepts of two-dimensional magnetism, including resonating valence bond state, Berezinskii–Kosterlitz–Thouless transition and Kitaev model.
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