Reentrant incommensurate order and anomalous magnetic torque in the Kitaev magnet β − Li 2 Ir O 3
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75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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Results for “Kitaev magnet”
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Signatures of non-Loudon-Fleury Raman scattering in the Kitaev magnet 𝛽−Li 2 IrO 3
We investigate the magnetic excitations of the hyperhoneycomb Kitaev magnet 𝛽−Li 2 IrO 3 by means of inelastic Raman scattering. The spectra exhibit the coexistence of a broad scattering continuum and two sharp low-energy peaks at 2.5 and 3 meV, with a distinctive polarization dependence. While the continuum is suggestive of fractional quasiparticles emerging from a proximate quantum spin liquid phase, the sharp peaks provide the first experimental signature of the “non-Loudon- Fleury” one-magnon scattering processes proposed recently. The corresponding microscopic mechanism is similar to the one leading to the symmetric off-diagonal exchange interaction Γ (because it involves a combination of both direct and ligand-mediated exchange paths) but is otherwise completely unexpected within the traditional Loudon-Fleury theory of Raman scattering. Furthermore, the present experimental verification therefore calls for a drastic reevaluation of Raman scattering in similar systems with strong spin-orbit coupling and multiple exchange paths.
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Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet β − Li 2 IrO 3
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Emergent orbital magnetization in Kitaev quantum magnets
Unambiguous identification of the Kitaev quantum spin liquid (QSL) in materials remains a huge challenge despite many encouraging signs from various measurements. To facilitate the experimental detection of the Kiteav QSL, here we propose to use remnant charge response in Mott insulators hosting QSL to identify the key signatures of QSL. We predict an emergent orbital magnetization in a Kitaev system in an external magnetic field. The direction of the orbital magnetization can be flipped by rotating the external magnetic field in the honeycomb plane. The orbital magnetization is demonstrated explicitly through a detailed microscopic analysis of the multiorbital Hubbard-Kanamori Hamiltonian and also supported by a phenomenological picture. We first derive the localized electrical loop current operator in terms of the spin degrees of freedom. Thereafter, utilizing the Majorana representation, we estimate the loop currents in the ground state of the chiral Kitaev QSL state, and obtain the consequent current textures, which are responsible for the emergent orbital magnetization. Finally, we discuss the possible experimental techniques to visualize the orbital magnetization which can be considered as the signatures of the underlying excitations.
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Signatures of a Majorana-Fermi surface in the Kitaev magnet Ag 3 LiIr 2 O 6
Detecting Majorana fermions in experimental realizations of the Kitaev honeycomb model is often complicated by non-trivial interactions inherent to potential spin liquid candidates. In this work, we identify several distinct thermodynamic signatures of massive, itinerant Majorana fermions within the well-established analytical paradigm of Landau-Fermi liquid theory. We find a qualitative and quantitative agreement between the salient features of our Landau-Majorana liquid theory and the Kitaev spin liquid candidate Ag 3 LiIr 2 O 6 . Our study presents strong evidence for a Fermi liquid-like ground state in the fundamental excitations of a honeycomb iridate, and opens new experimental avenues to detect itinerant Majorana fermions in condensed matter systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl 3
The honeycomb magnet α-RuCl 3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κ xy of Majorana fermions is predicted to be half-quantized. Half-quantization of κxy/T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κ xy on α-RuCl3 with the magnetic field B ∥ a (zigzag axis). In our experiment, κ xy /T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. In conclusion, the bosonic character is incompatible with half-quantization of κ xy /T.
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Signatures of fractionalization in the optical phonons of the hyperhoneycomb Kitaev magnet 𝛽−Li 2 IrO 3
Here, in this study, we propose that the signatures of spin fractionalization in quantum magnets can be identified through a detailed analysis of the temperature dependence of the asymmetric Fano lineshape of optical phonons overlapping with a continuum of spin excitations. We focus on the hyperhoneycomb magnet 𝛽−Li 2 IrO 3 , a promising candidate for being in proximity to a three-dimensional Kitaev quantum spin liquid. The Raman response in 𝛽−Li 2 IrO 3 notably displays a distinctive asymmetric Fano lineshape in the 24 meV Raman-active optical phonon. This asymmetry arises from the interaction between the discrete phonon mode and the spin excitation continuum, which could be fractionalized if the material is indeed near a quantum spin-liquid phase. Our theoretical model considers the coupling of this optical phonon to Majorana fermions in the Kitaev model on the hyperhoneycomb lattice. Our findings reveal that the temperature-dependent Fano lineshape is consistent with the fractionalization of spins into Majorana fermions and ℤ 2 fluxes.
