Session Y22: Quantum Spin Liquids V: Kagome and Dirac Systems

Quantum Spin Supersolid as a precursory Dirac Spin Liquid in a Triangular Lattice Cobaltate

Based on the idea that the Dirac spin liquid is the parent state for numerous competing orders, we propose the triangular lattice antiferromagnet Na2BaCo(PO4)2, which exhibits a quantum spin supersolid, to be a precursory Dirac spin liquid. Despite the presence of a three-sublattice magnetic order resembling a spin ``supersolid'', we suggest that this system is close to a Dirac spin liquid by exploring its spectroscopic response. The physical consequence is examined from the spectroscopic response, and we establish the continuous spectra near the M point in addition to the K point excitation from the spinon continuum on top of the three-sublattice order. This proposal offers a plausible understanding of the recent inelastic neutron scattering measurement in Na2BaCo(PO4)2 and could inspire further research in relevant models and materials.   

Fate of Dirac spin liquids in the presence of spin-phonon interactions

Recent numerical calculations and theoretical studies have provided important evidence that Dirac spin liquid phases may be realized in highly frustrated spin systems on non-bipartite networks, e.g. on the kagome and triangular lattices [1]. We address the question of the stability of U(1) Dirac spin liquids in the presence of interactions between spins and lattice distortions (phonons) [2]. This scenario is modeled by considering a spin-phonon Hamiltonian in which the exchange interaction between the spins is modulated by lattice distortions. Adopting a variational Monte Carlo approach based on parton wave functions and spin-phonon Jastrow factors [3], which allow for a full quantum treatment of both spin and lattice degrees of freedom, we study the phase diagram of the spin-phonon Hamiltonian on the kagome and triangular lattices, away from the regime of static distortions. Our results indicate that Dirac spin liquid ground states are not immediately unstable and that competing valence-bond orders take over only above a critical value of the spin-phonon coupling.

[1] X.-Y. Song, C. Wang, A. Vishwanath, Y.-C. He, Nat Commun 10, 4254 (2019).

[2] U.F.P. Seifert, J. Willsher, M. Drescher, F. Pollmann, J. Knolle, arXiv:2307.12295 (2023).

[3] F. Ferrari, R. Valenti, F. Becca, Phys. Rev. B 104, 035126 (2021).   

Mononpoles and Anomalies of an SU(3) Dirac Spin Liquid on the Kagome Lattice

Quantum spin liquids are a class of exotic phases of interacting spins that host interesting features ranging from long range entanglement to the emergence of gauge theories. We consider a version of an SU(3) Hubbard model on the Kagome lattice. At one-third filling, we obtain a candidate for a Dirac spin liquid (DSL), which does not have a quasi-particle description. We show how aspects of the band topology and crystalline symmetries can constrain the stability properties of the DSL through determining the quantum numbers of the monopole operators. This extends methods previously applied for SU(2) and SU(4) spin systems. Further, we calculate the quantum anomalies of the low energy quantum field theory and comment on the possible phases this system can realize.   

Spin excitation spectra of the spin-1/2 Kagome Heisenberg antiferromagnets

We present a large-scale numerical calculation on the dynamical correlation functions of spin-1/2 Kagome J1-J2 Heisenberg model using a state-of-the-art tensor network renormalization group method. The calculated results allow us to gain a comprehensive picture on the nature of spin excitation spectra of the Kagome J1-J2 Heisenberg model. The entire excitation spectra gradually gather from high energy to low energy as J2 decreases, and finally form a gapless low-energy continuum distributed in the J1 range when J2/J1 is less than about 0.05, implying that it has entered the gapless quantum spin liquid phase. Furthermore, combining with the static structure factor, we confirm that this gapless quantum spin liquid is more likely to be U(1) Dirac Spin Liquid, which is well consistent with our previous research (PRL 118, 137202 (2017)) on ground state properties.   

Probing Intrinsic and Magnetic Impurity Excitations in Single Crystals of the Kagome Quantum Spin Liquid Candidate Zn-Barlowite Using Inelastic Neutron Scattering

The spin-1/2 Heisenberg antiferromagnet on kagome lattice (KAF) is among the most promising models which could host a quantum spin liquid (QSL) in two-dimensions. Zn-Barlowite (Zn_xCu_4-x(OH)₆BrF) is a relatively new KAF material that shows strong signatures of a QSL ground state, including no measured magnetic order down to 50mK. Excitingly, Zn-Barlowite has a different interlayer impurity environment and a simpler A-A kagome layer stacking as compared to the related KAF material Herbersmithite (Zn_xCu_4-x(OH)₆Cl₂, with an A-B-C kagome layer stacking). This makes Zn-Barlowite promising as a potentially more pristine KAF QSL host and allows us to investigate the universality of the underlying kagome spin physics. Previous in-plane inelastic neutron scattering preformed by our group demonstrate a universality of behavior for excitations between Herbertsmithite and Zn-Barlowite at energies above ~1 meV, suggesting that these excitations arise from the similar undistorted spin-1/2  kagome layers that these materials host. Meanwhile, the excitations below 1 meV are qualitatively very different between the materials and therefore likely arise from interlayer magnetic impurities given the different impurity environments in these materials. In this talk, I present new out of plane inelastic neutron scattering data taken in Zn-Barlowite. This helps to shed light on the magnetic impurity excitations in this material so that more firm conclusions can be made about the intrinsic kagome layer physics.   

