Next-nearest Neighbor Research Articles

Partial phase transition and quantum effects in helimagnetic films under an applied magnetic field

We study the phase transition in a helimagnetic film with Heisenberg spins under an applied magnetic field in the c direction perpendicular to the film. The helical structure is due to the antiferromagnetic interaction between next-nearest neighbors in the c direction. Helimagnetic films in zero field are known to have a strong modification of the in-plane helical angle near the film surfaces. We show that spins react to a moderate applied magnetic field by creating a particular spin configuration along the c axis. With increasing temperature (T), using Monte Carlo simulations we show that the system undergoes a phase transition triggered by the destruction of the ordering of a number of layers. This partial phase transition is shown to be intimately related to the ground-state spin structure. We show why some layers undergo a phase transition while others do not. The Green's function method for non collinear magnets is also carried out to investigate effects of quantum fluctuations. Non-uniform zero-point spin contractions and a crossover of layer magnetizations at low T are shown and discussed.

Critical and compensation behavior of a mixed spin-3/2 and spin-5/2 Ising ferrimagnetic system in a graphene layer

We have studied the magnetic properties of the mixed spin σ=±32,±12 and spin S=±52,±32,±12 Ising ferrimagnetic system in a graphene layer by means of Monte Carlo simulations. The effects of next-nearest neighbors exchange interactions and crystal field anisotropy on the critical and compensation behavior of the system have been investigated. The results show that, for a system with given values of the crystal field anisotropy and exchange interaction constants, a compensation point only exists if the values of the spins in the ground state are such that |S|>|σ| and Jσ is higher than a certain value Jσmin. It was shown that the relationship between Jσmin and JS is linear for a given value of the crystal field constant. The compensation and the critical temperature are very sensitive to the change of JS and Jσ, respectively, while the crystal field anisotropy affects both temperatures to a large extent.

Model analysis of magnetic susceptibility of Sr2IrO4 : A two-dimensional Jeff=12 Heisenberg system with competing interlayer couplings

We report the analysis of magnetic susceptibility $\chi$($T$) of Sr$_2$IrO$_4$ single crystal in the paramagnetic phase. We formulate the theoretical susceptibility based on isotropic Heisenberg antiferromagnetism incorporating the Dzyaloshinsky-Moriya interaction exactly, and include the interlayer couplings in a mean-field approximation. $\chi$($T$) above $T_{\rm N}$ was found to be well described by the model, indicating the predominant Heisenberg exchange consistent with the microscopic theory. The analysis points to a competition of nearest and next-nearest neighbor interlayer couplings, which results in the up-up-down-down configuration of the in-plane canting moments identified by the diffraction experiments.

Topological Phases of Spin-1/2 Ferromagnetic–Antiferromagnetic Alternating Heisenberg Chains with Alternating Next-Nearest-Neighbour Interaction

A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the $\Delta$-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and trivial phases. It is found that the ground state phases boundaries are insensitive to the strength of the alternation in next-nearest neighbor interaction. These results are consistent with the analysis based on the nonlinear $\sigma$ model and exact solution on the ferromagnetic-nonmagnetic phase boundary.

Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: Pseudofermion functional renormalization group perspective

Quantum magnets on kagome lattice geometries in two and three spatial dimensions are archetypal examples of spin systems in which geometric frustration inhibits conventional magnetic ordering and instead benefits the emergence of long-range entangled spin liquids at low temperature. Here we employ a recently developed pseudo-fermion functional renormalization group (pf-FRG) approach to study the low-temperature quantum magnetism of kagome and hyperkagome spin systems with exchange interactions beyond the nearest neighbor coupling. We find that next-nearest neighbor couplings stabilize a variety of magnetic orders as well as induce additional spin liquid regimes giving rise to rather rich phase diagrams, which we characterize in detail. On a technical level, we find that the pf-FRG approach is in excellent quantitative agreement with high-temperature series expansions over their range of validity and it exhibits a systematic finite-size convergence in the temperature regime below. We discuss notable advantages and some current limitations of the pf-FRG approach in the ongoing search for unconventional forms of quantum magnetism.

Bosonic self-energy functional theory

We derive the self-energy functional theory for bosonic lattice systems with broken $U(1)$ symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamical-mean field theory when constraining to local fields, whereas when neglecting kinetic contributions of non-condensed bosons it reduces to the static mean-field approximation. To benchmark the theory we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest neighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase-boundaries, and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings we propose self-energy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g. in the presence of non-trivial gauge fields or frustration). Self-energy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters, but nevertheless remain computable by modest means.

Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain

We report on a detailed investigation of the spin-1 $J_1-J_2-J_3$ Heisenberg model, a frustrated model with nearest-neighbor coupling $J_1$, next-nearest neighbor coupling $J_2$, and a three site interaction $J_3\left[({\bf S}_{i-1}\cdot {\bf S}_i)({\bf S}_i\cdot {\bf S}_{i+1})+{\mathrm H.c.}\right]$ previously studied in [Phys. Rev. B 93, 241108(R) (2016)]. Using DMRG and exact diagonalizations, we show that the phase boundaries between the Haldane phase, the next-nearest neighbor Haldane phase and the dimerized phase can be very accurately determined by combining the information deduced from the dimerization, the ground-state energy, the entanglement spectrum and the Berry phase. By a careful investigation of the finite-size spectrum, we also show that the transition between the next-nearest neighbor Haldane phase and the dimerized phase is in the Ising universality class all along the critical line. Furthermore, we justify the conformal embedding of the $SU(2)_2$ Wess-Zumino-Witten conformal field theory in terms of a boson and an Ising field, and we explicitly derive a number of consequences of this embedding for the spectrum along the $SU(2)_2$ transition line between the Haldane phase and the dimerized phase. We also show that the solitons along the first-order transition line between the Haldane phase and the dimerized phase carry a spin-1/2, while those between different dimerization domains inside the dimerized phase carry a spin 1. Finally, we show that short-range correlations change character in the Haldane and dimerized phases through disorder and Lifshitz lines, as well as through the development of short-range dimer correlations in the Haldane phase, leading to a remarkably rich phase diagram.

Coordination of the Mn4+-Center in Layered Li[Co0.98Mn0.02]O2 Cathode Materials for Lithium-Ion Batteries

Abstract The local coordination of the manganese in Li[Co0.98Mn0.02]O2 cathode materials for lithium-ion batteries has been investigated by means of a joint XRD and multi-frequency electron paramagnetic resonance (EPR) characterization approach. EPR showed the manganese being in a tetravalent high-spin Mn4+-oxidation state with S = 3 2 . $S = {3 \over 2}.$ The set of spin-Hamiltonian parameters obtained from the multi-frequency EPR analysis with Larmor frequencies ranging between 9.4 and 406 GHz is transformed into structural information by means of the recently introduced Monte-Carlo Newman-superposition modeling. Based on this analysis, the Mn4+ are shown being incorporated for the Co3+-sites, i.e. acting as donor-type functional centers Mn Co • ${\rm{Mn}}_{{\rm{Co}}}^ \bullet $ . In that respect, for Mn4+ the negative sign of the axial second-order fine-structure interaction parameter B 2 0 $B_2^0$ is indicative of an elongated oxygen octahedron in its first coordination sphere, whereas B 2 0 > 0 $B_2^0 > 0$ rather points to a compressed octahedron coordinated about the Mn4+-centers. Furthermore, the results obtained here suggest that the oxygen octahedron about the Mn4+-ion is slightly distorted as compared to the CoO6 octahedron. Concerning the coordination to next-nearest neighbor ions, part of the manganese resides in manganese-rich domains, whereas the for the remaining centers the Co3+-site is randomly occupied with Co/Mn according to the effective stoichiometry of the compound. Finally, a structural stability range emerges from the Newman-modeling that supports the discussed ability of manganese to act as an structure-stabilizing element in layered oxides.

Comment on “Frustration and multicriticality in the antiferromagnetic spin-1 chain”

The phase diagram of the spin-1 chain with bilinear-biquadratic and next-nearest neighbor inter- actions, recently investigated by Pixley, Shashi and Nevidomskyy [Phys. Rev. B 90, 214426 (2014)], has been revisited in the light of results we have recently obtained on a similar model. Combining extensive Density Matrix Renormalization Group (DMRG) simulations with conformal-field theory arguments, we confirm the presence of the three phases identified by Pixley et al, a Haldane phase, a next-nearest neighbor (NNN) Haldane phase, and a dimerized phase, but we come to significantly different conclusions regarding the nature of the phase transitions to the dimerized phase: i) We provide numerical evidence of a continuous Ising transition between the NNN-Haldane phase and the dimerized phase; ii) We show that the tri-critical end point, where the continuous transition between the Haldane phase and the dimerized phase turns into a first order transition, is distinct from the triple point where the three phases meet; iii) Finally, we demonstrate that the tri-critical end point is in the same Wess-Zumino-Witten (WZW) SU(2) level 2 universality class as the continuous transition line that ends at this point

