Arnab Banerjee

Neutron scattering in the proximate quantum spin liquid α-RuCl3

Quantum matter provides an effective vacuum out of which arise emergent particles not corresponding to any experimentally detected elementary particle. Topological quantum materials in particular have become a focus of intense research in part because of the remarkable possibility to realize Majorana fermions, with their potential for new, decoherence-free quantum computing architectures. In this paper we undertake a study on high-quality single crystal of -RuCl3 which has been identified as a material realizing a proximate Kitaev state, a topological quantum state with magnetic Majorana fermions. Four-dimensional tomographic reconstruction of dynamical correlations measured using neutrons is uniquely powerful for probing such magnetic states. We discover unusual signals, including an unprecedented column of scattering over a large energy interval around the Brillouin zone center which is remarkably stable with temperature. This is straightforwardly accounted for in terms of the Majorana excitations present in Kitaevs topological quantum spin liquid. Other, more delicate, features in the scattering can be transparently associated with perturbations to an ideal model. This opens a window on emergent magnetic Majorana fermions in correlated materials.Sighting of magnetic Majorana fermions? Quantum spin liquids—materials whose magnetic spins do not settle into order even at absolute zero temperature—have long captured the interest of physicists. A particularly lofty goal is finding a material that can be described by the so-called Kitaev spin model, a network of spins on a honeycomb lattice that harbors Majorana fermions as its excitations. Banerjee et al. present a comprehensive inelastic neutron scattering study of single crystals of the material α-RuCl3, which has been predicted to a host a Kitaev spin liquid. The unusual dependence of the data on energy, momentum, and temperature is consistent with the Kitaev model. Science, this issue p. 1055 Unusual inelastic neutron scattering signal is consistent with predictions of the Kitaev spin model. The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The magnetic insulator α-RuCl3 is thought to realize a proximate KQSL. We used neutron scattering on single crystals of α-RuCl3 to reconstruct dynamical correlations in energy-momentum space. We discovered highly unusual signals, including a column of scattering over a large energy interval around the Brillouin zone center, which is very stable with temperature. This finding is consistent with scattering from the Majorana excitations of a KQSL. Other, more delicate experimental features can be transparently associated with perturbations to an ideal model. Our results encourage further study of this prototypical material and may open a window into investigating emergent magnetic Majorana fermions in correlated materials.

Excitations in the field-induced quantum spin liquid state of α-RuCl3

The celebrated Kitaev quantum spin liquid (QSL) is the paradigmatic example of a topological magnet with emergent excitations in the form of Majorana Fermions and gauge fluxes. Upon breaking of time-reversal symmetry, for example in an external magnetic field, these fractionalized quasiparticles acquire non-Abelian exchange statistics, an important ingredient for topologically protected quantum computing. Consequently, there has been enormous interest in exploring possible material realizations of Kitaev physics and several candidate materials have been put forward, recently including α-RuCl3. In the absence of a magnetic field this material orders at a finite temperature and exhibits low-energy spin wave excitations. However, at moderate energies, the spectrum is unconventional and the response shows evidence for fractional excitations. Here we use time-of-flight inelastic neutron scattering to show that the application of a sufficiently large magnetic field in the honeycomb plane suppresses the magnetic order and the spin waves, leaving a gapped continuum spectrum of magnetic excitations. Our comparisons of the scattering to the available calculations for a Kitaev QSL show that they are consistent with the magnetic field induced QSL phase.Condensed Matter Physics: magnetic field drives spins to a liquidA sufficiently large magnetic field suppresses long-range magnetic order in α-RuCl3, leaving a disordered state with a gapped continuum spectrum of magnetic excitations, similar to that expected for the famous Kitaev quantum spin liquid. An international team led by Stephen E. Nagler from Oak Ridge National Laboratory in the USA performed time-of-flight neutron scattering to study low energy magnetic excitations of α-RuCl3. They observed that the application of a sufficiently large magnetic field to this material suppressed spin waves associated with the long-range order, and drove it to an unusual excited state. By comparison with calculations, these results are consistent with the Kitaev quantum spin liquid state in a magnetic field. The results provide important information of a possible route to producing gapped excitations related to magnetic Majorana Fermions towards topologically protected quantum computation.

