Session B51: Kitaev Materials I

Kitaev Spin Liquid in 3d Transition Metal Compounds

We have proposed that 3d honeycomb cobaltates are very promising candidates to realize the Kitaev spin liquid state, thanks to the easy tunability of the exchange Hamiltonian in favor of Kitaev interaction [1-3]. The key parameters that have major impacts on the exchange constants, such as the charge-transfer gap and the trigonal crystal field, are discussed. Several materials are considered as examples to show the proximity to the Kitaev spin liquid phase, and can be driven into it by lattice engineering. Our theoretical predications suggest that cobaltates offer the most promising search area for Kitaev model physics.   

Thermal Transport of Co-based Kitaev Material BaCo2(AsO4)2

The Kitaev Quantum Spin Liquid (KQSL) has attracted much attention because the Kitaev Hamiltonian can be solved exactly and its excitations are Majorana fermions and vortices. Previous work has mostly focused on 4d and 5d transition metal based materials, such as a-RuCl3. Here we present measurements on a Co-based honeycomb material BaCo2(AsO4)2, which exhibits different interaction energy scales that may lead to a more ideal Kitaev material. For example, it has a lower critical field for suppressing antiferromagnetism than that in RuCl3. This enables easier access to the candidate field-induced spin liquid state. We have explored its rich temperature-field phase diagram via thermal transport measurements. Our results reveal remarkable sensitivity of the thermal conductivity to the underlying magnetic phases and transitions between them. In particular, we present magnetic hysteresis and thermal hall data that provide new information about the underlying states and Kitaev physics more broadly.

Supported by NSF DMR-2011750 and DOE (DE-SC0017863 and DE-SC0019331)   

Magnetic interactions in the quantum spin liquid candidate Na2BaCo(PO4)2

Motivated by the recent discovery of the quantum spin liquid (QSL) candidate material Na₂BaCo(PO₄)₂ (PNAS 116 (29) 14505-14510), we use inelastic neutron scattering to determine the magnetic interaction in this material. We find that an out-of-plane magnetic field of larger than 3 T is enough to destroy the QSL phase and polarize the spins in the system, where a well-defined spin wave dispersion emerges. By fitting the observed spin wave spectrum with a linear spin wave theory, we are able to obtain the magnetic interactions in the system. We find that the nearest neighbor exchange interaction is dominated by an easy-axis Ising interaction and a bond-dependent Kitaev-type exchange interaction. Our study paves the way to understand the nature of the plausible QSL phase in Na₂BaCo(PO₄)₂.   

Frustrated magnetism in Ising-Kitaev-Gamma model on the triangular lattice

Motivated by the discovery of quantum spin liquid candidate Na₂BaCo(PO₄)₂ and recent field-dependent inelastic neutron scattering study on this material, we theoretically investigate the phase diagram of a frustrated spin-1/2 model on the triangular lattice. Competing antiferromagnetic Ising, bond-dependent exchange (Kitaev) and anisotropic symmetric exchange (Gamma) interactions give rise to a rich phase diagram. Remarkably, aside from various magnetic orders, a gapless quantum spin liquid phase emerges. We present a comprehensive study of the phase diagram, by combining semiclassical method and numerical methods including exact diagonalization and density matrix renormalization group.     

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Since P.W. Anderson proposed the theoretical existence of the quantum spin liquid ground state in 1973, antiferromagnetic spin-1/2 systems exhibiting large quantum fluctuations have attracted significant interest as spin liquid candidates.  The experimental verification of the spin liquid ground state would not only advance fundamental condensed matter physics, but also provide a path forward to discovering new, exotic spin system ground states.  If only nearest neighbor interactions are considered, the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice should order in a Néel ground state. However, sufficiently strong next nearest neighbor interactions combined with a small coordination number and low dimensionality, which increase the role of quantum fluctuations, such as those exhibited in Ba₃Co₂O₆(CO₃)_0.7, could result in a quantum spin liquid ground state. For this reason, we have investigated the low temperature specific heat and magnetization of Ba₃Co₂O₆(CO₃)_0.7, a nonstoichiometric compound with the CoO₆ chains forming a honeycomb lattice. The magnetization exhibits an anomalous decrease in slope with increasing field beyond 10 T when the field is applied parallel to the c axis of the sample, indicating that randomness plays an important role in Ba₃Co₂O₆(CO₃)_0.7. Specific heat measurements failed to show any sign of ordering down to 160 mK in fields between zero and 18 T. This corroborates earlier measurements made at higher temperatures over a narrower field range by Igarashi et al. Further, the specific heat behaves linearly at temperatures below 700 mK. Interestingly, Ba₃Co₂O₆(CO₃)_0.7 has a very large Wilson ratio. Although not a theoretical prediction of any quantum spin liquid models, all known spin liquid candidates exhibit Wilson ratios greater than 1, often times greater by an order of magnitude. Herein we discuss our motivation, experiments, and results which advance strong evidence that Ba₃Co₂O₆(CO₃)_0.7 hosts a spin liquid ground state.   

New experimental strategies to explore the Kitaev interaction in honeycomb Mott insulators

Two-dimensional van der Waals honeycomb ferromagnets such as CrI₃ have attracted a lot of interest because of their potential applications in spintronics. We propose new experimental strategies to explore the bond-dependent interactions in honeycomb ferromagnets based on symmetries. These new methods can help resolve the debate on the importance of Kitaev interaction in CrI₃ from recent angle-dependent ferromagnetic resonance experiments and inelastic neutron scattering spin gap measurements. These strategies in general can be applied to other systems with similar symmetries.   

