Next-nearest Neighbor Interactions Research Articles

Extreme sensitivity of the magnetic ground state to halide composition in FeCl3−xBrx

Mixed halide chemistry has recently been utilized to tune the intrinsic magnetic properties of transition-metal halides---one of the largest families of magnetic van der Waals materials. Prior studies have shown that the strength of exchange interactions, hence the critical temperature, can be tuned smoothly with halide composition for a given ground state. Here we show that the ground state itself can be altered by a small change of halide composition in ${\mathrm{FeCl}}_{3\ensuremath{-}x}{\mathrm{Br}}_{x}$. Specifically, we find a threefold jump in the N\'eel temperature and a sign change in the Weiss temperature at $x=0.08$ corresponding to only $3%$ bromine doping. Using neutron scattering, we reveal a change of the ground state from spiral order in ${\mathrm{FeCl}}_{3}$ to $A$-type antiferromagnetic order in ${\mathrm{FeBr}}_{3}$. From first-principles calculations, we show that a delicate balance between nearest and next-nearest neighbor interactions is responsible for such a transition. These results demonstrate how varying the halide composition can tune the competing interactions and change the ground state of a spiral spin liquid system.

Singular flat bands in the modified Haldane-Dice model

Flat bands can be divided into singular and non-singular ones according to the behavior of their Bloch wave function around band-crossing points in momentum space. We analyze the flat band in the Dice model, which can be tuned by a uniaxial strain in the zigzag direction and a Haldane-type next-nearest neighbor interaction, and derive the topological phase diagram of the modified Haldane-Dice model to obtain all band-gap closings with the central band. When the central band is flat, we determine its compact localized state and classify its behavior at all band-touching points by means of the Hilbert–Schmidt quantum distance. We find that the flat band remains singular for all band-touching points (topological phase transitions) with a maximal quantum distance and give expressions for the resulting non-contractible loop states on the real-space torus.

Gauge theory description of Rydberg atom arrays with a tunable blockade radius

We discuss a Rydberg atom chain with a tunable blockade radius from the gauge theoretic perspective. When the blockade radius is one lattice spacing, this system can be formulated in terms of the PXP model, and there is a $\mathbb{Z}_2$ Ising phase transition known to be equivalent to a confinement-deconfinement transition in a gauge theory, the lattice Schwinger model. Further increasing the blockade radius, one can add a next-nearest neighbor (NNN) interaction into the PXP model. We discuss the interpretation of NNN interaction in terms of the gauge theory and how finite NNN interaction alters the deconfinement behavior and propose a corresponding experimental protocol. When the blockade radius reaches two lattice spacing, the model reduces to the PPXPP model. A novel gauge theory equivalent to the PPXPP model is formulated, and the phases in the two formulations are delineated. These results are readily explored experimentally in Rydberg quantum simulators.

Phase diagram of the square 2D Ising lattice with nearest neighbor and next-nearest neighbor interactions

We have determined the temperature dependent phase diagram of the square 2D Ising lattice with anisotropic nearest neighbor () and isotropic next-nearest neighbor () interactions. The phase boundaries between the various ordered phases (ferromagnetic, antiferromagnetic and striped antiferromagnetic) and the disordered phase (paramagnetic) are obtained by considering the domain wall free energy. Although the phase boundary equations are not exact, they provide a very accurate description when the nearest neighbor interactions are stronger than the next-nearest neighbor interaction. The square 2D Ising lattice does not exhibit a phase transition when if and have the same sign or if and have opposite signs.

Simulating topological phases with atom arrays in an optical waveguide

In this paper, we employ the atomic arrays in one-dimensional optical waveguides to simulate topological phases, where the waveguide is modeled as a one-dimensional infinitely long coupled cavity array. Under the Markov approximation, the coherent and dissipative coupling between atoms is established by eliminating waveguide modes. When the detuning between atoms and cavity fields lies in the band gap, the dynamics of the system is completely dominated by the coherent interaction. Under this condition, we designed three atomic arrays with different geometries and show that the topologically trivial and non-trivial phases of atomic arrays can be simulated. Furthermore, by introducing periodic atomic driving, the topological phase transition can be induced by adjusting the driving parameters. Finally, we investigate the effect of next-nearest neighbor interactions on topological state transfer and find that the next-nearest neighbor interactions break the degenerated bandgap state and establish a topological state transfer channel.

