Recent theoretical proposals have argued that cobaltates with edge-sharing octahedral coordination can have significant bond-dependent exchange couplings thus offering a platform in 3$d$ ions for such physics beyond the much-explored realizations in 4$d$ and 5$d$ materials. Here we present high-resolution inelastic neutron scattering data within the magnetically ordered phase of the stacked honeycomb magnet CoTiO$_3$ revealing the presence of a finite energy gap and demonstrate that this implies the presence of bond-dependent anisotropic couplings. We also show through an extensive theoretical analysis that the gap further implies the existence of a quantum order-by-disorder mechanism that, in this material, crucially involves virtual crystal field fluctuations. Our data also provide an experimental observation of a universal winding of the scattering intensity in angular scans around linear band-touching points for both magnons and dispersive spin-orbit excitons, which is directly related to the non-trivial topology of the quasiparticle wavefunction in momentum space near nodal points.
The quest for Kitaev quantum spin liquids has led to great interest in honeycomb quantum magnets with strong spin-orbit coupling. It has been recently proposed that even Mott insulators with $3d$ transition metal ions, having nominally weak spin-orbit coupling, can realize such exotic physics. Motivated by this, we study the rhombohedral honeycomb cobaltates CoTiO$_3$, BaCo$_2$(PO$_4$)$_2$, and BaCo$_2$(AsO$_4$)$_2$, using $\textit{ab initio}$ density functional theory, which takes into account realistic crystal field distortions and chemical information, in conjunction with exact diagonalizat…
University of Toronto（多伦多大学）；Canadian Institute for Advanced Research（加拿大高等研究院）
Recently, honeycomb cobaltates with 3$d^7$ were proposed to display Kitaev physics despite weak spin-orbit coupling. However, other theoretical and experimental works found leading XXZ Heisenberg and negligible Kitaev interactions in BaCo$_2$(AsO$_4$)$_2$ (BCAO), which calls for a further study to clarify the origin of the discrepancies. Here we derive the analytical expressions of the spin model using strong-coupling perturbation theory. With tight binding parameters obtained by {\it ab-initio} calculations for idealized honeycomb BCAO, we find that the largest intraorbital $t_{2g}-t_{2g}$ ex…
Recent experiments on the Co-based $d^7$ honeycomb materials BaCo$_2$(AsO$_4$)$_2$ and BaCo$_2$(PO$_4$)$_2$ have drawn renewed interest to XXZ models with competing interactions beyond the nearest neighbor exchange. While the case of dominant antiferromagnetic exchange has been extensively studied, the actual materials exhibit a ferromagnetic nearest neighbor exchange. Here we show that such a sign change of the dominant nearest neighbor coupling has substantial consequences on the phase diagram. In particular, the nature of the quantum disordered phase of interest changes from a plaquette val…
This paper reviews the current progress on searching the Kitaev spin liquid state in 3d electron systems. Honeycomb cobaltates were recently proposed as promising candidates to realize the Kitaev spin liquid state, due to the more localized wave functions of 3d ions compared with that of 4d and 5d ions, and also the easy tunability of the exchange Hamiltonian in favor of Kitaev interaction. Several key parameters that have large impacts on the exchange constants, such as the charge-transfer gap and the trigonal crystal field, are identified and discussed. Specifically, tuning crystal field eff…
We propose the existence of a symmetry-protected topological Dirac nodal line (DNL) magnonic phase in layered honeycomb collinear antiferromagnets even in the presence of spin-orbit Dzyaloshinskii-Moriya interaction. We show that the magnon spin Nernst effect, predicted to occur in strictly two-dimensional (2D) honeycomb collinear antiferromagnets cancels out in the layered honeycomb collinear antiferromagnets. In other words, the magnon spin Nernst effect in each 2D antiferromagnetic layer cancels out the succeeding layer. Hence, the Berry curvature vanish in the entire Brillouin zone due to …
Cobaltates with 3$d$ based layered honeycomb structure were recently proposed as Kitaev magnets and putative candidates to host the long-sought Kitaev spin liquid. Here we present inelastic neutron scattering results down to 50 mK for powder samples of Na$_3$Co$_2$SbO$_6$ and Na$_2$Co$_2$TeO$_6$, with high resolution in regions of low momentum and energy transfers. We compare the experimental data below the antiferromagnetic zigzag ordering temperature with dynamical structure factors obtained within spin wave theory. We search the wide parameter range of a $K$-$J_1$-$Γ$-$Γ^{\prime}$-$J_3$ spi…
