Antiferromagnetic Zigzag Research Articles

Phase diagrams of Kitaev models for arbitrary magnetic field orientations

The Kitaev model is an exactly solvable quantum spin model within the language of constrained real fermions. In spite of numerous studies for magnetic fields along special orientations, there is a limited amount of knowledge on the complete field-angle characterization, which can provide valuable information on the existence of fractionalized excitations. For this purpose, we first study the pure ferromagnetic and antiferromagnetic Kitaev models for arbitrary external magnetic field directions via a mean-field theory, showing that there are many topological phases with different (or zero) Chern numbers, depending on the magnetic field strength and orientations. However, a realistic description of the candidate Kitaev materials, within the edge-sharing octahedra paradigm, requires additional coupling terms, including a large off-diagonal term $\mathrm{\ensuremath{\Gamma}}$ along with possible anisotropic corrections ${\mathrm{\ensuremath{\Gamma}}}_{p}$. It is therefore not sufficient to rely on the topological properties of the bare Kitaev model as the basis for the observed thermal Hall-conductivity signals, and an understanding of these extended Kitaev models with a complete field response is demanded. Starting from the zero-field phase diagram of $\mathrm{K}\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}_{p}$ models, we identify, besides the Kitaev spin liquid phase, antiferromagnetic zigzag, ferromagnetic phases, as well as an unusual Kitaev(-$\mathrm{\ensuremath{\Gamma}}$) spin liquid phase. The magnetic field response of these phases for arbitrary field orientations provides a remarkably rich phase diagram. For an extended parameter range and just above the critical field where the zigzag phase is suppressed, there is an intermediate phase region with suppressed energy gaps and substantial spin fractionalization. To comply our findings with experiments, we also reproduce a large asymmetry in the extent of this intermediate phases specifically for the two different field directions $\ensuremath{\theta}=\ifmmode\pm\else\textpm\fi{}{60}^{o}$ with respect to the normal to the plane of the honeycomb lattice.

Dominant Kitaev interactions in the honeycomb materials Na3Co2SbO6 and Na2Co2TeO6

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 $K$-$J_1$-$\Gamma$-$\Gamma^{\prime}$-$J_3$ spin 1/2 model and identify the best fits to constant momentum cuts of the inelastic neutron data. The powder average limits the selection of a unique parameter set for each material, but we see clear trends towards ferromagnetic Kitaev exchange in both compounds, and ratios $|K/J_1|$ could be as large as $5\ldots 25$; in contrast, antiferromagnetic Kitaev exchange cannot be ruled out, but requires a fine-tuning of all involved spin exchange couplings with only moderate ratio $|K/J_1| \sim 1$. Our experimental data are incompatible with a purely isotropic Heisenberg model.

Influence of local structural distortion on the magnetism of Na2IrO3 compounds

First-principles calculations are conducted to investigate the magnetic properties of the ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ compounds. We reveal that the ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$'s local structural distortions are essential for an accurate description of the magnetism of such systems. They provide a feasible explanation for the experimentally observed antiferromagnetic zigzag magnetic ground state. We demonstrate that the underlying competition between the spin-orbit coupling and the crystal-field splitting rules the crystal structure and profoundly influences the strength of the magnetic exchange interactions. We unambiguously identify that the ${D}_{4h}$-type distortions, due to the Jahn-Teller effect, are disclosed in an elongation along the ${\mathrm{IrO}}_{6}$ polyhedra's apical axis in the $ac$ plane. On the other hand, the Ir atoms off-centering in the basal plane (perpendicular to the local ${D}_{4h}$ elongation axis) arises owing to an inhomogeneous cationic charge distribution of ${\mathrm{Ir}}^{4+}/{\mathrm{Na}}^{+}$ in the transition-metal layer resulting in both effects being decisive in controlling the magnetism of ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ together with the spin-orbit interactions.