Possible helimagnetic order in Co4+-containing perovskites Sr1−xCaxCoO3

We systematically synthesized perovskite-type oxides Sr1−xCaxCoO3 containing unusually high valence Co4+ ions by a high pressure technique and investigated the effect of systematic lattice change on the magnetic and electronic properties. As the Ca content x exceeds about 0.6, the structure changes from cubic to orthorhombic, which is supported by the first-principles calculations of enthalpy. Upon the orthorhombic distortion, the ground state remains to be apparently ferromagnetic, with a slight drop of the Curie temperature. Importantly, the compounds with x larger than 0.8 show antiferromagnetic behavior, with positive Weiss temperatures and nonlinear magnetization curves at the lowest temperature, implying that the ground state is non-collinear antiferromagnetic or helimagnetic. Considering the incoherent metallic behavior and the suppression of the electronic specific heat at the high x region, the possible emergence of a helimagnetic state in Sr1−xCaxCoO3 is discussed in terms of the bandwidth narrowing and the double-exchange mechanism with the negative charge transfer energy, as well as the spin frustration, owing to the next-nearest neighbor interaction.

Time oscillating magnetic field effect on critical behavior and dynamic phase transition of monolayer nanographene structure

ABSTRACT Dynamic magnetic properties of a ferrimagnetic mixed (1/2,1) Ising spin monolayer nanographene structure with a crystal-field interaction in a time oscillating magnetic field are studied by the use of the kinetic Monte Carlo simulation based on the Metropolis algorithm. Dynamic phase transitions are obtained, the effect of the next-nearest neighbor interactions, the crystal field, the amplitude, and the period of the external dynamic magnetic field on the critical and compensation behaviors and on the thermal variations of the dynamic order parameters are investigated. We have found that in the presence of the time oscillating field, the system may exhibit a dynamic phase transition from the ferrimagnetic to the paramagnetic phase at a critical point. The system may even present two dynamic compensation temperatures for appropriate values of the hamiltonian parameters. This behavior of dynamic compensation temperature has not been observed previously in published papers with kinetic Monte Carlo simulation.

Investigation of the monopole magneto-chemical potential in spin ices using capacitive torque magnetometry

The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength (Jeff) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho2Ti2O7, and show that the magneto-chemical potential depends on the spin sublattice (α or β), i.e., the Pauling state, involved in the transition. Monte Carlo simulations using the dipolar-spin-ice Hamiltonian support our findings of a sublattice-dependent magneto-chemical potential, but the model underestimates the Jeff for the β-sublattice. Additional simulations, including next-nearest neighbor interactions (J2), show that long-range exchange terms in the Hamiltonian are needed to describe the measurements. This demonstrates that torque magnetometry provides a sensitive test for Jeff and the spin-spin interactions that contribute to it.

Benchmark calculations of multiloop pseudofermion fRG

The pseudofermion functional renormalization group (pffRG) is a computational method for determining zero-temperature phase diagrams of frustrated quantum magnets. In a recent methodological advance, the commonly employed Katanin truncation of the flow equations was extended to include multiloop corrections, thereby capturing additional contributions from the three-particle vertex (Thoenniss et al. https://arxiv.org/abs/2011.01268; Kiese et al. https://arxiv.org/abs/2011.01269). This development has also stimulated significant progress in the numerical implementation of pffRG, allowing one to track the evolution of pseudofermion vertices under the renormalization group flow with unprecedented accuracy. However, cutting-edge solvers differ in their integration algorithms, heuristics to discretize Matsubara frequency grids, and more. To lend confidence in the numerical robustness of state-of-the-art multiloop pffRG codes, we present and compare results produced with two independently developed and algorithmically distinct solvers for Heisenberg models on three-dimensional lattice geometries. Using the cubic lattice Heisenberg (anti)ferromagnet with nearest and next-nearest neighbor interactions as a generic benchmark model, we find the two codes to quantitatively agree, often up to several orders of magnitude in digital precision, both on the level of spin-spin correlation functions and renormalized fermionic vertices for varying loop orders. These benchmark calculations further substantiate the usage of multiloop pffRG solvers to tackle unconventional forms of quantum magnetism.Graphic abstract

Phase transitions in the frustrated Potts model in the magnetic field

The influence of the magnetic field on phase transitions, magnetic and thermodynamic properties of the two-dimensional Potts model with q = 4 on a hexagonal lattice with the nearest and next-nearest neighbors interactions is studied using the replica algorithm of the Monte Carlo method . The studies are carried out in the magnetic field range −1.0 ≤ h ≤ 7.0 with a step of 0.1. A phase diagram of the magnetization dependence on magnetic field value is plotted. It is found that a first-order phase transition is observed in the ranges 0.0 ≤ h ≤ 1.0 and 2.0 ≤ h ≤ 3.5. A second-order phase transition is observed for the magnetic field value h = 1.5. It is revealed that there is no the ground-state degeneracy and the phase transition is smeared for magnetic field values of h ≥ 4.0. A phase diagram of the dependence of the critical temperature on the magnitude of the interaction of the next-nearest neighbors is constructed. • A two-dimensional frustrated Potts model are investigated. • The magnetic structures of the ground-state for considered model are obtained. • The phase diagram is plotted. • It is shown that magnetic fields destroyed the phase transition.

