Abstract Quantum spin liquids are outstanding examples of highly quantum entangled phases of matter and serve as a testbed to gauge central concepts of strongly correlated materials. Enormous research efforts in the past few decades have brought an in-depth understanding of these novel phases, although their conundrums have not yet been solved completely. In this review, we give an overview of the three different classes of spin-liquid materials: (i) a one-dimensional spin chain system KCuF 3 , (ii) a kagome antiferromagnet ZnCu 3 (OH) 6 Cl 2 , and (iii) a Kitaev honeycomb material -RuCl 3 . The emphasis is on demonstrating the success of the Raman scattering technique for probing fractionalized excitations in the aforementioned spin-liquid compounds, complementing a well-established neutron scattering method. Irrespective of dimensionality, spin topology, and spin-exchange type, the three materials share several common features in the spectral shape and temperature dependence of magnetic excitations, which can be taken as Raman spectroscopic fingerprints of quantum spin liquids.
Abstract Quantum spin liquids are outstanding examples of highly quantum entangled phases of matter and serve as a testbed to gauge central concepts of strongly correlated materials. Enormous research efforts in the past few decades have brought an in-depth understanding of these novel phases, although their conundrums have not yet been solved completely. In this review, we give an overview of the three different classes of spin-liquid materials: (i) a one-dimensional spin chain system KCuF 3 , (ii) a kagome antiferromagnet ZnCu 3 (OH) 6 Cl 2 , and (iii) a Kitaev honeycomb material -RuCl 3 . The emphasis is on demonstrating the success of the Raman scattering technique for probing fractionalized excitations in the aforementioned spin-liquid compounds, complementing a well-established neutron scattering method. Irrespective of dimensionality, spin topology, and spin-exchange type, the three materials share several common features in the spectral shape and temperature dependence of magnetic excitations, which can be taken as Raman spectroscopic fingerprints of quantum spin liquids.
Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples—they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li) 2 IrO 3 iridates and RuCl 3 . In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
Abstract The spin liquid phase is one of the prominent strongly interacting topological phases of matter whose unambiguous confirmation is yet to be reached despite intensive experimental efforts on numerous candidate materials. Recently, a new family of correlated honeycomb materials, in which strong spin-orbit coupling allows for various bond-dependent spin interactions, have been promising candidates to realize the Kitaev spin liquid. Here we study a model with bond-dependent spin interactions and show numerical evidence for the existence of an extended quantum spin liquid region, which is possibly connected to the Kitaev spin liquid state. These results are used to provide an explanation of the scattering continuum seen in neutron scattering on α-RuCl3.
Quantum spin liquids, a highly topologically entangled, dynamically correlated state where quantum fluctuations preclude any long-range ordering down to absolute zero. In the search for a topologically robust qubit, the scientific community has been in continuous hunt for real quantum spin liquid systems. Alexei Kitaev in his exactly solvable model for a spin-1/2 two-dimensional honeycomb lattice, presented a system that hosts a topologically protected state (Majorana zero-modes). Under an applied external field, the Kitaev spin liquids turn into a topologically non-trivial chiral spin-liquid state with non-abelian anionic excitations, which is crucial for quantum computing. Earlier theoretical predictions advocated that Kitaev physics can be realized in spin-orbit-coupled Mott insulators such as honeycomb irradiates and ruthenates. However, the experimental findings continuously challenge the theoretical aspects, indicating the presence of non-Kitaev interactions in real materials, where the dimensionality, disorder (vacancy), chemical composition, generalized spin-S, and external perturbations (pressure, magnetic field, temperature) can actively tune the Kitaev interactions and the ground state excitations. In this review article, a comprehensive discussion is included with an updated literature survey in the context of the potential of Raman spectroscopy as a probe for Kitaev quantum spin liquids.
Quantum spin liquids, systems in which quantum fluctuations prevent the magnetic ordering of the spin degrees of freedom down to zero temperature, have been the source of much recent theoretical and experimental interest. These systems are characterised by their long ranged entangled states, preserve symmetries down to zero Kelvin, and have been shown to exhibit fascinating properties such as a topological ground state degeneracy and fractionalised spin excitations. In this thesis, we study several of these phases. The first, Kitaev spin liquids, appear in strongly spin-orbit coupled systems, where the SU(2) spin symmetry is broken. Within our mean field approach, we study the quantum phase transition from the gapless Z 2 spin liquid to a magnetically ordered phase within the Heisenberg-Kitaev model. Beyond the mean field theory, we argue that the gauge structure of the spin liquid plays a crucial role in this transition, leading to a confinement of spinons and the generation of magnetic order. We also discuss the three-dimensional iridate compounds, where the Kitaev spin liquid phase has topologically protected bulk and surface excitations. We next discuss spin liquids appearing on the geometrically frustrated kagome lattice. First, we consider non-Kramers spin liquids, in which the spin structure of the theory is protected by lattice, rather than time-reversal, symmetry. As a result, more phases are allowed, which have different properties than those which transform as Kramers doublets. In addition, these may have positive experimental signatures in the Raman scattering intensity, offering a clear path to detect such a state. Finally, we examine possible spin liquid phases on a breathing kagome lattice, where we find a stable Z2 spin liquid to be the ground state. This may help to guide future numerical studies of the kagome lattice Heisenberg model, and may also be relevant to DQVOF, a recently discovered spin liquid candidate compound.
Magnetically frustrated spin systems compose a significant proportion of topological quantum spin liquid candidates. Evidence for spin liquids in these materials comes largely from the detection of fractionalised spin-1/2 quasiparticles, known as spinons. However, the one-dimensional Heisenberg chain, which is topologically trivial, also hosts spinons. Thus, observing spinons does not necessarily signify long-range entanglement. Here, we show that spinons arising from one-dimensional physics leave a clear fingerprint in magnetic Raman scattering. We achieve this by calculating the magnetic Raman intensity of coupled Heisenberg chains. Our findings are in excellent agreement with the magnetic Raman scattering measurements on the anisotropic triangular antiferromagnet Ca3ReO5Cl2.
We calculate the Raman response for the Kitaev spin model on the $\mathcal{H}\ensuremath{-}0, \mathcal{H}\ensuremath{-}1$, and $\mathcal{H}\ensuremath{-}\ensuremath{\infty}$ harmonic honeycomb lattices. We identify several quantitative features in the Raman spectrum that are characteristic of the spin liquid phase. Unlike the dynamical structure factor, which probes both the Majorana spinons and flux excitations that emerge from spin fractionalization, the Raman spectrum in the Kitaev models directly probes a density of states of pairs of fractional, dispersing Majorana spinons. As a consequence, the Raman spectrum in all these models is gapless for sufficiently isotropic couplings, with a low-energy power law that results from the Fermi lines (or points) of the dispersing Majorana spinons. We show that the polarization dependence of the Raman spectrum contains crucial information about the symmetry of the ground state. We also discuss to what extent the features of the Raman response that we find reflect generic properties of the spin liquid phase, and comment on their possible relevance to $\ensuremath{\alpha}$-, $\ensuremath{\beta}$-, and $\ensuremath{\gamma}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ compounds.