• Open Access

Global Formation of Topological Defects in the Multiferroic Hexagonal Manganites

Q. N. Meier, M. Lilienblum, S. M. Griffin, K. Conder, E. Pomjakushina, Z. Yan, E. Bourret, D. Meier, F. Lichtenberg, E. K. H. Salje, N. A. Spaldin, M. Fiebig, and A. Cano
Phys. Rev. X 7, 041014 – Published 20 October 2017

Abstract

The spontaneous transformations associated with symmetry-breaking phase transitions generate domain structures and defects that may be topological in nature. The formation of these defects can be described according to the Kibble-Zurek mechanism, which provides a generic relation that applies from cosmological to interatomic length scales. Its verification is challenging, however, in particular at the cosmological scale where experiments are impractical. While it has been demonstrated for selected condensed-matter systems, major questions remain regarding, e.g., its degree of universality. Here, we develop a global Kibble-Zurek picture from the condensed-matter level. We show theoretically that a transition between two fluctuation regimes (Ginzburg and mean field) can lead to an intermediate region with reversed scaling, and we verify experimentally this behavior for the structural transition in the series of multiferroic hexagonal manganites. Trends across the series allow us to identify additional intrinsic features of the defect formation beyond the original Kibble-Zurek paradigm.

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  • Received 13 April 2017

DOI:https://doi.org/10.1103/PhysRevX.7.041014

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Q. N. Meier1, M. Lilienblum1, S. M. Griffin2, K. Conder3, E. Pomjakushina3, Z. Yan4,5, E. Bourret4, D. Meier6, F. Lichtenberg1, E. K. H. Salje7, N. A. Spaldin1, M. Fiebig1, and A. Cano1,8

  • 1Department of Materials, ETH Zurich, 8093 Zürich, Switzerland
  • 2Department of Physics, University of California Berkeley, Berkeley, California 94720, USA and Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 3Laboratory for Scientific Developments and Novel Materials, Paul Scherrer Institute, 5232 Villigen, Switzerland
  • 4Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 5Department of Physics, ETH Zurich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
  • 6Department of Materials Science and Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway
  • 7Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, United Kingdom
  • 8CNRS, University of Bordeaux, ICMCB, UPR 9048, 33600 Pessac, France

Popular Summary

The Kibble-Zurek mechanism is one of the most overarching concepts in nature. It describes what happens when a physical system undergoes a continuous phase transition, a smooth change from one state of matter to another. Such transitions can have consequences for regimes ranging from the subatomic, where they underlie the mechanism responsible for assigning masses to fundamental particles (Higgs mechanism), to the cosmic, where they might have seeded the formation of galaxy clusters and voids. Previous attempts to verify the Kibble-Zurek mechanism have been narrowly focused on individual systems such as superfluid helium; the presupposed universality of the mechanism has been verified only to a limited extent. The Kibble-Zurek mechanism directly relies on critical fluctuations, which can be different at various stages of the phase-transition process. We developed a global Kibble-Zurek picture, revealing a new crossover region between strongly interacting fluctuations and ones that do not interact.

We combine the theory of critical phenomena with first-principles calculations to study the formation of vortices in a series of multiferroic compounds. Specifically, we compute dominant and subdominant contributions to the Kibble-Zurek scaling and compare the results with experiments. Thus, we reveal the degree of accuracy and the limitations of the standard picture and its natural extension with regard to the character (interacting vs noninteracting) of the critical fluctuations.

The Kibble-Zurek mechanism was originally discussed in the context of the early Universe, then verified in systems such as liquid crystals and superfluids. Our fundamental upgrade may reveal new behavior in other condensed-matter systems. This could also be an ideal playground for probing a wide range of phenomena and might be exploited to reveal microscopic information about how the laws of physics evolved during the early stages of the Universe.

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Vol. 7, Iss. 4 — October - December 2017

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