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Contrasting structural reversibility and magnetic correlations in isostructural honeycomb magnets CrCl3 and 𝛼−RuCl3
We report a comparative neutron single crystal diffraction study of the structural and magnetic properties of layered halides CrCl3 and 𝛼−RuCl3. They host a honeycomb arrangement of transition metal ions with distinct electronic configurations and undergo a first-order structural transition between high-temperature 𝐶2/𝑚 and low-temperature 𝑅‾‾‾3. Both compounds show a step-like change in the 𝑐-lattice parameter across the structure transition. In contrast, the in-plane lattice response is quite different: 𝛼−RuCl3 exhibits an abrupt hysteretic change across the transition accompanied by progressive crystalline degradation upon thermal cycling, whereas CrCl3 shows a smooth in-plane lattice evolution and remains structurally robust. Magnetically, CrCl3 orders into an A-type antiferromagnetic structure at 𝑇𝑁=14 K and exhibits pronounced diffuse magnetic scattering extending up to about 40 K. 𝛼−RuCl3 shows no observable magnetic diffuse scattering above its zigzag antiferromagnetic ordering temperature 𝑇𝑁=7.6 K. These results suggest that the contrasting structural responses arise from an interplay between interlayer sliding energetics, stacking-strain coupling, and elastic accommodation of the stacking transition. The distinct chemical bonding and electronic configurations of the two compounds provide a microscopic basis for their different lattice responses to the structure transition and magnetic correlations.
Evidence for field induced quantum spin liquid behavior in a spin-1/2 honeycomb magnet
One of the most important issues in modern condensed matter physics is the realization of fractionalized excitations, such as the Majorana excitations in the Kitaev quantum spin liquid. To this aim, the 3d-based Kitaev material Na 2 Co 2 TeO 6 is a promising candidate whose magnetic phase diagram of B // a* contains a field-induced intermediate magnetically disordered phase within 7.5 T < |B| < 10 T. The experimental observations, including the restoration of the crystalline point group symmetry in the angle-dependent torque and the coexisting magnon excitations and spinon-continuum in the inelastic neutron scattering spectrum, provide strong evidence that this disordered phase is a field induced quantum spin liquid with partially polarized spins. Our variational Monte Carlo simulation with the effective K-J 1 -Γ-Γ'-J 3 model reproduces the experimental data and further supports this conclusion.
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.
Static magnetic order with strong quantum fluctuations in spin-1/2 honeycomb magnet Na 2 Co 2 TeO 6
Kitaev interactions, arising from the interplay of frustration and bond anisotropy, can lead to strong quantum fluctuations and, in an ideal case, to a quantum-spin-liquid state. However, in many nonideal materials, spurious non-Kitaev interactions typically promote a zigzag antiferromagnetic order in the d-orbital transition-metal compounds. Here, by combining neutron scattering with muon-spin rotation and relaxation techniques, we provide mechanism insights into the exotic properties of Na 2 Co 2 TeO 6 , a candidate material of the Kitaev model. Below T N , the zero-field muon-spin relaxation rate becomes almost constant (~0.45 μs –1 ). We attribute this temperature-independent relaxation rate to the strong quantum fluctuations, as well as to the frustrated Kitaev interactions. As the magnetic field increases, neutron scattering data indicate a broader spin-wave excitation at the K-point. Therefore, quantum fluctuations seem not only robust but are even enhanced by the applied magnetic field. Our findings provide valuable hints for understanding the onset of the quantum-spin-liquid state in Kitaev materials.
Hydrostatic pressure effect on the Co-based honeycomb magnet BaCo 2 (AsO 4 ) 2
Here the honeycomb antiferromagnet BaCo 2 (AsO 4 ) 2 , in which small in-plane magnetic fields (H1 ≈ 0.26T and H2 ≈ 0.52T at T = 1.8 K < T N ≈ 5.4K) induce two magnetic phase transitions, has attracted attention as a possible candidate material for the realization of Kitaev physics based on the 3d element Co 2+ . Here, we report on the change in the transition temperature T N and the critical fields H1 and H2 of BaCo 2 (AsO 4 ) 2 with hydrostatic pressure up to ~20 kbar, as determined from magnetization and specific heat measurements. Within this pressure range, a marginal increase in the magnetic ordering temperature is observed. At the same time, the critical fields are changed significantly (up to ~25 –35%). Specifically, we find that H1 is increased with hydrostatic pressure, i.e., the antiferromagnetic state is stabilized, whereas H2, which was previously associated with a transition into a proposed Kitaev spin-liquid state, decreases with increasing pressure. We discuss to what extent these results are compatible with suggested models with sizable third-nearest-neighbor exchange. Overall, the results put constraints on the magnetic models that are used to describe the low-temperature magnetic properties of BaCo 2 (AsO 4 ) 2 .