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Competing antiferromagnetic-ferromagnetic states in a d 7 Kitaev honeycomb magnet
The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet Li 3 Co 2 SbO 6 , built of high-spin d 7 (Co 2+ ) ions, in contrast to the more typical low-spin d 5 electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of C C 2/m, below T N = 11K at μ 0 H = 0T. The magnetic entropy recovered between T = 2 and 50 K is estimated to be 0.6Rln2, in good agreement with the value expected for systems close to a Kitaev quantum spin liquid state. The temperature-dependent magnetic order parameter demonstrates a β value of 0.19(3), consistent with XY anisotropy and in-plane ordering, with Ising-like interactions between layers. Further, we observe a spin-flop-driven crossover to ferromagnetic order with space group of C2/m under an applied magnetic field of μ 0 H ≈ 0.7T at T = 2K. Magnetic structure analysis demonstrates these magnetic states are competing at finite applied magnetic fields even below the spin-flop transition. Both the d 7 compass model, a quantitative comparison of the specific heat of Li 3 Co 2 SbO 6 , and related honeycomb cobaltates to the anisotropic Kitaev model further support proximity to a Kitaev spin liquid state. Furthermore, this material demonstrates the rich playground of high-spin d 7 systems for spin liquid candidates and complements known d 5 Ir- and Ru-based materials.
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Out-of-plane magnetic phase diagram of the Kitaev quantum magnet Na 2 Co 2 TeO 6
We have investigated the magnetic properties and mapped out the phase diagram of the honeycomb magnet Na 2 Co 2 TeO 6 with Co 3d 7 in out-of-plane magnetic fields. This material has previously been proposed to show nearest-neighbor Kitaev interactions between Co spins and maybe even Kitaev quantum spin liquid behavior in high fields. At 0.01 T, we observe a thermal phase transition at T N = 27K, transitioning from a paramagnetic state to a canonical ferrimagnetic state. Upon increasing the magnetic field, a spin-floplike phase transition occurred before saturation of J = 1/2 between 10 K and T N . Below 10 K, a peak-dip-peak structure emerges between 10 and 17 T in the magnetic susceptibility (dM/dH) before the magnetic saturation, reminiscent of magnetization plateau behavior. The measurement of the magnetocaloric effect also shows dip-peak-dip behavior in this field range. Our data can be explained by an XXZ model with a single ion anisotropy and possibly small Kitaev and Γ exchange interactions. Finally, we also determined the magnetization saturation field that helps constrain the energy scale of the exchange interactions.
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Disorder-Enriched Magnetic Excitations in a Heisenberg-Kitaev Quantum Magnet Na 2 Co 2 TeO 6
Using optical magnetospectroscopy, we investigate the magnetic excitations of Na 2 Co 2 TeO 6 in a broad magnetic field range (0 T ≤ B ≤ 17.5 T) at low temperature. Our measurements reveal rich spectra of in-plane magnetic excitations with a surprisingly large number of modes, even in the high-field spin-polarized state. Theoretical calculations find that the Na-occupation disorder in Na 2 Co 2 TeO 6 plays a crucial role in generating these modes. Our Letter demonstrates the necessity to consider disorder in the spin environment in the search for Kitaev quantum spin liquid states in practicable materials.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Floquet engineering of Kitaev quantum magnets
Abstract In recent years, there has been an intense search for materials realizing the Kitaev quantum spin liquid model. A number of edge-shared compounds with strong spin-orbit coupling, such as RuCl 3 and iridates, have been proposed to realize this model. Nevertheless, an effective spin Hamiltonian derived from the microscopic model relevant to these compounds generally contains terms that are antagonistic toward the quantum spin liquid. This is consistent with the fact that the zero magnetic field ground state of these materials is generally magnetically ordered. It is a pressing issue to identify protocols to drive the system to the limit of the Kitaev quantum spin model. In this work, we propose Floquet engineering of these Kitaev quantum magnets by coupling materials to a circularly polarized laser. We demonstrate that all the magnetic interactions can be tuned in situ by the amplitude and frequency of the laser, hence providing a route to stabilize the Kitaev quantum spin liquid phase.
36 MATERIALS SCIENCE↗
Magnetic excitations and interactions in the Kitaev hyperhoneycomb iridate β –Li 2 IrO 3
Here, we present a thorough experimental study of the three-dimensional hyperhoneycomb Kitaev magnet β –Li 2 IrO 3 , using a combination of inelastic neutron scattering (INS), time-domain terahertz spectroscopy (TDTS), and heat capacity measurements. The main results include a massive low-temperature reorganization of the INS spectral weight that evolves into a broad peak centered around 12 meV, and a distinctive peak in the terahertz data at 2.8(1) meV. A detailed comparison to powder-averaged spin-wave theory calculations reveals that the positions of these two features are controlled by the anisotropic Γ coupling and the Heisenberg exchange J, respectively. The refined microscopic spin model places β –Li 2 IrO 3 in close proximity to the Kitaev spin liquid phase.