Bond disorder, frustration and polymorphism in the spontaneous crystallization of a polymer melt

The isothermal, isobaric spontaneous crystallization of a supercooled polymer melt is investigated by molecular-dynamics simulation of an ensemble of fully-flexible linear chains. Frustration is introduced via two incommensurate length scales set by the bond length and the position of the minimum of the non-bonding potential. Marked polymorphism with considerable bond disorder, distortions of both the local packing and the global monomer arrangements is observed. The analyses in terms of: i) orientational order parameters characterizing the global and the local order and ii) the angular distribution of the next-nearest neighbors of a monomer reach the conclusion that the polymorphs are arranged in distorted Bcc-like lattices.

Influence of frustrations on the thermodynamic properties of the low-dimensional Potts model studied by computer simulation

Influence of disorder in the form of frustration on the thermodynamic behavior of a two-dimensional three-vertex Potts model has been studied by the Monte Carlo method, taking into account the nearest and next-nearest neighbors. Systems with linear sizes of L × L = N (L = 9–48) on a triangular lattice have been considered. It has been shown that in the case of J1 > 0 and J2 < 0 frustrations appear in the spin system within the interval of 0.5 ≤ |r| ≤ 1.0. The model undergoes a phase transition outside this region.

Phase diagram of the ferrimagnetic mixed-spin Blume-Capel model with four-spin and next-nearest neighbor interactions

A finite cluster approximation based on a single cluster theory is developed for a ferrimagnetic mixed spin-1/2 and spin-1 Blume-Capel model with four-spin interaction J4 and next-nearest neighbor couplings J’. The state equations are derived for the two-dimensional square lattice and the phase diagram is explored. We found that the system can exhibits both critical and tricritical behavior according to appropriate values of J’, D and J4.

Search for the Heisenberg spin glass on rewired cubic lattices with antiferromagnetic interaction

Spin glass (SG) is a typical magnetic system which is mainly characterized by a frozen random spin orientation at low temperatures. Frustration and randomness are considered to be the key ingredients for the existence of SGs. Previously, Bartolozzi et al. [Phys. Rev. B73, 224419 (2006)] found that the antiferromagnetic (AF) Ising spins on scale free network (SFN) exhibited SG behavior. This is purely AF system, a new type of SG different from the canonical one which requires the presence of both FM and AF couplings. In this new system, frustration is purely due to a topological factor and its randomness is brought by irregular connectivity. Recently, it was reported that the AF Heisenberg model on SFN exhibited SG behavior [Surungan et al., JPCS, 640, 012005 (2015)/doi:10.1088/1742-6596/640/1/012005]. In order to accommodate the notion of spatial dimension, we further investigated this type of system by studying an AF Heisenberg model on rewired cubic lattices, constructed by adding one extra bond randomly connecting each spin to one of its next-nearest neighbors. We used Replica Exchange algorithm of Monte Carlo Method and calculated the SG order parameter to search for the existence of SG phase.

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.

Exact Solution to Spin Squeezing of the Arbitrary-Range Spin Interaction and Transverse Field Model**Supported by the National Natural Science Foundation of China under Grant No 51427801.

We investigate spin squeezing effects of trapped ions in an off-resonance optical potential system using the arbitrary range spin—spin interaction and transverse field model. The collective spin noises at any time are analyzed exactly. The general expression of spin squeezing factor is presented for arbitrary-range spin interaction. For the nearest-neighbor and next-nearest neighbor spin interaction model, the analytic solutions are reduced from the general expressions. It is shown that the maximum spin squeezing is enhanced for the general arbitrary-range spin interaction compared with the nearest-neighbor interaction model as the long-range interaction with arbitrary sites enforces stronger correlation.

Structure and Magnetic Behavior of Layered Honeycomb Tellurates, BiM(III)TeO6 (M = Cr, Mn, Fe).

