Fermionic response from fractionalization in an insulating two-dimensional magnet

Abstract

Conventionally ordered magnets possess bosonic elementary excitations, called magnons. By contrast, no magnetic insulators in more than one dimension are known whose excitations are not bosons but fermions. Theoretically, some quantum spin liquids (QSLs) -- new topological phases which can occur when quantum fluctuations preclude an ordered state -- are known to exhibit Majorana fermions as quasiparticles arising from fractionalization of spins. Alas, despite much searching, their experimental observation remains elusive. Here, we show that fermionic excitations are remarkably directly evident in experimental Raman scattering data across a broad energy and temperature range in the two-dimensional material $\alpha$-RuCl${}_3$. This shows the importance of magnetic materials as hosts of Majorana fermions. In turn, this first systematic evaluation of the dynamics of a QSL at finite temperature emphasizes the role of excited states for detecting such exotic properties associated with otherwise hard-to-identify topological QSLs.

5 pages, 3 figures

References in corpus (27)

• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Spin-lattice coupling in frustrated antiferromagnets
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Na2IrO3 as a spin-orbit-assisted antiferromagnetic insulator with a 340 meV gap
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Vaporization of Kitaev spin liquids
• Finite-temperature phase diagram of the Heisenberg-Kitaev model
• Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3
• Raman Scattering Signatures of Kitaev Spin Liquids in A${}_2$ IrO${}_3$ Iridates
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na${}_2$IrO${}_3$
• Magnetic excitation spectrum of Na2IrO3 probed with resonant inelastic x-ray scattering
• Theory of Raman response in three-dimensional Kitaev spin liquids: application to $\beta -$ and $\gamma -$Li${}_2$IrO${}_3$ compounds
• Numerical Calculations of the B1g Raman Spectrum of the Two-Dimensional Heisenberg Model

Cited by in corpus (193)

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• Excitations in the field-induced quantum spin liquid state of alpha-RuCl3
• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
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• Phase Diagram of $\alpha$-RuCl${}_3$ in an in-plane Magnetic Field
• Gapless Spin Excitations in the Field-Induced Quantum Spin Liquid Phase of alpha-RuCl3
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