Session D07: 2D Magnetism and Quantum Spin Liquids

Z2 spin liquids in the Higher spin Kitaev Honeycomb model: an exact Z2 gauge structure in a non-integrable model

The higher spin Kitaev models have extensive locally conserved quantities the same as the spin-1/2 Kitaev honeycomb model, although they are not exactly solvable. In this talk, I will present their exact gauge structure by introducing a Majorana parton construction for a general spin-S. These conserved quantities are exactly the Z2 gauge fluxes. Particularly, we find an even-odd effect that the Z2 gauge charges are fermions in the half integer spin model, but are bosons in the integer spin model. We further prove that the fermionic Z2 gauge charges are always deconfined; hence, the half integer spin Kitaev model would have nontrivial spin liquid ground states regardless of interaction strengths in the Hamiltonian. The bosonic Z2 gauge charges of the integer spin model could condense, leading to a trivial product state, and this is indeed the case at the anisotropic limit of the model.   

Quasicrystalline spin liquid

A quasicrystal (QC) is an atomic arrangement that is neither perfectly periodic nor randomly disordered. Ranging from the archetypal Al-Mn alloys to more recent moir'e materials, QCs have attracted a growing attention for their unique properties such as robust zero modes. However, the effect of strong electron correlations in the QC setting remains a largely unexplored aspect of the field. In this talk, we will present an exactly solvable Kitaev spin liquid on a tri-coordinated QC. We will discuss the properties of the ground state and low-energy excitations which are distinct from the crystalline counterpart.   

Synchrotron IXS study of phonon excitations in van der Waals honeycomb ferromagnet CrGeTe3

There is a great deal of research efforts to realize two dimensional (2D) magnetic devices based on robust monolayer ferromagnetism discovered recently in van der Waals (vdW) materials. Among them, those with 2D honeycomb lattices are particularly interesting as their magnon excitations resemble the electronic band structure of graphene exhibiting linearly dispersive Dirac modes and their crossings. In this work, we experimentally investigated the phonon excitations in the vdW honeycomb ferromagnet CrGeTe₃ where robust 2D magnetism as well as strong spin-lattice coupling have previously been reported. Our recent neutron scattering experiments have revealed anomalous and anisotropic broadening of ferromagnons in CrGeTe₃ [1], which was ascribed to the unconventional magnon-phonon coupling in the form of slow exchange fluctuations [2]. Using synchrotron inelastic x-ray scattering, the phonon intensities were measured along the wave vectors parallel and perpendicular to vdW layers, respectively, in the ferromagnetic phase as well as paramagnetic. The phonon band structure extended up to 37 meV and was broadly consistent with the recent LDA calculations. The LDA calculation was also used to identify the observed phonon modes. In this talk, we will also discuss the temperature dependence of phonon scattering and its relevance to the proposed magnon-phonon coupling.   

 

[1] L. Chen et al., Nature Comm. 13 4037 (2022)

[2] W. Webster et al., Phys. Rev. B 98 144411 (2018)   

What is the origin of the intermediate-temperature magnetic specific heat capacity in the spin-liquid candidate Ca10Cr7O28?

We present several approximate calculations of the specific heat capacity of the model for Ca₁₀Cr₇O₂₈ proposed by Balz et al. [Phys. Rev. B 95, 174414 (2017)], using methods including exact diagonalization, Thermal Pure Quantum States, and high-temperature expansions. In none of these cases are we able to reproduce the magnitude of the zero-field specific heat capacity shown in the intermediate-temperature (∼5−15K) experimental data. We discuss possible reasons for the discrepancy, and what it might tell us about the magnetic Hamiltonian for Ca₁₀Cr₇O₂₈.   

Correlation Driven Magnetic Frustration and Insulating Behavior of TiF3

We investigate the halide perovskite TiF₃, renowned for its intricate interplay between structure, electronic correlations, magnetism, and thermal expansion. Despite its simple structure, understanding its low-temperature magnetic behavior has been a challenge. Previous theories proposed antiferromagnetic ordering. In contrast, experimental signatures for an ordered magnetic state are absent down to 10~K. Our current study has successfully reevaluated the theoretical modeling of TiF$_3$, unveiling the significance of strong electronic correlations as the key driver for its insulating behavior and magnetic frustration. In addition, our frequency-dependent optical reflectivity measurements exhibit clear signs of an insulating state. Analysis of the calculated magnetic data gives an antiferromagnetic exchange coupling with a net Weiss temperature of order 25 K as well as a magnetic response consistent with a S=1/2 local moment per Ti³⁺. Yet, the system shows no susceptibility peak at this temperature scale and appears free of long-range antiferromagnetic order down to 1 K. Extending ab initio modeling of the material to larger unit cells shows a tendency for relaxing into a non-collinear magnetic ordering, with a shallow energy landscape between several magnetic ground states, promoting the status of this simple, nearly cubic perovskite structured material as a candidate spin liquid.

[1] Gayanath W. Fernando, Donal Sheets, Jason Hancock, Arthur Ernst, R. Matthias Geilhufe, Correlation Driven Magnetic Frustration and Insulating Behavior of TiF₃, arXiv:2310.12645 (2023)

[2] D. Sheets, K. Lyszak, M. Jain, J. Hancock, G. W. Fernando, I. Sochnikov, J. Franklin, and R. M. Geilhufe, Spin-1/2 Mott state in negative thermal expansion perovskite TiF3, in preparation (2023)   

High-field spin dynamics in Kitaev quantum spin liquid candidate α-RuCl3

We study the evolution of the high and low-energy magnetic excitations across the 7 T through 12 T regime in paradigmatic Kitaev spin liquid candidate a-RuCl3. Interestingly, the excitations behave differently depending on field directions H||armchair vs. zig-zag. We reveal distinct sharp spin wave patterns above 12 T which, on reducing the field to 8 T, transform into delocalized broad excitations for the field along zig-zag. However, sharp modes remain for the field along the armchair axis. Moreover, focusing on the low-energy part of the spectrum yields new insights into the nature of the spin gap.   