Pressure tuning of magnetism in pseudospin-1/2 honeycomb oxide Na2Co2TeO6

Honeycomb magnets have attracted significant interest because of their potential for realizing exotic magnetic states including the Kitaev quantum spin liquid phase. Among various Kitaev candidates, Na₂Co₂TeO₆ is a d⁷ high-spin compound in which the pseudospin-1/2 Co²⁺ ions form a long-range antiferromagnetic order below ~27 K. As pressure is an effective parameter to tune interactions in many systems, here we study the possibility of tuning the ordered state of Na₂Co₂TeO₆ into a spin disordered or liquid state under the application of hydrostatic pressure up to 13 kbar. Temperature dependence of magnetization at ambient pressure shows a magnetic phase transition at T_N ~27 K, which is followed by a minor kink at T_F~16 K. While pressure has a negligible influence on the magnetic ordering temperature, it reduces the out-of-plane magnetization between 16 K and 27 K. We will further discuss how the pressure influences the in-plane magnetization as well as the critical magnetic field at which a spin-disordered like state is induced.     

Magnetic Field Induced Disorder State in 3d Honeycomb Oxide Na2Co2TeO6

Investigating the exotic quantum phenomena and the related ground state of the frustrated quantum magnets is a focus of condensed matter physics  over the past years. While the realization of quantum spin liquid (QSL) without conventional magnetic ordering even down to 0 K is a challenging task, the Kitaev model is a prominent example with an exactly solvable spin model. The Kitaev materials so far have been focused on 4d/5d based systems with effective spin-1/2, such as H₃LiIr₂O₆, α-Li₂IrO₃, α-Na₂IrO_3, and α-RuCl₃, which exhibit zigzag antiferromagnetic (AFM) ordering at zero magnetic field owing to non-Kitaev interactions. Recently, the theoretical studies propose that the 3d-cobalt honeycomb magnets with effective spin-1/2 can be another playground to realize the Kitaev model. The non-Kitaev terms have been predicted to be almost vanishing with the small trigonal crystal fields acting on Co²⁺ ions, which makes the cobaltates as one good system for Kitaev physics. We studied the potential candidate Na₂Co₂TeO₆ and performed magnetization, heat capacity, high-field electric spin resonance, and inelastic neutron scattering (INS) measurements. A complicated magnetic field-temperature phase diagram was demonstrated with a zigzag AFM state and spin gap was observed in the spin dynamics. A quantum spin disordered state is induced by an ab-plane magnetic field between 7.5 and 10.5 T like the field-induced QSL in α-RuCl₃. Through detailed theoretical simulations on the INS spin-wave spectrum, we could obtain different ratios of the Kitaev interaction and the Heisenberg exchange. Hence, we anticipate our work will generate significant interest: it will trigger new experimental efforts for other realizations of magnetic field inducing the exotic quantum states and rejuvenate theoretical and computational efforts to understand the elusive dynamics in the Kitaev model for frustrated quantum magnetism.   

Infrared and Raman spectroscopy study of Co-based honeycomb Na2Co2TeO6

Layered honeycomb magnets have received lots of attention as potential candidates to realize Kitaev physics.  Current studies focus on 4d- or 5d-transition-metal honeycomb compounds for strong spin-orbit coupling. Recently, theoretical calculations propose that Kitaev interactions can also be realized in honeycomb magnets from 3d-transition-metal compounds [1,2]. Among them, Co-based honeycomb Na₂Co₂TeO₆ (NCTO) is antiferromagnetic ordered below T_N = 25K. More recent experimental studies on NCTO suggest that below T_N, magnetic field can suppress the long-range AFM order, and induce a disordered state in the field range of 7.5T < B < 10.5T before a field polarized state. Here we report the low-frequency infrared and Raman spectroscopy study on NCTO at low temperature and under high magnetic field up to 14T. A rich structure of magnetic excitations is observed across the AFM, disordered and polarized stats. The measurement results will be further discussed with theoretical calculations.

[1] Liu et. al., Phys. Rev. B 97, 014407 (2018)

[2] Liu et. al., Phys. Rev. Lett. 125, 047201 (2020)   

Antiferromagnetic Kitaev interaction in Jeff=1/2 cobalt honeycomb materials Na3Co2SbO6 and Na2Co2TeO6

Finding new materials with antiferromagnetic (AFM) Kitaev interaction is an urgent issue for quantum magnetism research [1]. In this work, we conclude that Na₃Co₂SbO₆ and Na₂Co₂TeO₆ are new honeycomb cobalt-based systems with AFM Kitaev interaction by carrying out inelastic neutron scattering experiments and subsequent analysis [1]. The spin-orbit excitons observed at 20-28 meV in both compounds strongly support the idea that Co²⁺ ions of both compounds have a spin-orbital entangled J_eff=1/2 state. Furthermore, we found that a generalized Kitaev-Heisenberg Hamiltonian can describe the spin-wave excitations of both compounds with additional 3^rd nearest-neighbor interaction. Our best-fit parameters show significant AFM Kitaev terms and off-diagonal symmetric anisotropy terms of a similar magnitude in both compounds. We also found a strong magnon-damping effect at the higher energy part of the spin waves, entirely consistent with observations in other Kitaev magnets. Our work suggests Na₃Co₂SbO₆ and Na₂Co₂TeO₆ as rare examples of the AFM Kitaev magnets based on the systematic studies of the spin waves and analysis.   

Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence

Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnetic field angles, and their shapes are determined by microscopic spin interactions. A chirality operator plays a key role in demonstrating microscopic dependences of the critical lines. We also show that the chirality operator can be used to evaluate topological properties of  the non-abelian Kitaev quantum spin liquid without relying on Majorana fermion descriptions. Experimental criteria for the non-abelian spin liquid state are provided for future experiments.