Third-neighbor Interactions Research Articles

Effects of third-neighbor interactions on the frustrated quantum Ising model.

We investigate thermal and quantum phase transitions of the J_{1}-J_{2}-J_{3} transverse Ising model on the square lattice. The model is studied within a cluster mean-field decoupling, which allows us to describe phase diagrams and the free-energy landscape in the neighborhood of phase transitions. Our findings indicate that the third-neighbor coupling (J_{3}) can affect the nature of phase transitions of the model. In particular, ferromagnetic third-neighbor couplings favor the onset of continuous order-disorder phase transitions, eliminating the tricritical point of the superantiferromagnetic-paramagnetic (SAFM-PM) phase boundary. On the other hand, the enhancement of frustration introduced by weak antiferromagnetic J_{3} gives rise to the staggered dimer phase favoring the onset of discontinuous classical phase transitions. Moreover, we find that quantum annealed criticality (QAC), which takes place when the classical discontinuous phase transition becomes critical by the enhancement of quantum fluctuations introduced by the transverse magnetic field, is eliminated from the SAFM-PM phase boundary by a relatively weak ferromagnetic J_{3}. Nevertheless, this change in the nature of phase transitions can still be observed in the presence of antiferromagnetic third-neighbor couplings being also found in the staggered-dimer phase boundary. Therefore, our findings support that QAC persists under the presence of frustrated antiferromagnetic third-neighbor couplings and is suppressed when these couplings are ferromagnetic, suggesting that frustration plays a central role in the onset of QAC.

Frustration and ordering in Ising chain in an external magnetic field with third-neighbor interactions

In this paper, the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice in an external magnetic field are investigated, taking into account the exchange interactions of atomic spins at the sites of the first, second, and third neighbors. Exact analytical expressions for the thermodynamic functions of the system are obtained by the Kramers–Wannier transfer-matrix method. A magnetic phase diagram of the ground state of such a spin system is constructed and studied thoroughly. The points and lines of frustrations of the system depending on the values and signs of exchange interactions and on an external magnetic field are found. The criteria for the occurrence of magnetic frustrations in the presence of competition between the energies of exchange interactions and an external magnetic field are formulated. The peculiar features are investigated and the values of entropy and magnetization of the ground state of this model are obtained in the frustration regime and beyond it. Various types of behavior of entropy, magnetization, and magnetic susceptibility depending on the model parameters are revealed.

Discrete modulation instability and localized modes in chiral molecular chains with first- and third-neighbor interactions

In this paper, we examined the behavior of the modulated wave patterns and nonlinear supratransmission phenomenon in gyrotropy molecular chains where the first-neighbor and third-neighbor interactions are considered. We have established the propagation modes through the dispersion law showing two cutoff frequencies. Through the numerical simulation, we have depicted modulated waves, solitons interaction as well as the modulation instability growth rates brought by the variation of the third-neighbor interaction and effective mass. As it was predicted that the group velocities vanish at the carrier waves, we have uncoupled a system of the coupled nonlinear Schrödinger equation by neglecting the elastic interaction to drive one end of the chains. The driven amplitude generates the train of waves in the system. For a specific time of propagation, we have shown how the variation of driven amplitude can induce instability in the forbidden gap. The obtained results have opened new features to the train of pulses in gyrotropy molecular chains.

Ab initio guided minimal model for the “Kitaev” material BaCo2 ( AsO4)2 : Importance of direct hopping, third-neighbor exchange, and quantum fluctuations

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 third-neighbor interactions, both isotropic and anisotropic, that are responsible for the standout double-zigzag ground state of BaCo$_2$(AsO$_4$)$_2$, stabilized by quantum fluctuations. A significantly large third-nearest neighbor hopping, observed in {\it ab initio}, supports the importance of the third-neighbor interactions in the stabilization of the unique ground state of BaCo$_2$(AsO$_4$)$_2$.

Frustration-induced complexity in order-disorder transitions of the J_{1}-J_{2}-J_{3} Ising model on the square lattice.