Magnetic properties of rare-earth zigzag chain systems RAgSe2 (R = Ho, Er, Tm, and Yb)

In an antiferromagnetic zigzag chain, competition between the nearest and next-nearest neighbor interactions could give rise to magnetic frustration. Magnetic semiconductors RAgSe2 (R = Ho, Er, Tm, and Yb) crystallize in the ErAgSe2-type orthorhombic structure, where the R ions form a zigzag chain along the orthorhombic a-axis. The magnetic susceptibility data for all the samples follow the Curie-Weiss law between 40 and 300 K. The values of the effective magnetic moment μ βα are close to those expected for the free R 3+ ions. Negative values of the paramagnetic Curie temperature θρ indicate antiferromagnetic interactions. For R = Ho and Tm, the specific heat C(T) data exhibit no anomaly down to 0.4 K, which is ascribed to the nonmagnetic singlet ground states under the crystalline electric fields. On the other hand, for R = Er, C(T) shows peaks at T 1 = 1.3 K and T2 = 0.9 K, indicating successive antiferromagnetic transitions. For R = Yb, C(T) shows a lambda-type anomaly at T m = 1.8 K. The magnetic entropy at T m is only 30% of Rln2 expected for the ground state doublet, suggesting magnetic fluctuations above T m.

Even–odd effect of electric and optical properties for antiferromagnetic zigzag phosphoene nanoribbons under an electric field

The study on the electronic especially optical properties of zigzag-edged phosphorene nanoribbons (ZPNRs) in an antiferromagnetic state has been rarely involved. Here we theoretically study the electronic and optical properties of a ZPNR with N chains (N-ZPNR) modulated by a vertical electric field (VEF). Within the Hubbard model Hamiltonian combined with the self-consistent calculation, and by adopting the Green’s function method, we obtain the band structure and corresponding conductance for the system. The corresponding optical absorption spectrum is further obtained based on the Kubo formula. It is interesting to find that there is an even–odd effect on the electronic and optical properties of N-ZPNR induced by the VEF, which may fundamentally originate from the parity of the wavefunctions. The VEF lifts the degeneracy of the two edge bands for 12-ZPNR, but it only bends and shifts the two edge bands without lifting the spin degeneracy for 13-ZPNR. We further present the spatial distribution of the corresponding wavefunction to understand this even–odd effect more intuitively. As expected, the VEF can separate the spin-up and -down optical absorption for 12-ZPNR, but it does not break the spin degeneracy of the optical absorption for 13-ZPNR. Our results may provide a further understanding on the electronic and optical properties of N-ZPNR with an antiferromagnetic state, and may be useful to identify the even–odd property of ZPNR samples by detecting the optical absorption in experiment.

Magnetostriction of α-RuCl3 Flakes in the Zigzag Phase

Motivated by the possibility of an intermediate U(1) quantum spin liquid phase in out-of-plane magnetic fields and enhanced magnetic fluctuations in exfoliated {\alpha}-RuCl3 flakes, we study magneto-Raman spectra of exfoliated multilayer {\alpha}-RuCl3 in out-of-plane magnetic fields of -6 T to 6 T at temperatures of 670 mK - 4 K. While the literature currently suggests that bulk {\alpha}-RuCl3 is in an antiferromagnetic zigzag phase with R3bar symmetry at low temperature, we do not observe R3bar symmetry in exfoliated {\alpha}-RuCl3 at low temperatures. While we saw no magnetic field driven transitions, the Raman modes exhibit unexpected stochastic shifts in response to applied magnetic field that are above the uncertainties inferred from Bayesian analysis. These stochastic shifts are consistent with the emergence of magnetostrictive interactions in exfoliated {\alpha}-RuCl3.

Spin current distribution in antiferromagnetic zigzag graphene nanoribbons under transverse electric fields

The spin current transmission properties of narrow zigzag graphene nanoribbons (zGNRs) have been the focus of much computational research, investigating the potential application of zGNRs in spintronic devices. Doping, fuctionalization, edge modification, and external electric fields have been studied as methods for spin current control, and the performance of zGNRs initialized in both ferromagnetic and antiferromagnetic spin states has been modeled. Recent work has shown that precise fabrication of narrow zGNRs is possible, and has addressed long debated questions on their magnetic order and stability. This work has revived interest in the application of antiferromagnetic zGNR configurations in spintronics. A general ab initio analysis of narrow antiferromagnetic zGNR performance under a combination of bias voltage and transverse electric field loading shows that their current transmission characteristics differ sharply from those of their ferromagnetic counterparts. At relatively modest field strengths, both majority and minority spin currents react strongly to the applied field. Analysis of band gaps and current transmission pathways explains the presence of negative differential resistance effects and the development of spatially periodic electron transport structures in these nanoribbons.

