Biquadratic Interaction Research Articles

Exactly solvable mixed-spin Ising-Heisenberg diamond chain with biquadratic interactions and single-ion anisotropy

An exactly solvable variant of mixed spin-(1/2,1) Ising-Heisenberg diamond chain is considered. Vertical spin-1 dimers are taken as quantum ones with Heisenberg bilinear and biquadratic interactions and with single-ion anisotropy, while all interactions between spin-1 and spin-1/2 residing on the intermediate sites are taken in the Ising form. The detailed analysis of the $T=0$ ground state phase diagram is presented. The phase diagrams have shown to be rather rich, demonstrating large variety of ground states: saturated one, three ferrimagnetic with magnetization equal to 3/5 and another four ferrimagnetic ground states with magnetization equal to 1/5. There are also two frustrated macroscopically degenerated ground states which could exist at zero magnetic filed. Solving the model exactly within classical transfer-matrix formalism we obtain an exact expressions for all thermodynamic function of the system. The thermodynamic properties of the model have been described exactly by exact calculation of partition function within the direct classical transfer-matrix formalism, the entries of transfer matrix, in their turn, contain the information about quantum states of vertical spin-1 XXZ dimer (eigenvalues of local hamiltonian for vertical link).

Consistent model of magnetism in ferropnictides

The discovery of superconductivity in LaFeAsO introduced the ferropnictides as a major new class of superconducting compounds with critical temperatures second only to cuprates. The presence of magnetic iron makes ferropnictides radically different from cuprates. Antiferromagnetism of the parent compounds strongly suggests that superconductivity and magnetism are closely related. However, the character of magnetic interactions and spin fluctuations in ferropnictides, in spite of vigorous efforts, has until now resisted understanding within any conventional model of magnetism. Here we show that the most puzzling features can be naturally reconciled within a rather simple effective spin model with biquadratic interactions, which is consistent with electronic structure calculations. By going beyond the Heisenberg model, this description explains numerous experimentally observed properties, including the peculiarities of the spin wave spectrum, thin domain walls, crossover from first to second order phase transition under doping in some compounds, and offers new insight in the occurrence of the nematic phase above the antiferromagnetic phase transition.

Deconfined criticality for theS=1spin model on the spatially anisotropic triangular lattice

The quantum $S=1$ spin model on the spatially anisotropic triangular lattice is investigated numerically. The nematic and valence-bond-solid (VBS) phases are realized by adjusting the spatial anisotropy and the biquadratic interaction. The phase transition between the nematic and VBS phases is expected to be a continuous one with unconventional critical indices (deconfined criticality). The geometrical character (spatial anisotropy) is taken into account by imposing the screw-boundary condition (Novotny's method). Diagonalizing the finite-size cluster with $N\ensuremath{\leqslant}20$ spins, we observe a clear indication of continuous phase transition. The correlation-length critical exponent is estimated as $\ensuremath{\nu}=0.92(10)$.

Exotic phases induced by strong spin-orbit coupling in ordered double perovskites

We construct and analyze a microscopic model for insulating rocksalt ordered double perovskites, with the chemical formula ${A}_{2}B{B}^{\ensuremath{'}}{\text{O}}_{6}$, where the ${B}^{\ensuremath{'}}$ atom has a $4{d}^{1}$ or $5{d}^{1}$ electronic configuration and forms a face-centered-cubic lattice. The combination of the triply degenerate ${t}_{2g}$ orbital and strong spin-orbit coupling forms local quadruplets with an effective spin moment $j=3/2$. Moreover, due to strongly orbital-dependent exchange, the effective spins have substantial biquadratic and bicubic interactions (fourth and sixth order in the spins, respectively). This leads, at the mean-field level, to three main phases: an unusual antiferromagnet with dominant octupolar order, a ferromagnetic phase with magnetization along the [110] direction, and a nonmagnetic but quadrupolar ordered phase, which is stabilized by thermal fluctuations and intermediate temperatures. All these phases have a two-sublattice structure described by the ordering wave vector $\mathbit{Q}=2\ensuremath{\pi}(001)$. We consider quantum fluctuations and argue that in the regime of dominant antiferromagnetic exchange, a nonmagnetic valence-bond solid or quantum-spin-liquid state may be favored instead. Candidate quantum-spin-liquid states and their basic properties are described. We also address the effect of single-site anisotropy driven by lattice distortions. Existing and possible future experiments are discussed in light of these results.

