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Anisotropic-Exchange Magnets on a Triangular Lattice: Spin Waves, Accidental Degeneracies, and Dual Spin Liquids

P. A. Maksimov, Zhenyue Zhu, Steven R. White, and A. L. Chernyshev
Phys. Rev. X 9, 021017 – Published 25 April 2019; Erratum Phys. Rev. X 12, 019902 (2022)

Abstract

We present an extensive overview of the phase diagram, spin-wave excitations, and finite-temperature transitions of the anisotropic-exchange magnets on an ideal nearest-neighbor triangular lattice. We investigate transitions between five principal classical phases of the corresponding model: ferromagnetic, Néel, its dual, and the two stripe phases. Transitions are identified by the spin-wave instabilities and by the Luttinger-Tisza approach, and we highlight the benefits of the former while outlining the shortcomings of the latter. Some of the transitions are direct and others occur via intermediate phases with more complicated forms of ordering. The spin-wave spectrum in the Néel phase is obtained and is shown to be nonreciprocal, ϵα,kϵα,k, in the presence of anisotropic bond-dependent interactions. In a portion of the Néel phase, we find spin-wave instabilities to a long-range spiral-like state. This transition boundary is similar to that of the spin-liquid phase of the S=1/2 model discovered in our prior work, suggesting a possible connection between the two. Further, in the stripe phases, quantum fluctuations are mostly negligible, leaving the ordered moment nearly saturated even for the S=1/2 case. However, for a two-dimensional surface of the full 3D parameter space, the spin-wave spectrum in one of the stripe phases exhibits an enigmatic accidental degeneracy manifested by pseudo-Goldstone modes. As a result, despite the nearly classical ground state, the ordering transition temperature in a wide region of the phase diagram is significantly suppressed from the mean-field expectation. We identify this accidental degeneracy as due to an exact correspondence to an extended Kitaev-Heisenberg model with emergent symmetries that naturally lead to the pseudo-Goldstone modes. There are previously studied dualities within the Kitaev-Heisenberg model on the triangular lattice that are exposed here in a wider parameter space. One important implication of this correspondence for the S=1/2 case is the existence of a region of the spin-liquid phase that is dual to the spin-liquid phase discovered recently by us. We complement our studies by the density-matrix renormalization group of the S=1/2 model to confirm some of the duality relations and to verify the existence of the dual spin-liquid phase.

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  • Received 9 November 2018
  • Revised 29 January 2019

DOI:https://doi.org/10.1103/PhysRevX.9.021017

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

Erratum

Authors & Affiliations

P. A. Maksimov, Zhenyue Zhu, Steven R. White, and A. L. Chernyshev

  • Department of Physics and Astronomy, University of California, Irvine, California 92697, USA

Popular Summary

Magnetic materials with strong spin-orbit interactions offer rich opportunities for finding unconventional states of matter such as spin liquids and exotic magnetic orders. A model that combines the paradigmatic geometrical frustration of spins on a triangular lattice with strong spin-orbit-induced interactions has recently emerged as a very promising experimental and theoretical playground for realizing such states. Here, we provide an extensive, if not exhaustive, theoretical overview of the phase diagram of this model, which is relevant to a family of rare-earth-based magnets and other related materials.

To better understand this model, we classify its phases and excitations, identify instabilities, and describe various quantum and thermal effects. We also find a particularly fruitful connection that relates different parts of the phase diagram to each other. In a rather spectacular manifestation of that correspondence, we use an unbiased numerical approach to demonstrate, for the first time, the existence of two spin-liquid states that are related to each other via a duality transformation.

Our work creates a foundation for the studies of a large group of materials with anisotropic exchanges, sets up a consistent interpretation of current and future experiments, and gives important new insights into fundamental properties of a class of quantum magnets.

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Vol. 9, Iss. 2 — April - June 2019

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