We revisit the field-free Ising model on a square lattice with up to third-neighbor (NNNN) interactions, also known as the J_{1}-J_{2}-J_{3} model, in the mean-field approximation. Using a systematic enumeration procedure, we show that the region of phase space in which the high-temperature disordered phase is stable against all modes representing periodic magnetization patterns up to a given size is a convex polytope that can be obtained by solving a standard vertex enumeration problem. Each face of this polytope corresponds to a set of coupling constants for which a single set of modes, equivalent up to a symmetry of the lattice, bifurcates from the disordered solution. While the structure of this polytope is simple in the half-space J_{3}>0, where the NNNN interaction is ferromagnetic, it becomes increasingly complex in the half-space J_{3}<0, where the antiferromagnetic NNNN interaction induces strong frustration. We then pass to the limit N→∞ giving a closed-form description of the order-disorder surface in the thermodynamic limit, which shows that for J_{3}<0, the emergent ordered phases will have a "devil's surface"-like mode structure. Finally, using Monte Carlo simulations, we show that for small periodic systems, the mean-field analysis correctly predicts the dominant modes of the ordered phases that develop for coupling constants associated with the centroid of the faces of the disorder polytope.

Frustrations in the Ising chain with the third-neighbor interactions

We study the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice, taking into account the exchange interactions of atomic spins at the sites of the nearest, next-nearest, and third neighbors. The exact analytical expressions for the thermodynamic functions of the system are obtained using the Kramers-Wannier transfer matrix technique. Criteria for the emergence of magnetic frustrations in the presence of competition between the energies of exchange interactions are formulated. The points and intervals of the existence of frustrations, which depend on the values and signs of the exchange interactions, are found. The features of the entropy and heat capacity of this model in the frustration regime and its vicinity are investigated. Non-zero entropy values of the ground state of a frustrated system, as well as a two-peak temperature structure of the heat capacity in the vicinity of the frustration point, are found.

Emergent snake magnetic domains in canted kagome ice

We study the two-dimensional kagome-ice model derived from a pyrochlore lattice with second- and third-neighbor interactions. The canted moments align along the local $\langle 111 \rangle$ axes of the pyrochlore and respond to both in-plane and out-of-plane external fields. We find that the combination of further-neighbor interactions together with the external fields introduces a rich phase diagram with different spin textures. Close to the phase boundaries, metastable $\textit{"snake"}$ domains emerge with extremely long relaxation time. Our kinetic Monte Carlo analysis of the magnetic-field quench process from saturated state shows unusually slow dynamics. Despite that the interior spins are almost frozen in snake domains, the spins on the edge are free to fluctuate locally, leading to frequent creation and annihilation of monopole-anti-monopole bound states. Once the domains are formed, these excitations are localized and can hardly propagate due to the energy barrier of snakes. The emergence of such snake domains may shed light on the experimental observation of dipolar spin ice under tilted fields, and provide a new strategy to manipulate both spin and charge textures in artificial spin ice.

Effect of perturbations on the kagome S=12 antiferromagnet at all temperatures

The ground state of the $S=\frac{1}{2}$ kagome Heisenberg antiferromagnet is now recognized as a spin liquid, but its precise nature remains unsettled, even if more and more clues point towards a gapless spin liquid. We use high-temperature series expansions (HTSEs) to extrapolate the specific heat ${c}_{V}(T)$ and the magnetic susceptibility $\ensuremath{\chi}(T)$ over the full temperature range, using an improved entropy method with a self-determination of the ground-state energy per site ${e}_{0}$. Optimized algorithms give HTSE coefficients up to unprecedented orders (20 in $1/T$) and as exact functions of the magnetic field. Three extrapolations are presented for different low-$T$ behaviors of ${c}_{V}$: exponential (for a gapped system), and linear or quadratic (for two different types of gapless spin liquids). We study the effects of various perturbations to the Heisenberg Hamiltonian: Ising anisotropy, Dzyaloshinskii-Moriya interactions, second- and third-neighbor interactions, and randomly distributed magnetic vacancies. We propose an experimental determination of $\ensuremath{\chi}(T=0)$, which could be nonzero, from ${c}_{V}$ measurements under different magnetic fields.

