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).

–

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