Unconventional spin dynamics in the honeycomb-lattice material α-RuCl3 : High-field electron spin resonance studies

The honeycomb-lattice material

Atomic-scale observation of structural and electronic orders in the layered compound α-RuCl3

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Continuous and discontinuous quantum phase transitions in a model two-dimensional magnet.

-RuCl

Emergence of long-range order in sheets of magnetic dimers

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Magnetism, structure, and charge correlation at a pressure-induced Mott-Hubbard insulator-metal transition

is a prime candidate for exhibiting Kitaev spin-liquid physics. Here, the authors employ high-field electron spin resonance spectroscopy to probe its spin dynamics across different regions of the phase diagram. Apart from two modes of antiferromagnetic resonance in the zigzag-ordered phase, a rich excitation spectrum was observed in the field-induced quantum disordered state. The authors compare their observations with results of recent numerical calculations, revealing a complex multiparticle nature of magnetic excitations in the field-induced phase.

Comprehensive study of the dynamics of a classical Kitaev Spin Liquid

A pseudospin-1/2 Mott phase on a honeycomb lattice is proposed to host the celebrated two-dimensional Kitaev model which has an elusive quantum spin liquid ground state, and fascinating physics relevant to the development of future templates towards topological quantum bits. Here we report a comprehensive, atomically resolved real-space study by scanning transmission electron and scanning tunnelling microscopies on a novel layered material displaying Kitaev physics, α-RuCl3. Our local crystallography analysis reveals considerable variations in the geometry of the ligand sublattice in thin films of α-RuCl3 that opens a way to realization of a spatially inhomogeneous magnetic ground state at the nanometre length scale. Using scanning tunnelling techniques, we observe the electronic energy gap of ≈0.25 eV and intra-unit cell symmetry breaking of charge distribution in individual α-RuCl3 surface layer. The corresponding charge-ordered pattern has a fine structure associated with two different types of charge disproportionation at Cl-terminated surface.

Destabilization of Magnetic Order in a Dilute Kitaev Spin Liquid Candidate

The Shasty–Sutherland model, which consists of a set of spin 1/2 dimers on a 2D square lattice, is simple and soluble but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model Shastry–Sutherland material, SrCu2(BO3)2, in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution X-ray measurements exploit what emerges as a remarkably strong spin-lattice coupling to both monitor the magnetic behavior and the absence or presence of structural discontinuities. In the low-pressure spin-singlet regime, the onset of magnetism results in an expansion of the lattice with decreasing temperature, which permits a determination of the pressure-dependent energy gap and the almost isotropic spin-lattice coupling energies. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure.

Sub-Kelvin magnetic and electrical measurements in a diamond anvil cell with in situ tunability

Significance Magnetic materials are composed of individual spins that interact with each other and under suitable conditions can arrange themselves in an ordered array. When spins are confined to two-dimensional sheets, small perturbations can disrupt their order and destroy the magnetic state. We show how a set of interacting, quantum-mechanical spins placed on the corners of a square array evolves from a set of locally bonded entities to a globally ordered structure. The system stabilizes itself against fluctuations through subtle local contractions, elongations, and tilts. The combination of neutron and X-ray scattering at pressures up to 60,000 atmospheres reveals the complex interplay of structural distortions and spin alignments that permit long-range order to emerge in this model quantum magnet. Quantum spins placed on the corners of a square lattice can dimerize and form singlets, which then can be transformed into a magnetic state as the interactions between dimers increase beyond threshold. This is a strictly 2D transition in theory, but real-world materials often need the third dimension to stabilize long-range order. We use high pressures to convert sheets of Cu2+ spin 1/2 dimers from local singlets to global antiferromagnet in the model system SrCu2(BO3)2. Single-crystal neutron diffraction measurements at pressures above 5 GPa provide a direct signature of the antiferromagnetic ordered state, whereas high-resolution neutron powder and X-ray diffraction at commensurate pressures reveal a tilting of the Cu spins out of the plane with a critical exponent characteristic of 3D transitions. The addition of anisotropic, interplane, spin–orbit terms in the venerable Shastry–Sutherland Hamiltonian accounts for the influence of the third dimension.