In the quest for materials hosting Kitaev spin liquids, much of the efforts have been focused on the fourth- and fifth-row transition metal compounds, which are spin-orbit coupling assisted Mott insulators. Here, we study the structural and magnetic properties of 3$d$ transition metal oxides, Na$_2$Co$_2$TeO$_6$ and Na$_3$Co$_2$SbO$_6$. The partial occupancy of sodium in former compound is addressed using a cluster expansion, and a honeycomb lattice of sodiums is found to be energetically favored. Starting from the \textit{ab initio} band structures, a many-body second order perturbation theor…
Competing Interactions and the Effects of Uniaxial Out-of-plane Perturbations in the Honeycomb Antiferromagnet Na$_2$Co$_2$TeO$_6$
Kirchhoff Institute for Physics, Heidelberg University（海德堡大学基尔霍夫物理研究所）；Institute of Physics, Academia Sinica（中央研究院物理学研究所）；Department of Physics, Sungkyunkwan University（成均馆大学物理系）
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 $Li_3Co_2SbO_6$, built of high-spin $\it{d^7}$ ($Co^{2+}$) ions, in contrast to the more typical low-spin $\it{d^5}$ 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 $\it{C_C}2/\…
By considering two {\it ab initio}-based complementary approaches, we analyze the electronic structure and extract effective spin models of BaCo$_2$(AsO$_4$)$_2$, a honeycomb material which has been proposed as a candidate for Kitaev physics. Both methods show that the dominant direct hopping makes the bond-dependent Kitaev term negligible averting the material away from the sought-after spin-liquid regime. As a result, we present a simple three-parameter exchange model to describe the interactions of the lowest doublet of the honeycomb cobaltate BaCo$_2$(AsO$_4$)$_2$. Remarkably, it is the th…
The Johns Hopkins University（约翰斯·霍普金斯大学）；Institute for Quantum Matter, William H. Miller III Department of Physics and Astronomy（量子物质研究所，威廉·H·米勒三世物理与天文系）；Quantum Matter Institute, University of British Columbia（不列颠哥伦比亚大学量子物质研究所）；Neutron Scattering Division, Oak Ridge National Laboratory（橡树岭国家实验室中子散射部）；Department of Physics & Astronomy, University of British Columbia（不列颠哥伦比亚大学物理与天文系）；Centre for Molecular and Materials Science, TRIUMF（TRIUMF分子与材料科学中心）
Search for higher-order topological insulators, characterized by topologically protected gapless boundary states of codimension higher than one, in bosonic systems has attracted growing interest. Here, we establish twisted bilayer honeycomb magnets as a new platform for hosting second-order topological magnon insulators (SOTMIs) without fine-tuning. We employ a simple, minimal Heisenberg spin model to describe misaligned bilayer sheets of honeycomb ferromagnetic magnets with a large commensurate twist angle. We found that the higher-order topology in this bilayer system shows a significant dep…
The two-dimensional kagome lattice hosts Dirac fermions at its Brillouin zone corners K and K', analogous to the honeycomb lattice. In the density functional theory electronic structure of ferromagnetic kagome metal Fe$_3$Sn$_2$, without spin-orbit coupling we identify two energetically split helical nodal lines winding along $z$ in the vicinity of K and K' resulting from the trigonal stacking of the kagome layers. We find that hopping across A-A stacking introduces a layer splitting in energy while that across A-B stacking controls the momentum space amplitude of the helical nodal lines. The …
Mechanism of Incommensurate Magnetic Order in $\mathrm{BaCo_2(AsO_4)_2}$: Interplay of Frustrated Further-Neighbor Exchanges and Bond-Directional Anisotropy
Qom University of Technology（库姆理工大学）；University of Toronto（多伦多大学）；Shahrekord University（沙赫里克尔德大学）
Very recently, a 3$d$ based honeycomb cobaltate Na$_2$Co$_2$TeO$_6$ has garnered tremendous attention due to the proposed proximity to the Kitaev spin-liquid state as its 4$d$/5$d$ counterparts. Here, we use Zn to substitute Co in a broad range and perform systematic studies on Na$_2$Co$_{2-x}$Zn$_x$TeO$_6$ by structural, magnetic, and thermodynamic measurements, and track the doping evolution of its magnetic ground states. Due to the extremely close radii of Zn$^{2+}$ and high-spin Co$^{2+}$ ions, the substitution can be easily achieved. X-ray diffractions reveal no structural transition but …
FePS$_3$ is a van der Waals compound with a honeycomb lattice that is a good example of a two-dimensional antiferromagnet with Ising-like anisotropy. Neutron spectroscopy data from FePS3 were previously analysed using a straight-forward Heisenberg Hamiltonian with a single-ion anisotropy. The analysis captured most of the elements of the data, however some significant discrepancies remained. The discrepancies were most obvious at the Brillouin zone boundaries. The data are subsequently reanalysed allowing for unequal exchange between nominally equivalent nearest-neighbours, which resolves the …
