Multiferroic Vortices and Graph Theory

ORAL

Abstract

Hexagonal REMnO$_{3}$ (RE= rare earths) with RE=Ho-Lu, Y, and Sc, is an improper ferroelectric where the size mismatch between RE and Mn induces a trimerization-type structural phase transition, and this structural transition leads to three structural domains, each of which can support two directions of ferroelectric polarization. We reported that domains in h-REMnO$_{3}$ meet in cloverleaf arrangements that cycle through all six domain configurations, Occurring in pairs, the cloverleafs can be viewed as vortices and antivortices, in which the cycle of domain configurations is reversed. Vortices and antivortices are topological defects: even in a strong electric field they won't annihilate. Recently we have found intriguing, but seemingly irregular configurations of a zoo of topological vortices and antivortices in h-REMnO$_{3}$. These configurations can be neatly analyzed in terms of graph theory.

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Authors

  • S.W. Cheong

    Rutgers University, Rutgers Center for Emergent Materials, Rutgers University, USA, Rutgers Univ. Physics Dept., Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

  • S.C. Chae

    Rutgers Center for Emergent Materials, Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

  • Yoichi Horibe

    Rutgers Center for Emergent Materials and Department of Physics \& Astronomy, Rutgers University, Rutgers Center for Emergent Materials, Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA, Rutgers University

  • D.Y. Jeong

    Department of Mathematics, Soongsil University, Korea

  • Nara Lee

    Rutgers Center for Emergent Materials, Rutgers University, Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

  • S. Rodan

    Rutgers Center for Emergent Materials, Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

  • T. Choi

    Rutgers Center for Emergent Materials