Nearest-neighbour Exchange Interactions Research Articles

Staircases of magnetic structure along the axial direction in the layered magnet Rb2MnF4

The authors present new results of neutron scattering experiments on the magnetic structure of the layered antiferromagnet Rb2MnF4. The results show mixed stacking patterns of spin arrangements along the axial c direction, that is udud. . ., uuuu. . . and uuduud. . . (u=up, d=down), below its Neel temperature. A possible interpretation for this novel phenomenon is that it is due to the competition between antiferromagnetic nearest-neighbour exchange interaction and long-ranged ferromagnetic dipolar interactions in the axial c direction, which would give rise to the staircase behaviour.

Magnetic excitations in the Ising-like layer compound (Co( γ-CH3-C5H4NO)6)(ClO4)2

The results of ESR experiments on the 2D antiferromagnetic Ising system (Co( gamma -CH3-C5H4NO)6)(ClO4)2 in the temperature range 1.2-4.2 K are reported. The observed absorption signals are found to originate from single-spin reversals and can be associated with nearest-neighbour configurations of different forms. The magnetic field dependence of the excitation energies has been interpreted on the basis of a rectangular (2D) Ising lattice with nearest-neighbour exchange interactions. The signal intensities show a behaviour that can qualitatively be explained in terms of the predictions for a 2D Ising model.

Exchange interactions in BaFe12O19

In the scope of the mean field approximation the nine nearest neighbour exchange interactions existing among the ferric ions in BaFe12O19 hexagonal ferrite have been determined from the experimental sublattice magnetizations. It is shown that these exchange interactions are well explained by means of the superexchange theory. It is also concluded that some direct exchange interaction does exist among the octahedral 4f VI ions. The calculated magnetization, paramagnetic susceptibility, and Curie temperature are in good agreement with the corresponding experimental values. The stability of the collinear Gorter-type magnetic structure of BaFe12O19 is discussed as well.

Dynamical algebra of spin waves in localised-spin models

The idea of the spectrum generating algebra (SGA) is used to study the low-lying excitations in various localised-spin models of ferromagnetic, ferrimagnetic and antiferromagnetic solids. The noncompact algebra SO(2,1) approximately SU(1,1) is found to generate the spin wave or the magnon spectrum for ferromagnetic, ferrimagnetic and antiferromagnetic Bravais lattices with nearest-neighbour exchange interactions (Heisenberg model). The ferromagnetic case is treated including dipolar interactions in the model. For a quadratic antiferromagnet with easy-plane anisotropy the SGA is found to be the direct product SO(2,1)(X)SO(2,1) approximately SO(2,2). For the XY and the Heisenberg-Ising models of an antiferromagnetic linear chain the SGA is the compact counterpart of SO(2,1), i.e. SO(3) approximately SU(2). It is concluded that if the magnons are quantised as bosons then the SGA is the noncompact algebra SO(2,1), and if they are quantised as fermions then the SGA is the compact angular momentum algebra SO(3).

Monte Carlo studies of spin glasses with nonaxial anisotropy

Monte Carlo simulations are performed on two- and three-dimensional vector spin glasses with nearest-neighbour random gaussian exchange interactions and single-ion nonaxial anisotropy. Models with site-independent anisotropy energy, D, and with random, +or-D, site-dependent anisotropy are studied. The resulting phase diagrams differ in detail from the mean-field theory but retain the feature of a double transition. Variation of ordering temperature with simulation run-time indicates that the observed transitions are non-equilibrium phenomena.

Spin-Lattice Coupling in an Ising Chain with Nearest Neighbour and Next Nearest Neighbour Exchange Interactions

A one-dimensional Ising chain in which nearest neighbour (n.n.) and next nearest neighbour (n.n.n.) exchange interactions depend linearly on the distance between the spins is considered. The magnetic field and temperature dependence of the chain length is exactly calculated by use of a transfer matrix. It is shown that the chain length changes variously because of the competition among the n.n. and n.n.n. exchange interactions and the magnetic field. The zero-temperature phase diagram is also determined, which is composed of four spin states ↑, ↑↓, ↑↑↓ and ↑↑↓↓ (the smallest units of repetitions are shown). Dimerization and trimerization of the lattice are found in the ↑↑↓↓ and ↑↑↓ states respectively.