Investigation of the thermal Hall effect in a Kagome antiferromagnet

Quantum spin liquid (QSL) is an exotic quantum state of matter in which spins are highly entangled and disordered at zero temperature. The recently discovered Kagome lattice antiferromagnet YCu3-Br has become a promising QSL candidate. The experimental results, including low-temperature magnetization, heat capacity, inelastic neutron scattering, and magnetic oscillations, are all consistent with the expectation of QSL with Dirac spinon.

On the other hand, the thermal Hall effect has emerged as a probe of QSL. For QSLs with spinon Fermi surfaces, it was theoretically proposed that the external magnetic field generates an internal gauge field and could exert Lorentz force on the neutral spinon, leading to a significant thermal Hall effect. We present a comprehensive study of thermal conductivity as well as the thermal hall effect in the YCu3-Br single crystals. The experimental methods, verification, and possible explanations will be discussed.   

Unusual magnetic oscillations in a quantum spin liquid candidate

Quantum spin liquid (QSL) is a state where magnetic order can not exist due to strong frustration. The two-dimensional spin-1/2 Heisenberg Kagome lattice antiferromagnet (AFM) is an ideal playground. Recently, a promising Dirac spin liquid candidateYCu₃(OH)₆Br₂[Br_1-x(OH)_x] has been discovered without magnetic order down to 50 mK. Interestingly the heat capacity is found to be proportional to temperature T² and is enhanced by magnetic field, leading to the proposal that these compounds are spin liquids with Dirac spinons. This motivates us to study the behavior of this compound under intense magnetic fields B. Here we report we observed an unconventional plateau at magnetization equal to 1/9 Bohr magneton per magnetic ion in magnetization measurements [1]. More surprisingly, magnetic oscillations were observed in this robust insulator which are roughly periodic in B instead of 1/B, while their temperature dependence follows the Lifshitz-Kosevich formula, a defining characteristic of quantum oscillations due to fermions. These phenomena are consistent with a QSL state whose excitations are fermionic spinons with a Dirac-like spectrum. Our results provide strong evidence that fractionalized particles in QSL have been observed. 

[1] G. Zheng et al., Unconventional Magnetic Oscillations in Kagome Mott Insulators. arXiv preprint arXiv:2310.07989,  (2023).    

Electronic and magnetic properties of a novel rare-earth-based Kagome lattice candidate

We discuss the susceptibility, transport and heat capacity results from high-quality single crystals of a rare-earth-based Kagome metal candidate. While the low-temperature ground state is antiferromagnetic, there is a broad maximum at around 60 K for certain directions of magnetic field robust up to 7 T. Combined with a reduced value of moment in ab-plane and a huge anisotropy, we could interpret the state as a short-range correlated state reminiscent of a thermally-driven spin liquid.   

Magnetoresistance in Conical Magnets

Materials with spin-spiral textures can have substantially different electric transport properties compared to topologically trivial materials. We analyse field dependent transport properties in conical magnets, accounting for the change in conical angle with field. We analytically find expressions for the energy bands and eigenstates in the general case. We employ two computational approaches to find current densities, used to find field dependent transport properties such as Hall effects and magnetoresistance. The first approach uses the Boltzmann equation to calculate transition rates in the first Born approximation, accounting for electron phonon scattering. The second approach uses a spin independent approximation for the relaxation time, but is integrated more accurately over the k-volume. We observe several non-trivial behaviors in transport properties. They are explained due to the field dependent bandstructure, as the material transition from a helimagnet to a ferromagnet. The differences between the two approaches show the effects of spin transitions in these materials.   

Field-induced spin reorientation transition in Ca$_2$Ru$_{1-x}$Fe$_x$O$_4$

Ca$_2$RuO$_4$ serves as a promising arena for exploring Mott physics. The persistent controversies regarding the nature of its magnetic ground state stem from the uncertain effect of the spin-orbit coupling. Two similar magnetic orders, A-centered and B-centered, were found to compete in Ca$_2$RuO$_4$ and its derivative compounds. This neuron scattering investigation on Ca$_2$Ru$_{1-x}$Fe$_x$O$_4$ (x=0.02, 0.05 and 0.08) reveals that the magnetic field, when applied in the right direction, has strong effect on tipping the balance between the two magnetic orders, evidencing the subtle canting of the Ru$^{3+}$ spins, the existence of antisymmetric exchange and the role of spin-orbit coupling.   

Quantifying magnetic field driven lattice distortions in kagome metals at femto-scale using scanning tunneling microscopy

A wide array of unusual phenomena has recently been uncovered in kagome solids. In particular, the charge density wave (CDW) state in the kagome superconductor AV₃Sb₅ (A = Cs, Rb, K) intrigued the community as it appears to break time-reversal symmetry despite the absence of spin magnetism. This has been tied to exotic orbital loop currents possibly intertwined with magnetic field tunable crystal distortions. To test this connection, precise determination of the lattice response to applied magnetic field is crucial, but can be challenging at the atomic-scale. We establish a new scanning tunneling microscopy based method to map the evolution of AV₃Sb₅ atomic structure as a function of the magnetic field. We study and discuss the response of both in-plane and out-of-plane lattice constants to 3D vector magnetic fields. The method substantially reduces errors present in typical STM measurements, and can be widely applied to extract the field-lattice coupling in other quantum materials.