Introducing the monoclinic polymorph of the honeycomb magnet Na 2 Co 2 TeO 6
Recent theoretical studies have suggested that the low-energy Hamiltonian of honeycomb cobaltate systems could be dominated by anisotropic Kitaev interactions. Motivated by the theory, a honeycomb layered material Na 2 Co 2 TeO 6 with a hexagonal unit cell has been studied and found to exhibit antiferromagnetic (AFM) ordering at 27 K with two spin reorientation transitions at 15 and 5 K. Here we report a monoclinic polymorph of Na 2 Co 2 TeO 6 , also with honeycomb layered structure but with a single AFM transition at 9.6 K and without spin reorientation transitions at lower temperatures. Here, using neutron diffraction, we identify an in-plane zigzag AFM order in the ground state with the spins canted out of the honeycomb planes and ferromagnetically coupled between them. The zigzag order is suppressed by a magnetic field of 6T. The lower critical temperature and field, positive Curie-Weiss temperature, and out-of-plane canting of spins in the monoclinic Na 2 Co 2 TeO 6 suggest enhanced frustration in this polymorph compared to the hexagonal one.
Magnetic charge's relaxation propelled electricity in two-dimensional magnetic honeycomb lattice
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Massless Dirac magnons in the two dimensional van der Waals honeycomb magnet CrCl 3
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Chemical tuning of a honeycomb magnet through a critical point
BaCo 2 (AsO 4 ) 2 (BCAO) has seen extensive study since its initial identification as a proximate Kitaev quantum spin liquid candidate. Thought to be described by the highly anisotropic XXZ-J 1 -J 3 model, the ease with which magnetic order is suppressed in the system indicates proximity to a spin liquid phase. Upon chemical tuning via partial arsenic substitution with vanadium, we show an initial suppression of long-range incommensurate order in the BCAO system to T ≈ 3.0 K, followed by increased spin freezing at higher substitution levels. Between these two regions, at around 10% substitution, the system is shown to pass through a critical point where the competing J 1 /J 3 exchange interactions become more balanced, producing a more complex magnetic ground state, likely stabilized by quantum fluctuations. Here, this state shows how slight compositional change in magnetically frustrated systems may be leveraged to tune ground state degeneracies and potentially realize a quantum spin liquid state.
Spin-orbit exciton in a honeycomb lattice magnet CoTiO 3 : Revealing a link between magnetism in d - and f -electron systems
We carried out inelastic neutron scattering to study the spin-orbital (SO) exciton in a single crystal sample of CoTiO 3 as a function of temperature. CoTiO 3 is a honeycomb magnet with dominant XY-type magnetic interaction and an A-type antiferromagnetic order below T N ≈ 38 K. We found that the SO exciton becomes softer, but acquires a larger bandwidth in the paramagnetic phase, compared to that in the magnetically ordered phase. Moreover, an additional mode is only observed in the intermediate temperature range, as the sample is warmed up above the lowest accessible temperature below T N . Such an unusual temperature dependence observed in this material suggests that its ground states (an S eff = 1 2 doublet) and excited states multiplets are strongly coupled, and therefore cannot be treated independently, as often done in a pseudo-spin model. Furthermore, our observations can be explained by a multi-level theory within random phase approximation that explicitly takes into account both the ground and excited multiplets. The success of our theory, which is originally developed to explain temperature dependence of magnetic excitations in the rare-earth magnets, highlight the similarity between the magnetic excitations in rare-earth systems and those in transition metal systems with strong spin orbit coupling.
Dirac Magnon in Honeycomb Lattice Magnet NiTiO 3
We performed inelastic neutron scattering experiments on single-crystal samples of the honeycomb lattice magnet, ilmenite NiTiO 3 . Below the Néel temperature of 22 K, spin wave excitations with a band energy of 3.7 meV were observed. Further, the neutron energy spectra were well-reproduced by modeling the system as a ferromagnetic honeycomb lattice with antiferromagnetic interlayer coupling, using linear spin wave theory. Similar to another ilmenite CoTiO 3 , a crossing structure was observed at the K point, suggesting the presence of Dirac magnons in NiTiO 3 . Further calculations suggested the formation of Dirac nodal line.