Thickness dependence of electronic structure and optical properties of a correlated van der Waals antiferromagnetic NiPS3 thin film

We study the thickness dependence of the electronic, magnetic, and optical properties of a NiPS$_3$ thin film, an antiferromagnetic charge-transfer insulator. Utilizing state-of-the-art advanced density functionals, we find the antiferromagnetic Zig-Zag order, the band gap, and the main peaks in the dielectric tensor are all in good agreement with the corresponding experimental values. Upon thinning, the Zig-Zag antiferromagnetic order becomes virtually degenerate with a competing N\'eel order, consistent with the suppression of long-range order observed by Raman spectroscopy due to strong magnetic fluctuations. Additionally, due to the robustness of the electronic band gap observed by spectroscopic ellipsometry measurements above $T_N$, we suggest that the persistence of the band gap is driven by strong electronic correlations. Other systematic changes in electronic dispersion, effective mass, and Kerr angle with thickness are also discussed. Finally, an applied external electric field is found to suppress the band gap by up to 13%, until precipitating an insulator-metal transition at a critical field value of $0.7$ eV/\r{A}.

Nonlinear soliton confinement in weakly coupled antiferromagnetic spin chains

We analyze the low-energy dynamics of quasi one dimensional, large-$S$ quantum antiferromagnets with easy-axis anisotropy, using a semi-classical non-linear sigma model. The saddle point approximation leads to a sine Gordon equation which supports soliton solutions. These correspond to the movement of spatially extended domain walls. Long-range magnetic order is a consequence of a weak inter-chain coupling. Below the ordering temperature, the coupling to nearby chains leads to an energy cost associated with the separation of two domain walls. From the kink-antikink two-soliton solution, we compute the effective confinement potential. At distances large compared to the size of the solitons the potential is linear, as expected for point-like domain walls. At small distances the gradual annihilation of the solitons weakens the effective attraction and renders the potential quadratic. From numerically solving the effective one dimensional Schr\"oedinger equation with this non-linear confinement potential we compute the soliton bound state spectrum. We apply the theory to CaFe$_{2}$O$_{4}$, an anisotropic $S=5/2$ magnet based upon antiferromagnetic zig-zag chains. Using inelastic neutron scattering, we are able to resolve seven discrete energy levels for spectra recorded slightly below the N\'eel temperature $T_\textrm{N}\approx 200$~K. These modes are well described by our non-linear confinement model in the regime of large spatially extended solitons.

Spin photocurrents in zigzag phosphorene nanoribbons: From infrared to ultraviolet

Using the self-consistent non-equilibrium Green’s function model and the mean-field Hubbard approximation, we studied the possibility of inducing the spin-photovoltaic effects in zigzag phosphorene nanoribbons. We numerically showed that an applied electric field could induce a spin-semiconducting behavior with anisotropic and localized band structures around the Fermi energy in the antiferromagnetic zigzag phosphorene nanoribbons. Moreover, a tunable energy gap with an electric field could induce a spin photocurrent in a wide range of photon energies. Interestingly, increasing the electric field strength induces the spin-valve effect from terahertz to infrared irradiation. Furthermore, ferromagnetic zigzag phosphorene nanoribbons reveal a spin-dependent photoresponsivity, which is induced by infrared to ultraviolet frequencies. These results could enhance photovoltaic effects with a generation of the spin photocurrent in phosphorene junctions.

Field-induced transitions in the Kitaev material α−RuCl3 probed by thermal expansion and magnetostriction

High-resolution thermal expansion and magnetostriction measurements were performed on single crystals of $\alpha$-RuCl$_3$ in magnetic fields applied parallel to the Ru-Ru bonds. The length changes were measured in the direction perpendicular to the honeycomb planes. Our data show clear thermodynamic characteristics for the field-induced phase transition at the critical field $\mu_0H_{c1} = 7.8(2)$ T where the antiferromagnetic zigzag order is suppressed. At higher fields, a kink in the magnetostriction coefficient signals an additional phase transition around $\mu_0H_{c2} \approx 11$ T. The extracted Gr\"uneisen parameter shows typical hallmarks for quantum criticality near $H_{c1}$, but also displays anomalous behavior above $H_{c1}$. We compare our experimental data with linear spin-wave calculations employing a minimal Kitaev-Heisenberg model in the semiclassical limit. Most of the salient features are in agreement with each other, however, the peculiar features in the high-field region above $H_{c1}$ cannot be accounted for in our modelling and hence suggest a genuine quantum nature. We construct a phase diagram for $\alpha$-RuCl$_3$ showing two low-temperature transitions induced by an in-plane field along the Ru-Ru bonds.

