Abstract
The discovery of the Dirac electron dispersion in graphene [A. H. Castro Neto, et al., The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009)] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [T. O. Wehling, et al., Dirac Materials, Adv. Phys. 63, 1 (2014)], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides (, Cl, Br and I), that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single-particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [F. J. Dyson, General Theory of Spin-Wave Interactions, Phys. Rev. 102, 1217 (1956), F. J. Dyson, Thermodynamic Behavior of an Ideal Ferromagnet, Phys. Rev. 102, 1230 (1956)] to the case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in nearly half-century-old magnetic neutron-scattering data for [W. B. Yelon and R. Silberglitt, Renormalization of Large-Wave-Vector Magnons in Ferromagnetic Studied by Inelastic Neutron Scattering: Spin-Wave Correlation Effects, Phys. Rev. B 4, 2280 (1971), E. J. Samuelsen, et al., Spin Waves in Ferromagnetic Studied by Inelastic Neutron Scattering, Phys. Rev. B 3, 157 (1971)]. We also show that honeycomb ferromagnets display dispersive surface and edge states, unlike their electronic analogs.
- Received 11 June 2017
DOI:https://doi.org/10.1103/PhysRevX.8.011010
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)
Popular Summary
The discovery of graphene in 2004 was a milestone, partly because of the unusual behavior of its electrons, which all move at the same speed and have no inertia, as if they were massless. Since then, numerous other materials with similar so-called “Dirac particles” have been isolated, and they are interesting for fundamental science and applications because they display more pronounced quantum effects in their optical and electrical properties than ordinary metals. To date, most Dirac particles have been fermions—particles that cannot be at the same place at the same time. This raises the question of whether Dirac particles that are bosons—particles that do not avoid each other—have the same properties as electrons in the fermionic systems. To address this question, we compare the electrons in graphene to the excitations in “magnetic graphene,” a ferromagnet in which the spins occupy the vertices of a honeycomb lattice.
The quantized deviations from ferromagnetism are bosonic Dirac quasiparticles called “spin waves,” and in the absence of surfaces and interactions, they are indistinguishable from the electrons in graphene. However, once surfaces or interactions between the quasiparticles are introduced, the dispersion relations are dramatically different from what is found for electrons in graphene. The surface states are no longer dispersionless, and there is a linear, rather than logarithmic, correction to the quasiparticle dispersion. The latter finding explains a nearly 50-year-old puzzle posed by spin-wave data for a realization of magnetic graphene, .
Our discoveries will guide work on lithographically defined and chemically synthesized bosonic Dirac matter, including the ongoing magneto-optical measurements of isolated flakes of the transition metal trihalides, the class of materials to which belongs.