Magnetotransport in Fe-intercalated TS2 : Comparison between T=Ti and Ta

Sharp magnetization switching and large magnetoresistance (MR) were previously discovered in single crystals of 2H-${\mathrm{Fe}}_{x}{\mathrm{TaS}}_{2}$ and attributed to the Fe superstructure and its defects. We report similar sharp switching and large MR in 1T-${\mathrm{Fe}}_{x}{\mathrm{TiS}}_{2}$ ($0.086\phantom{\rule{0.28em}{0ex}}\ensuremath{\le}\phantom{\rule{0.28em}{0ex}}x\phantom{\rule{0.28em}{0ex}}\ensuremath{\le}0.703$) while providing a side-by-side comparison of the only two such ferromagnetic transition-metal dichalcogenides. The switching field ${H}_{s}$ and MR values are similar in both 1T-${\mathrm{Fe}}_{x}{\mathrm{TiS}}_{2}$ and 2H-${\mathrm{Fe}}_{x}{\mathrm{TaS}}_{2}$, with a larger than expected bowtie $\ensuremath{\rho}(H)$ and a sharper hysteresis loop for $H\ensuremath{\parallel}c$ in the former. The Curie and Weiss temperatures remain roughly constant below $x\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}1/3$ in the $T=\text{Ti}$ single crystals before increasing monotonically for higher $x$, while ${H}_{s}$ and MR reach maxima where defects in the superstructure exist, or a minimum near superstructure compositions, and they remain constant above $x\ensuremath{\sim}0.4$. Despite previous reports, electron diffraction shows only the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ superstructure in 1T-${\mathrm{Fe}}_{x}{\mathrm{TiS}}_{2}$. Glassy behavior is shown to coexist within the ferromagnetic state in 1T-${\mathrm{Fe}}_{x}{\mathrm{TiS}}_{2}$ for compositions between 0.1 and 0.703. A simple theoretical model considering first-, second- and third-neighbor interactions yields a phase diagram that accounts for both spin glass behavior and different superstructures.

Model of directed lines for square ice with second-neighbor and third-neighbor interactions

The investigation of the properties of nanoconfined systems is one of the most rapidly developing scientific fields. Recently it has been established that water monolayer between two graphene sheets forms square ice. Because of the energetic disadvantage, in the structure of the square ice there are no longitudinally arranged molecules. The result is that the structure is formed by unidirectional straight-lines of hydrogen bonds only. A simple but accurate discrete model of square ice with second-neighbor and third-neighbor interactions is proposed. According to this model, the ground state includes all configurations which do not contain three neighboring unidirectional chains of hydrogen bonds. Each triplet increases the energy by the same value. This new model differs from an analogous model with long-range interactions where in the ground state all neighboring chains are antiparallel. The new model is suitable for the corresponding system of point electric (and magnetic) dipoles on the square lattice. It allows separately estimating the different contributions to the total binding energy and helps to understand the properties of infinite monolayers and finite nanostructures. Calculations of the binding energy for square ice and for point dipole system are performed using the packages TINKER and LAMMPS.

Lifshitz Transition in Topological Insulators with Second and Third-Neighbor Interactions

Lifshitz Transition in Topological Insulators with Second and Third-Neighbor Interactions

Stripe order on the spin-1 stacked honeycomb lattice inBa2Ni(PO4)2

We report a comprehensive investigation of the crystal structure and magnetic behavior of the $S=1$ compound ${\mathrm{Ba}}_{2}\mathrm{Ni}{({\mathrm{PO}}_{4})}_{2}$ with a honeycomblike topology of the spin lattice. Magnetic susceptibility and specific-heat data reveal two successive transitions at ${T}_{N1}=5\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and ${T}_{N2}=4.6\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. Additionally, these data demonstrate a broad peak at ${T}_{max}\ensuremath{\sim}8\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, indicative of the short-range magnetic order above ${T}_{N1}$, whereas below ${T}_{N1}$ field-induced transitions around 4 and 10 T are identified from the magnetization measurements. Neutron diffraction in zero field establishes stripe antiferromagnetic order below ${T}_{N2}$ with the ordered moment of $1.75(8){\ensuremath{\mu}}_{B}/{\mathrm{Ni}}^{2+}$ at 1.5 K. Density-functional band-structure calculations reveal the leading interaction ${J}_{3}=3.5\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ running perpendicular to the honeycomb planes, and weaker interactions ${J}_{1}=0.5\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and ${J}_{4}=1.8\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ within the honeycomb planes, whereas the stripe order is stabilized by the diagonal interlayer interaction ${J}_{2}=1.3\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ that frustrates ${J}_{1}$. This is in contrast to the usually expected scenario where the competing second- and third-neighbor interactions on the honeycomb lattice stabilize the stripe order. The ${\mathrm{Ni}}^{2+}$ ions feature a sizable easy-plane anisotropy $A\ensuremath{\simeq}10.5\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, but the position of the easy plane changes from one atom to another, thus amplifying magnetic frustration.