A new single-layer structure of MBene family: Ti2B

In this manuscript, we have carried out a combined study of density functional theory and Monte Carlo (MC) simulations for a thorough examination of a single-layer (SL) Ti2B structure. On the basis of first-principles, spin-polarized density functional calculations, we showed that a free standing SL-Ti2B structure is dynamically and thermally stable. The atomic structure, phonon spectrum, electronic and magnetic properties of the SL-Ti2B structure are analyzed. In order to determine ground state, the structure of Ti2B is optimized for four types of spin oriented configurations, namely ferromagnetic (FM), antiferromagnetic Néel, antiferromagnetic Zigzag and antiferromagnetic Stripy and non-magnetic states. We found that the spin configuration FM corresponds to the ground state for SL-Ti2B. We also found that the Raman-active modes are softening in the antiferromagnetic cases. On the basis of these results, MC simulations show that the magnetic susceptibility, thermal variations of magnetization, and specific heat curves of Ti2B exhibit a phase transition between paramagnetic and FM phases at the Curie temperature of 39.06 K. While SL-Ti2B possess a little out-of-plane magnetic anisotropy, it has not any in plane magnetic anisotropy energy.

Strain effects on electronic and magnetic properties of the monolayer α-RuCl3: A first-principles and Monte Carlo study

The electronic and magnetic properties of a material can be altered by strain engineering. We elucidate the strain dependence of electronic and magnetic properties in α-RuCl3 monolayer by varying the biaxial in-plane tensile strain from 1% to 8%. The magnetic ground state of the α-RuCl3 monolayer evolves from antiferromagnetic zigzag (AFM-ZZ) configuration to ferromagnetic (FM) under a biaxial in-plane tensile strain higher than 2%. In a strain-free state, the FM configuration has a direct bandgap of 0.54 eV, and the AFM-ZZ configuration has an indirect bandgap of 0.73 eV. The energy bandgap of the α-RuCl3 monolayer undergoes a change by the variation of the tensile strain. Furthermore, a detailed Monte Carlo simulation has been implemented to investigate the magnetic properties of the considered system for varying values of tensile strain. Temperature dependencies of the thermodynamic quantities of interest as functions of strains display strong evidence supporting the first-principles calculations within density functional theory. Our Monte Carlo findings also suggest that the Curie temperature of the α-RuCl3 monolayer tends to get higher up to 20.11 K with a tensile strain 8%, which means that applying a strain leads to getting a more stable FM ground state. In addition, we find that magnetocrystalline anisotropy in the α-RuCl3 monolayer can be controlled by the applied strain.

Exploring the electronic and magnetic properties of new metal halides from bulk to two-dimensional monolayer: RuX3 (X = Br, I)

Theoretical and experimental studies present that metal halogens in MX$_3$ forms can show very interesting electronic and magnetic properties in their bulk and monolayer phases. Many MX$_3$ materials have layered structures in their bulk phases, while RuBr$_3$ and RuI$_3$ have one-dimensional chains in plane. In this paper, we show that these metal halogens can also form two-dimensional layered structures in the bulk phase similar to other metal halogens, and cleavage energy values confirm that the monolayers of RuX$_3$ can be possible to be synthesised. We also find that monolayers of RuX$_3$ prefer ferromagnetic spin orientation in the plane for Ru atoms. Their ferromagnetic ground state, however, changes to antiferromagnetic zigzag state after U is included. Calculations using PBE+U with SOC predict indirect band gap of 0.70 eV and 0.32 eV for the optimized structure of RuBr$_3$ and RuI$_3$, respectively. Calculation based on the Monte Carlo simulations reveal interesting magnetic properties of RuBr$_3$, such as large Curie temperature against RuI$_3$, both in bulk and monolayer cases. Moreover, as a result of varying exchange couplings between neighboring magnetic moments, magnetic properties of RuBr$_3$ and RuI$_3$ can undergo drastic changes from bulk to monolayer. We hope our findings can be useful to attempt to fabricate the bulk and monolayer of RuBr$_3$ and RuI$_3$.

Spectral and magnetic properties of Na2RuO3

We present measurements of resistivity, x-ray absorption (XAS) and emission (XES) spectroscopy together with ab initio band structure calculations for quasi two dimensional ruthenate Na2RuO3. Density function calculations (DFT) and XAS and XES spectra both show that Na2RuO3 is a semiconductor with an activation energy of ∼80 meV. Our DFT calculations reveal large magneto-elastic coupling in Na2RuO3 and predict that the ground state of Na2RuO3 should be antiferromagnetic zig–zag.

Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for α−RuCl3 and Na2IrO3

We study the field-induced magnetization processes of extended Heisenberg-Kitaev models on the honeycomb lattice, taking into account off-diagonal and longer-range exchange interactions, using a combination of Monte-Carlo simulations, classical energy minimization, and spin-wave theory. We consider a number of different parameter sets, previously proposed to describe the magnetic behavior of $\alpha$-RuCl$_3$ and Na$_2$IrO$_3$ with their antiferromagnetic zigzag ground states. By classifying these parameter sets, we reveal the existence of three distinct mechanisms to stabilize zigzag states, which differ in the sign of the nearest-neighbor Kitaev interaction, the role of longer-range interactions, and the magnitude of the off-diagonal $\Gamma_1$ interaction. While experimentally hardly distinguishable at zero field, we find that the three different scenarios lead to significantly different magnetization processes in applied magnetic fields. In particular, we show that a sizable off-diagonal interaction $\Gamma_1 > 0$ naturally explains the strongly anisotropic field responses observed in $\alpha$-RuCl$_3$ without the need for a strong anisotropy in the effective $g$ tensor. Moreover, for a generic field direction, it leads to a high-field state with a finite transversal magnetization, which should be observable in $\alpha$-RuCl$_3$.

Modified Heisenberg model for the zig-zag structure in multiferroic RMn2O5

The class of RMn2O5 (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn4+ and Mn3+ magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.

Spin-asymmetric graphene nanoribbons in graphane on silicon dioxide

Hydrogenated graphene, graphane, is studied on an oxygen-terminated silicon dioxide substrate using ab initio calculations. The two lowest-energy structures with quarter and half monolayer hydrogen coverage are presented. We form zigzag graphene nanoribbons by selectively removing hydrogens from the epitaxial graphane layer. In these ribbons the spin degeneracy of the free-standing antiferromagnetic zigzag ribbons is broken, and band gaps of different magnitude emerge for the opposite spin species. This degeneracy breaking is due to a charge imbalance in the substrate below the ribbon, introduced through the asymmetric alignment of the substrate atoms with respect to the edges of the graphene ribbon. As the edge geometry is restricted by the neighboring graphane, the zigzag edges are robust to reconstructions that are suggested to destroy edge magnetism in free-standing graphene ribbons.

Magnetic structure of the zigzag chain familyNaxCa1−xV2O4determined by muon-spin rotation

We present muon-spin-rotation measurements on polycrystalline samples of the complete family of the antiferromagnetic (AF) zigzag chain compounds, ${\text{Na}}_{x}{\text{Ca}}_{1\ensuremath{-}x}{\text{V}}_{2}{\text{O}}_{4}$. In this family, we explore the magnetic properties from the metallic ${\text{NaV}}_{2}{\text{O}}_{4}$ to the insulating ${\text{CaV}}_{2}{\text{O}}_{4}$. We find a critical ${x}_{c}(\ensuremath{\sim}0.833)$ which separates the low and high Na-concentration-dependent transition temperature and its magnetic ground state. In the $x<{x}_{c}$ compounds, the magnetic ordered phase is characterized by a single homogenous phase and the formation of incommensurate spin-density-wave order. Whereas in the $x>{x}_{c}$ compounds, multiple subphases appear with temperature and $x$. Based on the muon data obtained in zero external magnetic field, a careful dipolar field simulation was able to reproduce the muon behavior and indicates a modulated helical incommensurate spin structure of the metallic AF phase. The incommensurate modulation period obtained by the simulation agrees with that determined by neutron diffraction.

Structure, Stability, Edge States, and Aromaticity of Graphene Ribbons

We determine the stability, the geometry, the electronic, and magnetic structure of hydrogen-terminated graphene-nanoribbon edges as a function of the hydrogen content of the environment by means of density functional theory. Antiferromagnetic zigzag ribbons are stable only at extremely low ultravacuum pressures. Under more standard conditions, the most stable structures are the mono- and dihydrogenated armchair edges and a zigzag edge reconstruction with one di- and two monohydrogenated sites. At high hydrogen concentration "bulk" graphene is not stable and spontaneously breaks to form ribbons, in analogy to the spontaneous breaking of graphene into small-width nanoribbons observed experimentally in solution. The stability and the existence of exotic edge electronic states and/or magnetism is rationalized in terms of simple concepts from organic chemistry (Clar's rule).