Geometrical Frustration Beyond Magnets

 · Invited

Abstract

Geometrical frustration – the inability of a system to satisfy all of its interactions simultaneously because of geometrical constraints – can suppress conventional ordering and promote the formation of exotic states that are disordered, yet strongly correlated. Materials in which magnetic spins occupy lattices built from corner or edge-sharing triangles have provided many examples of novel magnetic behavior due to frustration. In this talk, I will discuss how frustration of structural (nonmagnetic) degrees of freedom – charge states, orbital orientations, or chain displacements – can determine the structures and properties of materials. I will also discuss how the nonmagnetic frustrated interactions can be mapped to equivalent “toy” spin Hamiltonians, including those that are challenging to realize experimentally in magnets. I illustrate these points using three real examples of nonmagnetic frustration. First, I discuss how the solid phases of silver(I) and/or gold(I) cyanides, in which polymeric chains occupy a triangular lattice, can host structural analogs of the spin vortices of triangular XY magnets [1]. Second, I discuss the pyrochlore oxide Y2Mo2O7, and explain how orbital dimerization of Jahn-Teller active Mo4+ ions on the frustrated pyrochlore lattice may yield an orbital-ice analog of spin-ice and water-ice states [2]. Finally, I discuss the triangular-lattice-based system YbMgGaO4 [3,4] – of interest because of proposed quantum-spin-liquid-like behaviour of its magnetic Yb3+ ions – and show how the charge difference between nonmagnetic Mg2+and Ga3+generates a structurally-frustrated state, with implications for the proposed quantum-spin-liquid behaviour.

[1] Cairns, Cliffe, Paddison et al., Nat Chem 8, 442 (2016).
[2] Thygesen, Paddison, Zhang et al., PRL 118, 067201 (2017).
[3] Li, Chen, Tong et al., PRL 115, 167203 (2015).
[4] Paddison, Daum, Dun et al., Nat Phys 13, 117 (2017).

*Churchill College, Cambridge (JAMP); EPSRC EP/G004528/2 (JAMP, ALG, MJC, ABC).

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Presenters

  • Joseph Paddison

    • Churchill College, University of Cambridge
    • Cambridge
    • University of Cambridge
    • Georgia Institute of Technology
    • Univserity of Cambridge
    • Department of Physics, University of Cambridge

Authors

  • Joseph Paddison

    • Churchill College, University of Cambridge
    • Cambridge
    • University of Cambridge
    • Georgia Institute of Technology
    • Univserity of Cambridge
    • Department of Physics, University of Cambridge

  • Zhiling Dun

    • School of Physics, Georgia Institute of Technology
    • Georgia Institute of Technology
    • School of Physics, Georgia Tech
    • University of Tennessee
    • Department of Physics, University of Tennessee

  • Marcus Daum

    • School of Physics, Georgia Tech
    • Georgia Institute of Technology

  • Andrew Cairns

    • Department of Chemistry, University of Oxford

  • Peter Thygesen

    • Department of Chemistry, University of Oxford

  • Matthew J Cliffe

    • University of Cambridge

  • Matthew G. Tucker

    • Oak Ridge National Laboratory

  • Yaohua Liu

    • Oak Ridge National Laboratory
    • Neutron Scattering Division, Oak Ridge National Laboratory

  • Helen Playford

    • ISIS Neutron and Muon Source

  • David Keen

    • ISIS Neutron and Muon Source

  • Karena Chapman

    • Argonne National Laboratory

  • Kevin Beyer

    • Argonne National Laboratory

  • Arkadiy Simonov

    • Department of Chemistry, University of Oxford

  • Michael Hayward

    • Department of Chemistry, University of Oxford

  • Ronghuan Zhang

    • Department of Chemistry, University of Oxford

  • Amber Thompson

    • Department of Chemistry, University of Oxford

  • Dominik Daisenberger

    • Diamond Light Source

  • FX Coudert

    • Institut de Recherche de Chimie Paris, CNRS / Chimie ParisTech

  • Haidong Zhou

    • University of Tennessee
    • Department of Physics and Astronomy, University of Tennessee
    • University of Tennessee, Knoxville
    • Physics, University of Tennessee, Knoxville, TN, United States
    • Physics, University of Tennessee
    • Department of Physics and Astronomy, The University of Tennessee, Knoxville
    • Department of Physics and Astronomy, University of Tennessee, Knoxville
    • Department of Physics, University of Tennessee

  • Martin Mourigal

    • School of Physics, Georgia Institute of Technology
    • Georgia Institute of Technology
    • School of Physics, Georgia Tech

  • Andrew Goodwin

    • Department of Chemistry, University of Oxford