Influence of quantum phase transition on spin conductivity in the anisotropic three-dimensional ferromagnetic model

We use the SU(3) Schwinger boson formalism to study the spin transport in the three-dimensional S=1 Heisenberg ferromagnet in the cubic lattice with an easy plane crystal field, considering first-, second- and third-neighbor interactions. We have got one single peak for the spin conductivity for this system at ω=ωk and a variation of the height of the peak with the parameters Dc and η, and hence an influence of the quantum phase transition, between the disordered paramagnetic phase and the ordered ones, on the spin conductivity of this system. We have considered the exchange interaction J1 as ferromagnetic and the interactions J2 and J3 as antiferromagnetic.

Emergent quasi-one-dimensionality in a kagome magnet: A simple route to complexity

We study the ground state phase diagram of the quantum spin-$1/2$ Heisenberg model on the kagom\'{e} lattice with first- ($J_1 < 0$), second- ($J_2 < 0$), and third-neighbor interactions ($J_d > 0$) by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the $J_d$-dominant regime in terms of three sets of spin chains weakly coupled by the ferromagnetic inter-chain interactions $J_{1,2}$. When either $J_1$ or $J_2$ is dominant, the model is found to support one of two cuboctohedral phases, cuboc1 and cuboc2. These cuboc states host non-coplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime $J_1 \simeq J_2$, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional (2d) quantum antiferromagnet. We find no evidence of either the one-dimensional (1d) gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean field theories.

Frustrations and Phase Transitions in Low-Dimensional Magnetic Systems

We studied magnetic orderings and frustrations on 1D chain and 2D lattices: square, triangular, kagome, and hexagonal in the Ising, 3-state Potts and standard 4-state Potts models. The spins interrelate with one another via the nearest-neighbor, the next-nearest-neighbor or the third-neighbor exchange interactions and by an external magnetic field. For problem solving we mainly calculated the entropy and specific heat using the rigorous analytical solutions for maximum eigenvalue of Kramers-Wannier transfer-matrix and exploiting computer simulation, par excellence, by Wang-Landau algorithm. Whether a system is ordered or frustrated is related to the signs and values of exchange interactions. An external magnetic field may both favor the ordering of a system and create frustrations. With the help of calculations of the entropy, the specific heat and magnetic parameters, we obtained the points and ranges of frustrations, the frustration fields and the phase transition points. The results obtained also show that the same exchange interactions my either be competing or noncompeting which depends on the topology of a lattice.

Phase Diagram of Modulated Structures in Ferroelectric Crystals Based on Quantum Ising Model with Third-Neighbor Interactions

Incommensurate–commensurate phase transitions are analyzed using a model derived from the normal coordinate Hamiltonian for a crystal lattice. The Hamiltonian consists of a local self-potential and effective third-neighbor interactions. Free energies of various modulated phases are calculated with a mean-field approximation under the condition that two quantum states within the local potential are important at low temperature. It is demonstrated that the quantum effect works to stabilize the incommensurate phase rather than the commensurate phase. Even at zero temperature, the incommensurate phase can occupy a finite region in the phase diagram. This situation is similar to quantum paraelectricity in some ferroelectrics, and can be expected as a general feature of modulated structures of dielectric crystals. The phase diagram for ferroic first- and third-neighbor interactions but antiferroic second-neighbor interactions is constructed theoretically and is discussed in detail to explain qualitatively the l...