New layered honeycomb tellurates, BiM(III)TeO6 (M = Cr, Mn, Fe) were synthesized and characterized. BiM(III)TeO6 (M = Cr, Fe) species crystallize in a trigonal space group, P3̅1c (No. 163), of edge-sharing M3+/Te6+O6 octahedra, which form honeycomb-like double layers in the ab plane with Bi3+ cations located between the layers. Interestingly, the structure of BiMnTeO6 is similar to those of the Cr/Fe analogues, but with monoclinic space group, P21/c (No. 14), attributed to the strong Jahn-Teller distortion of Mn3+ cations. The crystal structure of BiM(III)TeO6 is a superstructure of PbSb2O6-related materials (ABB'O6). The Cr3+ and Fe3+ cations are ordered 80% and 90%, respectively, while the Mn3+ ions are completely ordered on the B-site of the ABB'O6 structure. BiCrTeO6 shows a broad antiferromagnetic transition (AFM) at ∼17 K with a Weiss temperature (θ) of -59.85 K, while BiFeTeO6 and BiMnTeO6 show sharp AFM transitions at ∼11 K with θ of -27.56 K and at ∼9.5 K with θ of -17.57 K, respectively. These differences in the magnetic behavior are ascribed to the different concentration of magnetic nearest versus next-nearest neighbor interactions of magnetic cations due to the relative differences in the extent of M/Te ordering.

Universal behavior of the Shannon mutual information in nonintegrable self-dual quantum chains

An existing conjecture states that the Shannon mutual information contained in the ground state wavefunction of conformally invariant quantum chains, on periodic lattices, has a leading finite-size scaling behavior that, similarly as the von Neumann entanglement entropy, depends on the value of the central charge of the underlying conformal field theory describing the physical properties. This conjecture applies whenever the ground state wavefunction is expressed in some special basis (conformal basis). Its formulation comes mainly from numerical evidences on exactly integrable quantum chains. In this paper the above conjecture was tested for several general non-integrable quantum chains. We introduce new families of self-dual $Z(Q)$ symmetric quantum chains ($Q=2,3,\ldots$). These quantum chains contain nearest neighbour as well next-nearest neighbour interactions (coupling constant $p$). In the cases $Q=2$ and $Q=3$ they are extensions of the standard quantum Ising and 3-state Potts chains, respectively. For $Q=4$ and $Q\geq 5$ they are extensions of the Ashkin-Teller and $Z(Q)$ parafermionic quantum chains. Our studies indicate that these models are interesting on their own. They are critical, conformally invariant, and share the same universality class in a continuous critical line. Moreover, our numerical analysis for $Q=2-8$ indicate that the Shannon mutual information exhibits the conjectured behaviour irrespective if the conformally invariant quantum chain is exactly integrable or not. For completeness we also calculated, for these new families of quantum chains, the two existing generalizations of the Shannon mutual information, which are based on the R\'enyi entropy and on the R\'enyi divergence.

Superconducting Phase Diagram of the Paramagnetic One-Band Hubbard Model

We study spin-fluctuation-mediated superconductivity in the one-band Hubbard model. Higher-order effective interactions in U give rise to a superconducting instability which is very sensitive to changes in the Fermi surface topology arising as a function of doping and changes in the band structure. We show the superconducting phase diagram as a function of doping and next-nearest neighbor hopping in the limit of very small Coulomb interaction strength and discuss peculiarities arising at the phase boundaries separating different superconducting domains.

The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model.

Allowing a single electron to hop to next-nearest neighbours (NNN) in addition to the closest atomic sites in the Holstein model, a modified Trugman method is applied to exactly calculate the effect on the polaronic effective mass in one, two, and three dimensions, building on the previous study of the one-dimensional NNN Holstein model. We also present perturbative calculations and a heuristic scaling factor for the coupling strength and ion frequency to nearly map the NNN Holstein model back onto the original Holstein model. When account is taken of the modified electronic bandwidth near the electron energy, we find that including NNN hopping effectively increases the polaron effective mass.

Knots in finite memory walks

We investigate the occurrence and size of knots in a continuum polymer model with finite memory via Monte Carlo simulations. Excluded volume interactions are local and extend only to a fixed number of successive beads along the chain, ensuring that at short length scales the excluded volume effect dominates, while at longer length scales the polymer behaves like a random walk. As such, this model may be useful for understanding the behavior of polymers in a melt or semi-dilute solution, where exactly the same crossover is believed to occur. In particular, finite memory walks allow us to investigate the role of local interactions in the transition from highly knotted ideal polymers to almost unknotted self-avoiding polymers. Even though knotting decreases substantially when a few next-nearest neighbor interactions are considered, we find that the knotting probability of a polymer chain of modest length of 500 steps only decays slowly as a function of the range of the excluded volume interaction. In this context, we also find evidence that for length scales up to the interaction length the knotting behavior of the finite memory walk resembles that of a self-avoiding walk (effectively suppressing small knots), while for larger length scales it resembles that of a random walk.