Isotropic Non-Heisenberg Behavior in M3(dpa)4Cl2 Extended Metal Atom Chains

Isotropic deviations to the standard Heisenberg Hamiltonian have been extracted for a series of trinuclear extended metal atom chain complexes, namely, [Ni(3)(dpa)(4)Cl(2)], and the hypothetical [NiPdNi(dpa)(4)Cl(2)] and [Pd(3)(dpa)(4)Cl(2)], following a scheme recently proposed by Labéguerie and co-workers (J. Chem. Phys 2008, 129, 154110) within the density functional theory framework. Energy calculations of broken symmetry monodeterminantal solutions of intermediate M(s,tot.) values can provide an estimate of the magnitude of the biquadratic exchange interaction (λ) that accounts for these deviations in systems with S = 1 magnetic sites. With the B3LYP functional, we obtain λ = 1.37, 13.8, and 498 cm(-1) for the three molecules, respectively, meaning that a simple Heisenberg Hamiltonian is enough for describing the magnetic behavior of the Ni(3) complex but definitely not for Pd(3). In the latter case, the origin of such extreme deviation arises from (i) an energetically affordable local non-Hund state (small intrasite exchange integral, K ∼ 1960 cm(-1)) and (ii) a very effective overlap between Pd-4d orbitals and a large J. Furthermore, this procedure enables us to determine the relative weights of the two types of magnetic interactions, σ- and δ-like, that contribute to the total magnetic exchange (J = J(σ) + J(δ)). In all of the systems, J is governed by the σ interaction by 95-98%.

Time-reversal symmetry-breaking in two-band superconductors

Competition between an interband Josephson interaction and a biquadratic interband interaction can break time-reversal symmetry when the interband interactions are very weak compared with the intraband interaction. We demonstrate this using the phenomenological Ginzburg–Landau free energy, taking into account terms essential for this phenomenon. This time-reversal symmetry-breaking state peels away a sheet of an interband phase difference soliton wall. This sheet is the domain wall between two different chiral states. The peeling reduces the formation energy of the domain wall. The domain wall can simultaneously erase the Meissner effect and the specific heat jump when the entropy invokes many domain walls, and its life time is prolonged by a pinning owing to an inhomogeneity such as surface roughness.

Relaxation theory of spin-3/2 Ising system near phase transition temperatures

Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics. First, the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures, i.e. the first- and second-order and the tricritical points. Then, the Onsager theory is applied to the model and the kinetic or rate equations are obtained. By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points. Moreover, the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically, and they are found to be in good agrement.

Frustrated Classical Heisenberg andXYModels in Two Dimensions with Nearest-Neighbor Biquadratic Exchange: Exact Solution for the Ground-State Phase Diagram

The ground-state phase diagram is determined exactly for the frustrated classical Heisenberg model plus nearest-neighbor biquadratic exchange interactions on a two-dimensional lattice. A square- and a rhombic-symmetry version are considered. There appear ferromagnetic, incommensurate-spiral, "up-up-down-down" (UUDD), and canted ferromagnetic states, a nonspiral coplanar state that is an ordered vortex lattice, plus a noncoplanar ordered state (a "conical vortex lattice"). In the rhombic case, which adds biquadratic terms to the Heisenberg model used widely for insulating manganites, the UUDD state found is the E-type state observed; this, along with accounting essentially for the variety of ground states observed in these materials, shows that this model probably contains the long-sought mechanism behind the UUDD state.

Phase transitions as a function of material constants and temperature in intermetallic compounds of the terfenol-D type

A model of magnetic and magnetoelastic properties of intermetallic compounds has been considered with the inclusion of the influence of the “giant” magnetoelastic coupling and the biquadratic exchange interaction. The phase transitions as a function of material constants and temperature have been investigated in the framework of the proposed model. It has been demonstrated that the ferromagnetic and quadrupole phases can be formed in the system under consideration. In this case, the phase transition between these phases is a first-order transition and occurs through the intermediate, i.e., quadrupole-ferromagnetic, state. The dependences of the phase transition temperature on the Heisenberg and biquadratic exchange interaction constants have been obtained for compounds of the terfenol-D type.

Magnetic and neutron spectroscopic properties of the tetrameric nickel compound[Mo12O28(μ2-OH)9(μ3-OH)3{Ni(H2O)3}4]⋅13H2O

We present results of inelastic neutron scattering experiments performed for the compound $[{\text{Mo}}_{12}{\text{O}}_{28}{({\ensuremath{\mu}}_{2}\text{-OH})}_{9}{({\ensuremath{\mu}}_{3}\text{-OH})}_{3}{{\text{Ni}{({\text{H}}_{2}\text{O})}_{3}}}_{4}]\ensuremath{\cdot}13{\text{H}}_{2}\text{O}$, which is a molecular magnet with antiferromagnetically coupled ${\text{Ni}}^{2+}$ ions forming nearly ideal tetrahedra in a diamagnetic molybdate matrix. The neutron spectroscopic data are analyzed together with high-field magnetization data (taken from the literature), which exhibit four steps at non-equidistant field intervals. The experimental data can be excellently described by antiferromagnetic Heisenberg-type exchange interactions as well as an axial single-ion anisotropy within a distorted tetrahedron of ${\text{Ni}}^{2+}$ ions characterized by x-ray single-crystal diffraction. Our analysis contrasts to recently proposed models, which are based on the existence of extremely large biquadratic (and three-ion) exchange interactions and/or on a strong field dependence of the Heisenberg coupling parameters.