From SU(2)5 to SU(2)3 Wess-Zumino-Witten transitions in a frustrated spin- 52 chain

We investigate the properties of a frustrated spin-5/2 chain with next-nearest neighbor two and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possible presence of a critical floating phase at intermediate values of the next-nearest neighbor interaction. We provide strong evidence that the continuous transition into the dimerized phase, which has been found to be generically in the Wess-Zumino-Witten SU(2)$_{2S}$ universality class up to spin $S=2$, is SU(2)$_5$ only at two isolated points of the phase diagram, and that it is SU(2)$_3$ in between, in agreement with the presence of two relevant operators allowed by symmetry for SU(2)$_5$, and with the conservation of the parity of the level index along the renormalization flow between SU(2)$_k$ theories with different values of $k$. We also find that the dimerization induced by the next-nearest neighbor interaction is a three step process, with first a small partially dimerized phase followed by a broad critical floating phase with incommensurate correlations before the fully dimerized phase is reached. Implications for the iron oxide ${\mathrm{Bi}}_{3}{\mathrm{FeMo}}_{2}{\mathrm{O}}_{12}$ are briefly discussed.

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.

Loss of classicality in alternating spin-/spin-1 chain, in the presence of next-neighbor couplings and Dzyaloshinskii–Moriya interactions

We have considered and alternating spin-/spin-1 chain with nearest-neighbor (NN) (J 1), next-nearest neighbor (NNN) (J 2) antiferromagnetic (AFM) Heisenberg interactions along with z-component of the Dzyaloshinskii–Moriya (DM) (Dz ) interaction. The Hamiltonian has been studied using (a) linear spin-wave theory and (b) density matrix renormalization group. The system had been reported earlier as a classical ferrimagnet only when NN exchange interactions are present. Both the AFM NNN interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero J 2 introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of J 1 along with Dz introduces a short range order but develops long range order along the XY plane. J 1 along with J 2 induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the D z term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.

Critical temperature of one-dimensional Ising model with long-range interaction revisited

We present a generalized expression for the transfer matrix of finite and infinite one-dimensional spin chains within a magnetic field with spin pair interaction J/rp, where r∈{1,2,3,…,nv} is the distance between two spins, nv is the number of nearest neighbors reached by the interaction, and 1≤p≤2. Using this transfer matrix, we calculate the partition function, the Helmholtz free energy, and the specific heat for both finite and infinite ferromagnetic 1D Ising models within a zero external magnetic field. We focus on the temperature Tmax where the specific heat reaches its maximum, needed to compute J/(kBTmax) numerically for every value of nv∈{1,2,3,…,30}, which we interpolate and then extrapolate up to the critical temperature as a function of p, by using a novel inter-extrapolation function. We use two different procedures to reach the infinite spin chain with an infinite interaction range: increasing the chain size as well as the interaction range by the same amount and increasing the interaction range for the infinite chain. As we expected, both extrapolations lead to the same critical temperature within their uncertainties by two different concurrent curves. Critical temperatures fall within the upper and lower bounds reported in the literature, showing a better coincidence with many existing approximations for p close to 1 than the p values near 2. It is worth mentioning that the well-known cases for nearest (original Ising model) and next-nearest neighbor interactions are recovered doing nv=1 and nv=2, respectively.

Simulation of cellular-dendritic solidification structures of binary alloys in three-dimensional growth using a multiparticle diffusion-limited aggregation model

Abstract Solidification in binary alloy melts was simulated with two different three-dimensional models, that differ in the way the role of the solid/liquid interface energy on the solidification is expressed: either surface rearrangement or a surface curvature-dependent attachment probability was applied. In the melt, the simultaneous diffusion of all diffusing particles (atoms) was taken into account. Cellular –dendritic growth modes, as observed in practice, could be well simulated. The surface rearrangement model is essential for exhibiting details (as facetting) and the effect of the next-nearest neighbour interaction.