Stoichiometry engineering of ternary oxide ultrathin films:BaxTi2O3on Au(111)

Ternary oxide ${\mathrm{Ba}}_{x}{\mathrm{Ti}}_{2}{\mathrm{O}}_{3}$ ultrathin films on Au(111) substrates $(x\ensuremath{\le}2/3)$ have been studied using a joint experimental and theoretical approach, including the use of scanning tunneling microscopy (STM), first principles calculations, and Monte Carlo simulations. The films are created by first covering the Au(111) substrate with a ${\mathrm{Ti}}_{2}{\mathrm{O}}_{3}\phantom{\rule{0.28em}{0ex}}(2\ifmmode\times\else\texttimes\fi{}2)$ honeycomb (HC) network and then evaporating low concentrations of Ba atoms onto this film. STM imaging shows that the Ba atoms adsorb individually in the hollow sites of the HC network. Depending on the Ba coverage $x$, which ranges from 0 to 2/3, two ordered phases can be identified at $x=1/3$ and $x=2/3$. A disordered labyrinthlike phase is observed for values of $x$ between 1/3 and 2/3. Theoretical modeling shows that the structural character of these films is driven by the charge transfer that occurs between the electropositive Ba atoms and the electronegative ${\mathrm{Ti}}_{2}{\mathrm{O}}_{3}$/Au substrate. This results in a number of calculated effects including an increase in the film rumpling and a reduction of the film work function with increasing $x$. The evolution of the structure of the thin films as a function of Ba coverage can be described by a lattice gas model with first-, second-, and third-neighbor Ba-Ba repulsive interactions. The range of the dipolar interactions is a key factor in understanding the behavior of Ba ordering. The structural and electronic flexibility, which can be engineered through stoichiometry, temperature, or support control, makes these ultrathin films promising materials for applications related to adsorption or reactivity, or as template supports for the growth of size-selected clusters.

Ising model on a square lattice with second-neighbor and third-neighbor interactions

We studied the phase transitions and magnetic properties of the Ising model on a square lattice by the replica Monte Carlo method and by the method of transfer-matrix, the maximum eigenvalue of which was found by Lanczos method. The competing exchange interactions between nearest neighbors J1, second J2, third neighbors J3 and an external magnetic field were taken into account. We found the frustration points and expressions for the frustration fields, at crossing of which cardinal changes of magnetic structures (translational invariance changes discontinuously) take place. A comparative analysis with 1D Ising model was performed and it was shown that the behavior of magnetic properties of the 1D model and the 2D model with J1 and J3 interactions reveals detailed similarity only distinguishing in scales of magnetic field and temperature.

Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice

We study the quantum phase diagram of the spin-$1/2$ Heisenberg model on the kagom\'e lattice with first-, second-, and third-neighbor interactions $J_1$, $J_2$, and $J_3$ by means of density matrix renormalization group. For small $J_2$ and $J_3$, this model sustains a time-reversal invariant quantum spin liquid phase. With increasing $J_2$ and $J_3$, we find in addition a $q=(0,0)$ N\'{e}el phase, a chiral spin liquid phase, a valence-bond crystal phase, and a complex non-coplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first order phase transition. The transitions from the chiral spin liquid to both the $q=(0,0)$ phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions.

Distinct spin liquids and their transitions in spin-1/2 XXZ kagome antiferromagnets.

By using the density matrix renormalization group approach, we study spin-liquid phases of spin-1/2 XXZ kagome antiferromagnets. We find that the emergence of the spin-liquid phase is independent of the anisotropy of the XXZ interaction. In particular, the two extreme limits-the Ising (a strong S^{z} interaction) and the XY (zero S^{z} interaction)-host the same spin-liquid phases as the isotropic Heisenberg model. Both a time-reversal-invariant spin liquid and a chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show that they evolve continuously into each other by tuning the second- and the third-neighbor interactions. And last, we discuss possible implications of our results for the nature of spin liquid in nearest-neighbor XXZ kagome antiferromagnets, including the nearest-neighbor spin-1/2 kagome antiferromagnetic Heisenberg model.