Spiral magnetic structure in Heisenberg and non-Heisenberg magnets

The possibility of forming a modulated (spiral) magnetic structure in anisotropic Heisenberg and non-Heisenberg magnets with a frustrated Heisenberg exchange interaction has been investigated. It has been demonstrated that, apart from homogeneous (ferromagnetic and quadrupole) states, the Heisenberg magnets with a strong easy-plane anisotropy can have a spiral magnetic structure. The axis of the spiral coincides with the direction of the external magnetic field. The inclusion of the biquadratic exchange interaction leads to a narrowing of the magnetic field region of the existence of the spiral structure. In the absence of the external magnetic field, the spiral structure can be formed only in the case of easy-axis anisotropy.

Criticality of the [formula omitted]-dimensional [formula omitted] transverse-field Ising model with extended interactions: Suppression of corrections to scaling

The criticality of the ( 2 + 1 ) -dimensional S = 1 transverse-field Ising model is investigated with the numerical diagonalization method. The scaling behavior is improved by tuning the coupling-constant parameters; the S = 1 spin model allows us to incorporate a variety of interactions such as the single-ion anisotropy and the biquadratic interactions. Simulating the clusters with N = 6 , 8 , … , 20 spins, we estimate the critical indices as 1 / ν = 1.586 ( 6 ) and η = 0.034 ( 4 ) .

Coupled spin–phonon excitations in helical multiferroics

AbstractBoth the Dzyaloshiskii–Moriya interaction and the exchange striction are shown to affect dynamically the magnetoelectric excitations in the helical multiferroics. The exchange striction results in a biquadratic interaction between the spins and the transverse phonons, giving rise to quantum fluctuations of the ferroelectric polarization P. This leads to low‐lying phonon modes that are perpendicular to P and to the helical spins at small wave vector but are parallel to P at a wave vector close to the magnetic modulation vector. For spin‐1/2 helimagnet, the local polarization can be completely reversed by the spin fluctuation, and so does the direction of the on‐site spin chirality, which allows for a finite differential scattering intensity of polarized neutrons from a cycloidal magnet.

Magnetic behavior of a spin-1 Blume-Emery-Griffiths model

I study the one-dimensional spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field under an applied magnetic field. This model can be exactly mapped into a tight-binding Hubbard model - extended to include intersite interactions - provided one renormalizes the chemical and the on-site potentials, which become temperature dependent. After this transformation, I provide the exact solution of the Blume-Emery-Griffiths model in one dimension by means of the Green's functions and equations of motion formalism. I investigate the magnetic variations of physical quantities - such as magnetization, quadrupolar moment, susceptibility - for different values of the interaction parameters and of the applied field, focusing on the role played by the biquadratic interaction in the breakdown of the magnetization plateaus.

Monte Carlo simulations of the Spin-2 Blume-Emery-Griffiths model

The magnetic properties of the spin S = 2 Ising system with the bilinear exchange interaction J1SizSjz, the biquadratic exchange interaction J2Siz2Sjz2 and the single-ion anisotropy DSiz2are discussed by making use of the Monte Carlo (MC) simulation for the magnetization <Sz>, sub-lattice magnetizations <Sz(A)> and <Sz(B)>, the magnetic specific heat CM and spin structures. This Ising spin system of S = 2 with interactions J1 and J2 and with anisotropy D corresponds to the spin-2 Blume-Emery-Griffiths model. The phase diagram of this Ising spin system on a two-dimensional square lattice has been obtained for exchange parameter J2/J1 and anisotropy parameter D/J1. The shapes of the temperature dependence of sublattice magnetizations <Sz(A)> and <Sz(B)> are related with abnormal behavior of temperature dependence of <Sz> at low temperatures and affected significantly by the single-ion anisotropy D. The staggered quadrupolar (SQ) ordering turns out to be different largely between Ising systems with the single-ion anisotropy (D ≠ 0) and without the one (D = 0).