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Quantum-classical crossover in the spin- 1 2 Heisenberg-Kitaev kagome magnet
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75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Scaling behavior and giant field enhancement of the thermal conductivity in the honeycomb antiferromagnet BaCo 2 (AsO 4 ) 2
The layered honeycomb material BaCo 2 (AsO 4 ) 2 is of topical interest because its magnetic state is related to that of the Kitaev magnet α-RuCl 3 . Using thermal transport to probe how magnetic excitations interact with phonons in the magnetically disordered regime, we have uncovered an unusually large enhancement of the thermal conductivity κ xx in an in-plane magnetic field H. Just above the Néel temperature T N , a field of 13 T increases κ xx by a factor of ∼ 211, which is very large compared to other magnetic insulators. Interestingly, κ xx (H, T) exhibits a scaling behavior in the entire magnetically disordered region that surrounds the ordered zigzag state. The ratio Δκ xx (H, T)/κ xx (13, T), measured throughout the disordered region, collapses to a one-parameter scaling function exp(−1/gx) (where x = μ B B/k B T and g is a constant).
36 MATERIALS SCIENCE↗
In-plane multi-q magnetic ground state of Na 3 Co 2 SbO 6
We report Na 3 Co 2 SbO 6 is a potential Kitaev magnet with a monoclinic layered crystal structure. Recent investigations of the C3-symmetric sister compound Na 2 Co 2 TeO 6 have uncovered a unique triple-q magnetic ground state, as opposed to a single-q (zigzag) one, prompting us to examine the influence of the reduced structural symmetry of Na 3 Co 2 SbO 6 on its ground state. Neutron diffraction data obtained on a twin-free crystal reveal that the ground state remains a multi-q state, despite the system's strong non-C 3 -symmetric anisotropy. This robustness of multi-q orders suggests that they are driven by a common mechanism in the honeycomb cobaltates, such as interactions beyond the bilinear order. Spin-polarized neutron diffraction results show that the ordered moments are entirely in plane, with each staggered component orthogonal to the propagating wave vector. The inferred ground state appears more compatible with the so-called XXZ easy-plane anisotropy than the Kitaev anisotropy, and features unequal ordered moments reduced by strong quantum fluctuations.
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Giant phonon anomalies in the proximate Kitaev quantum spin liquid α-RuCl 3
The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z 2 gauge flux. Here, it was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we detect anomalous phonon effects in α-RuCl 3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, J K ~8 meV, that coincides with a giant acoustic phonon softening near the Z 2 gauge flux energy scale. These phonon anomalies signify the coupling of phonon and Kitaev magnetic excitations in α-RuCl 3 and demonstrates a proof-of-principle method to detect anomalous excitations in topological quantum materials.
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Thermal Probes of Phonon-Coupled Kitaev Spin Liquids: From Accurate Extraction of Quantized Edge Transport to Anyon Interferometry
Recent theoretical studies inspired by experiments on the Kitaev magnet α-RuCl 3 highlight the nontrivial impact of phonons on the thermal Hall conductivity of chiral topological phases. Here, we introduce mixed mesoscopic-macroscopic devices that allow refined thermal-transport probes of non-Abelian spin liquids with Ising topological order. These devices feature a quantum-coherent region with quantized or negligible phonon conductance, flanked by macroscopic lobes that facilitate efficient thermalization between chiral Majorana edge modes and bulk phonons. We show that our devices enable (i) accurate determination of the quantized thermal Hall conductivity, (ii) identification of non-Abelian Ising anyons via the temperature dependence of the thermal conductance, and, most interestingly, (iii) single-anyon detection through heat-based anyon interferometry. Analogous results apply broadly to phonon-coupled chiral topological orders.
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Review of honeycomb-based Kitaev materials with zigzag magnetic ordering
The search for a Kitaev quantum spin liquid in crystalline magnetic materials has fueled intense interest in the two-dimensional honeycomb systems. Many promising candidate Kitaev systems are characterized by a long-range-ordered magnetic structure with an antiferromagnetic zigzag-type order, where the static moments form alternating ferromagnetic chains. Recent experiments on high-quality single crystals uncovered the existence of intriguing multi-k magnetic structures, which evolved from zigzag structures. Those discoveries have sparked new theoretical developments and amplified interest in these materials. We present an overview of the honeycomb materials known to display this type of magnetic structure and provide detailed crystallographic information for the possible single- and multi-k variants.
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