Multiple magnetization plateaus induced by farther neighbor interactions in an S=1 two-leg Heisenberg spin ladder

We study the magnetization process of the $S=1$ Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.

Influence of the next-nearest neighbor and the boson–boson interactions on U-shaped, W-shaped profile and modulation instability gain spectra in a zig–zag optical lattice

In this paper, we employ the auxiliary equation method (AEM) to show the leverage of the nearest neighbors hopping and the boson–boson interaction in a zig zag optical lattice on the stressed optical solitons (os) and the Modulation Instability (MI) gain of cold bosonic atoms. The pedestal of the work is set on the continuum approximation of a cold bosonic atoms in a zig zag optical lattice which has demonstrated in detailed in refs. [Tala-Tebue E, Rezazadeh H, Djoufack ZI, et al. Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44; Djoufack ZI, TalaTebue E, FotsaNgafo F, et al. Quantum breathers associated with modulational instability in 1D ultracold boson in optical lattices involving nextnearest neighbor interactions. Optik 164(2018):575–589]. The results collected have enclosed bright, dark optical solitons and the combined bright-dark and bright-bright optical solitons. Compared the acquired results with Tala-Tebue et al. [Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44], further the os including U-shaped and W-shaped profile have been drop in and the powerful of the nearest neighbors hopping and the boson–boson interaction has been exposed across the spatiotemporal and plot evolution of the bright and dark os. Therewith, the MI bands have been stressed and it is observed some new attitude of the MI gain spectra under the induction of the model parameters. The collected results are new in literature in our knowledge and will improve the previous results acquired in refs. [Tala-Tebue E, Rezazadeh H, Djoufack ZI, et al. Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44; Djoufack ZI, TalaTebue E, FotsaNgafo F, et al. Quantum breathers associated with modulational instability in 1D ultracold boson in optical lattices involving nextnearest neighbor interactions. Optik 164(2018):575–589; Zhao XH, Tian B, Liu DY, et al. Dark solitons interaction for a (2+1)-dimensional nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain. Superlattices Microstruct 100(2016):587–595; Uddin MF, Hafez MG, Hammouch Z, et al. Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness. Waves Random Complex Media 2020. https://doi.org/10.1080/17455030.2020.1722331; Inc M, Aliyu AI, Yusuf A. Optical solitons to the nonlinear Shrdingers equation with spatio-temporal dispersion using complex amplitude ansatz. J Mod Opt 2017;64(21):2273–2280].

Magnetic Field Effect on Topological Spin Excitations in CrI3

The search for topological spin excitations in recently discovered two-dimensional (2D) van der Waals (vdW) magnetic materials is important because of their potential applications in dissipation-less spintronics. In the 2D vdW ferromagnetic (FM) honeycomb lattice CrI$_3$(T$_C$= 61 K), acoustic and optical spin waves were found to be separated by a gap at the Dirac points. The presence of such a gap is a signature of topological spin excitations if it arises from the next nearest neighbor(NNN) Dzyaloshinskii-Moriya (DM) or bond-angle dependent Kitaev interactions within the Cr honeycomb lattice. Alternatively, the gap is suggested to arise from an electron correlation effect not associated with topological spin excitations. Here we use inelastic neutron scattering to conclusively demonstrate that the Kitaev interactions and electron correlation effects cannot describe spin waves, Dirac gap and their in-plane magnetic field dependence. Our results support the DM interactions being the microscopic origin of the observed Dirac gap. Moreover, we find that the nearest neighbor (NN) magnetic exchange interactions along the axis are antiferromagnetic (AF)and the NNN interactions are FM. Therefore, our results unveil the origin of the observedcaxisAF order in thin layers of CrI$_3$, firmly determine the microscopic spin interactions in bulk CrI$_3$, and provide a new understanding of topology-driven spin excitations in 2D vdW magnets.

Distribution of Cracks in a Chain of Atoms at Low Temperature

We consider a one-dimensional classical many-body system with interaction potential of Lennard–Jones type in the thermodynamic limit at low temperature 1/beta in (0,infty ). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of Nexp (- beta e_mathrm {surf}/2) with e_mathrm {surf}>0 a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.

Two-dimensional Bose-Hubbard model for helium on graphene

An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a systems of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons $(U\approx\infty)$, repulsive nearest-neighbor $(V>0)$ and small attractive $(V'<0)$ next-nearest neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively point-like, the detailed microscopic form of the short range electrostatic and long range dispersion interactions in the helium-graphene system are crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of $^4$He adsorbed on graphene deep in the commensurate solid phase with $1/3$ of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.