Probing Majorana wavefunctions in Kitaev honeycomb spin liquids with second-order two-dimensional spectroscopy

Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing the properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ⁽²⁾_yzx(ω₁,ω₂) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z₂ flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wavefunctions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our work can guide future 2DCS experiments on Kitaev magnets.   

Van der Waals epitaxy of layered ferromagnet Cr2Ge2Te6 and its heterostructure with topological insulator (Bi,Sb)2Te3

Heterostructures or multilayers made of magnetic materials and topological insulators (TIs) have been of great interest due to the novel phenomena arising from the interfaces, such as quantum anomalous Hall effect and topological Hall effect, as well as their potential applications in spintronics. Although many magnetic TI heterostructures have been achieved, most of the magnetic layers on the top of TIs are metallic, hindering the study of electrical transport in TIs. Growing a magnetic insulator on top of TI in a large area is challenging due to limitations in sample preparation. Cr₂Ge₂Te₆ (CGT), a layered ferromagnetic semiconductor with a crystal structure similar to BST, is a suitable candidate and becomes insulating at low temperatures. In this work, we report the van der Waals epitaxy of CGT on (Bi,Sb)₂Te₃ (BST)/sapphire using molecular beam epitaxy. Compared to polycrystalline CGT films directly grown on sapphire substrates, single crystalline CGT films were achieved on the BST surface. Square magnetic hysteresis with an easy axis along c-axis was observed in a 12 nm CGT grown on 3 nm BST/sapphire; the saturation magnetization was 37 emu/cm³ at 10 K and the Curie temperature (T_c) was 67 K, slightly higher than the value of bulk single crystal of 61 K. Furthermore, large anomalous Hall hysteresis was observed below T_c, which could be attributed to the magnetized BST.   

Schwinger boson symmetric spin liquids of Shastry-Sutherland model

Motivated by recent experimental and numerical evidences of deconfined quantum critical point and quantum spin-liquid states in spin-1/2 Heisenberg model on Shastry-Sutherland lattice, we studied possible symmetric spin liquid states and their proximate ordered states under Schwinger boson formalism. We found a symmetric gapped Z2 spin-liquid state for intermediate model parameter (J_1/J_2 between 0.66 and 0.71) under mean-field approximation. The Schwinger boson mean-field picture is partially supported by exact-diagonalization and self-consistent spin wave theory results.   

Lieb-Schultz-Mattis constraints in 3D: application to the pyrochlore and the diamond lattices

Lieb-Schultz-Mattis theorems are a powerful family of constraints restricting the types of ground states of a lattice magnet. Two formalisms have been established: one uses the notation of lattice homotopy [Po et al., PRL 119, 127202 (2017)] and the other uses the idea of quantum anomalies [Else and Thorngren, PRB 101 224437, (2020)]. Here we discuss how these seemingly unrelated formalisms are related, and how these ideas can be employed to obtain a set of complete LSM constraints in three-dimensional lattice magnets. We will focus on the LSM theorems and filling constraints on the pyrochlore, diamond, and breathing pyrochlore lattices, which host some of the prototypical spin liquids in three dimensions. We go beyond the existing notation of classification by giving a detailed analysis of the microscopic origin for the nontrivial topological classes. This analysis allows us to obtain and track the trivialization of these anomalies under the breaking of lattice symmetries. Finally, we discuss the matching of the LSM anomalies and anomalies in quantum spin liquids. The principles and calculation methods presented in this work can be applied to all 3D lattice magnets.   

Electromagnetic signatures of a chiral quantum spin liquid

Quantum spin liquids (QSL) have emerged as a captivating subject within interacting spin systems that exhibit no magnetic ordering even at the lowest temperature accessible experimentally. However, definitive experimental evidence remains elusive. In light of the recent surge in theoretical and experimental interest in the half-filled Hubbard model on a triangular lattice, which offers the potential for stabilizing a chiral QSL, we investigate the electromagnetic signatures of this phase to facilitate experimental detection. Utilizing a combination of parton mean-field theory and unbiased density-matrix renormalization group calculations, we systematically examine the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL. Additionally, we calculate the longitudinal and transverse optical conductivities below the Mott gap. Furthermore, employing quantum field theory analysis, we unravel the connection between spinon excitations and emergent as well as physical gauge fields. Our results demonstrate that the chiral QSL phase exhibits a distinct electromagnetic response, even within a Mott insulator regime. This finding holds great potential for enabling the experimental detection of this long-sought-after phase.   

Thickness dependence of the anomalous and topological hall effects in layered Fe3GaTe2

Fe3GaTe2 is a two-dimensional (2D) van der Waals (vdW) ferromagnet displaying large anomalous and topological hall effects. Here, we report the properties of mechanically exfoliated Fe3GaTe2 grown via a chemical vapor transport (CVT) method whose thickness was determined via atomic force microscopy. Our Lorentz Transmission electron microscopy reveals a large density of skyrmions at temperatures exceeding room temperature. We observe giant anomalous Hall and topological Hall effects in both bulk and exfoliated samples. We will discuss their thickness, temperature and magnet field dependence.