Enhanced hybridization in the electronic ground state of the intercalated honeycomb iridate Ag 3 LiIr 2 O 6
In this work, we use x-ray spectroscopy at the Ir L 3 /L 2 absorption edge to study powder samples of the intercalated honeycomb magnet Ag 3 LiIr 2 O 6 . Based on x-ray absorption and resonant inelastic x-ray scattering measurements, and exact diagonalization calculations including nearest-neighbor Ir-Ir electron hopping integrals, we argue that the intercalation of Ag atoms results in a delocalized electronic structure with enhanced Ir-O hybridization, departing from the local relativistic j eff =1/2 state. We find that the relative orbital contribution to the magnetic moment is increased and the magnetization density is spatially extended and asymmetric in this hybridized state. Our results confirm the importance of metal-ligand hybridization in the magnetism of transition metal oxides and provide empirical guidance for understanding the collective magnetism in intercalated honeycomb iridates.
Interplay of itinerant electrons and Ising moments in a hybrid honeycomb quantum magnet TmNi 3 Al 9
The interplay between itinerant electrons and local magnetic moments in quantum materials brings about rich and fascinating phenomena and stimulates various developments in the theoretical framework. In this work, thermodynamic, electric transport, and neutron diffraction measurements were performed on a newly synthesized honeycomb lattice magnet TmNi 3 Al 9 . Based on the experimental data, a magnetic-field–temperature phase diagram was constructed, exhibiting three essentially different magnetic regions. Below T N =2.97±0.02KTm 3+ , moments order antiferromagnetically in zero field. We found that the Tm 3+ ions form a pseudodoublet ground state with the Ising-like moments lying normal to the two-dimensional honeycomb layers. Application of a magnetic field along the easy axis gradually suppresses the antiferromagnetic order in favor of an induced ferromagnetic state above the critical field B c =0.92±0.05T. In the vicinity of B c , a strong enhancement of the quantum spin fluctuations was observed. The quantum Ising nature of the local moments and the coupling to itinerant electrons are discussed.
K 2 Co 2 TeO 6 : A layered magnet with a S = 1 2 Co 2 + honeycomb lattice
Recent observations of Kitaev interactions in d 7 electron configurations have generated research interest in Co 2+ based honeycomb magnets. Here, we report the synthesis of a K 2 Co 2 TeO 6 single crystal. X-ray diffraction and electron microscopy experiments show that K 2 Co 2 TeO 6 crystallizes in a $P$6 3 /$mcm$ space group with undistorted honeycomb layers of Co 2+ ions. Anisotropic magnetic and thermodynamic characterizations demonstrate an effective S = $\frac{1}{2}$ state of Co 2+ at low temperature, competing magnetic phases, and weak magnetic transitions that can be suppressed by applying fields. Moreover, the interlayer K disorder level is tunable by thermal treatments, and it affects the magnetic features obviously. In conclusion, our findings provide a new and promising platform for studying Kitaev physics.
Two methods to study inelastic neutron-scattering measurements based on ω n (q) versus S(q, ω) applied to the magnetic open honeycomb lattice Tb 2 Ir 3 Ga 9
This work describes two methods to fit the inelastic neutron-scattering spectrum S(q, ω) with wavevector q and frequency ω. The common and well-established method extracts the experimental spin-wave branches ω n (q) from the measured spectra S(q, ω) and then minimizes the difference between the observed and predicted frequencies. When n branches of frequencies are predicted but the measured frequencies overlap to produce only m < n branches, the weighted average of the predicted frequencies must be compared to the observed frequencies. A penalty is then exacted when the width of the predicted frequencies exceeds the width of the observed frequencies. The second method directly compares the measured and predicted intensities S(q, ω) over a grid {q i , ω j } in wavevector and frequency space. After subtracting background noise from the observed intensities, the theoretical intensities are scaled by a simple wavevector-dependent function that reflects the instrumental resolution. Furthermore, the advantages and disadvantages of each approach are demonstrated by studying the open honeycomb material Tb 2 Ir 3 Ga 9 .
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.