Searching for Si-based spintronics by first principles calculations

Density functional theory (DFT) calculations are used to study the epitaxial growth and the magnetic properties of thin films of MnSi on the Si(001) surface. For adsorption of a single Mn atom, we find that binding at the subsurface site below the Si surface dimers is the most stable adsorption site. There is an energy barrier of only 0.3 eV for adsorbed Mn to go subsurface, and an energy barrier of 1.3 eV for penetration to deeper layers. From the calculated potential-energy surface for the Mn adatom we conclude that the most stable site on the surface corresponds to the hollow site where Mn is placed between two Si surface dimers. Despite Si(001) geometrically being an anisotropic surface, the on-surface diffusion for both directions along and perpendicular to the Si dimer rows has almost the same diffusion barrier of 0.65 eV. For coverage above 1 ML, the lowest energy structure is a pure Mn subsurface layer, capped by a layer of Si adatoms. We conclude that the Mn-silicide films stabilize in an epitaxially CsCl-like (B2) crystal structure. Such MnSi films are found to have sizable magnetic moments at the Mn atoms near the surface and interface, and ferromagnetic coupling of the Mn clarify within the layers. Layer-resolved electronic densities-of-states are presented that show a high degree of spin polarization at the Fermi level, up to 30 and 50% for films with one or two MnSi films, respectively.In order to clarify the stability of ferromagnetism at finite temperatures we estimate the Curie temperature (Tc) of MnSi films using a multiple-sublattice Heisenberg model with first- and second-nearest neighbor interactions determined from DFT calculations for various collinear spin configurations. The Curie temperature is calculated both in the mean-field approximation (MFA) and in the random-phase approximation (RPA). In the latter case, we find a weak logarithmic dependence of Tc on the magnetic anisotropy parameter, which was calculated to be 0.4 meV. Large Curie temperatures of above 200 K for a monolayer MnSi film, and above 300 K for a 2 ML MnSi film are obtained within the RPA, and even higher values in MFA.Complementary calculations are performed for non-collinear spin structures to study the limitations of the mapping of the system onto a Heisenberg model. We demonstrate that biquadratic interatomic exchange interactions and longitudinal fluctuations of atomic moments give important contributions to the energetics of the system.

Dynamic phase diagrams of a mixed spin-1 and spin-5/2 Ising system in an oscillating magnetic field

We study the nonequilibrium aspects of the kinetics of a mixed spin-1 and spin-5/2 Ising system, including the biquadratic nearest-neighbor pair interaction (K) and the crystal-field interaction (D), under the presence of a time-dependent oscillating external magnetic field within a mean-field approach. The set of mean-field dynamic equations is obtained by employing the Glauber transition rates. We investigate the time variations of the average order parameters to find the phases in the system. We also study the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the phase transitions and to obtain the dynamic phase transition (DPT) points. The dynamic phase diagrams are presented in three dierent planes. The phase diagrams are discussed, and a comparison is made with the results of other kinetic mixed spin Ising systems.

Finite-Temperature Transition in the Spin-Dimer Antiferromagnet BaCuSi2O6

We consider a classical XY-like Hamiltonian on a body-centered tetragonal lattice, focusing on the role of interlayer frustration. A three-dimensional (3D) ordered phase is realized via thermal fluctuations, breaking the mirror-image reflection symmetry in addition to the XY symmetry. A heuristic field-theoretical model of the transition has a decoupled fixed point in the 3D XY universality, and our Monte Carlo simulation suggests that there is such a temperature region where long-wavelength fluctuations can be described by this fixed point. However, it is shown using scaling arguments that the decoupled fixed point is unstable against a fluctuation-induced biquadratic interaction, indicating that a crossover to nontrivial critical phenomena with different exponents appears as one approaches the critical point beyond the transient temperature region. This new scenario clearly contradicts the previous notion of the 3D XY universality.

Influence of magnetic dipole and magnetoelastic interactions on the phase states of 2D non-Heisenberg ferromagnetic with complex exchange interactions

The phase states of the 2D non-Heisenberg ferromagnetic with anisotropic bilinear and biquadratic exchange interactions are investigated. The limiting cases of the system under consideration are the two-dimensional XY-model with biquadratic exchange interaction and the isotropic Heisenberg ferromagnetic. The account of the magnetic dipole interaction leads to the realization of spatially inhomogeneous quadrupolar phase. The stability regions of various phase transitions for different values of the material parameters are studied. The phase diagram is built. Besides, the temperature phase transitions are investigated. The influence of the magnetoelastic interaction on the formation of the long-range quadrupolar order is determined.

Frustrated classical Heisenberg model in one dimension with nearest-neighbor biquadratic exchange: Exact solution for the ground-state phase diagram

The ground-state phase diagram is determined exactly for the frustrated classical Heisenberg chain with added nearest-neighbor biquadratic exchange interactions. There appear ferromagnetic, incommensurate-spiral, ``up-up-down-down'' (uudd) phases, and disordered states. The model contains an isotropic version of the antiferromagnetic next-nearest-neighbor Ising model, i.e., an isotropic Ising model. It is closely related to a model proposed for some manganites, suggesting a possible mechanism for the observed uudd state.