Temperature-dependent fourth moment of the relaxation function for cubic Heisenberg paramagnets

Useful expressions, solely in terms of appropriate lattice Green functions, are derived for the fourth moment of the relaxation function of a Heisenberg paramagnet having cubic symmetry (s.c., b.c.c. and f.c.c.) and nearest-neighbour exchange interactions. As is customary, the temperature dependence was estimated on the basis of the spherical model and with a simple random-phase type decoupling of the four-spin correlation functions.

The spin-Hamiltonian parameter temperature dependence of the EPR spectra of Gd3+ impurity ions in Y(OH)3 and Eu(OH)3

The 9.23 GHz electron paramagnetic resonance (EPR) spectrum of ~1% Gd3+ impurity ions in Y(OH)3 and Eu(OH)3 monocrystals has been measured from 11 to 296 K. These spectra have been analyzed using a C3h symmetry, phenomenological spin-Hamiltonian. The temperature variation of the spin-Hamiltonian parameters was fitted to empirical root-mean-square (rms) best-fit expressions. It was found that the g values are linear functions of the temperature and that the nearest neighbour (nn) exchange interaction, Jnn = +0.23(5) cm−1 for (Gd3+−Eu3+) ion pairs, can be estimated from the single ion data. This is in satisfactory agreement with Jnn = +0.06(9) cm−1 obtained from ion pair data. The temperature variation of the zero field splitting (ZFS) parameters B20 and B40was found to fit cubic expressions over the temperature measurement interval and the magnitude of B20 increased as the temperature increased, corroborating the earlier conclusion that the host lattice effect in the Ln(OH)3 series cannot be explained using a point charge model for the crystalline electric field.

Charge Density Wave-Soliton Model for Se and Te

A new microscopic theory is proposed for the electronic and lattice structures of crystal and defects of Se and Te. Consideration of the valence bond picture shows that electron correlation in valence P electrons produces a charge density wave (CDW) of vector nature, the vector CDW (VCDW), which has the period of three and keeps every atom neutral. Defects including valence alternation pairs and recombinations of helical chains may be generated as' low energy solitonic excitations of the VCDW. Amorphous Se and Te may be regarded as an assembly of solitonic excitations in the VCDW. A formulation of the VCDW and its soli tonic excitations is given in the HF approximation. Valence P electrons are described by an INDO type Hamiltonian with the nearest neighbour transfer and exchange interactions, intraatomic Coulomb repulsion and exchange and interatomic Coulomb repulsion. The remaining closed shell part of each atom is represented as a core with a repulsive potential. The lattice geometry is determined by the balance of the cohesive force of P electrons and the repulsion of cores. The effective intraatomic Coulomb interaction in a neutral atom has the form of a negative on-site interaction which stabilizes the VCDW. An equation is obtained which determines self-consistently the electronic and lattice structures of the VCDW and its solitonic defects. The VCDW and its defects always accompany not only an electron density modulation but also a bond order modulation so that they have lattice structures distorted from a standard cubic lattice. The trigonal lattice of the crystalline Se and Te can be explained as due to the presence of the VCDW.

The spin-peierls critical temperature in an XY quasi-one-dimensional system with nearest and next-nearest neighbour interactions

The mean field critical temperature for the spin-Peierls phase transition in the XY antiferromagnetic chain is obtained for nearest and next nearest neighbour exchange interaction. An increase in T c is predicted for next nearest neighbour antiferromagnetic exchange and a decrease is obtained for ferromagnetic exchange. This model is applied to the alkali-TCNQ salts, which are treated in the framework of the highly correlated Hubbard model.

Theory of Electronic Structures and Lattice Distortions in Polyacetylene and Itinerant Peierls Systems. II: Coulomb Interaction Dependences of the HF Ground State, Lattice Dimerization and 1Bu Excited State in Regular Trans-Polyacetylene

We study the Coulomb interaction dependences of the HF ground state, lattice dimerization and I Bu excited state in regular trans-poly acetylene using the PPP hamiltonian model developed in a previous paper. The nature of the HF ground state is determined by the relative magnitudes of the on site and nearest neighbour parts and the screening of the longer range part of the effective Coulomb potential. The Coulomb interaction with relatively large nearest neighbour part and not too strongly screened longer range part induces lattice dimerization. The driving force of the Coulomb induced dimerization is the nearest neighbour exchange interaction. The lattice dimerization in polyacetylene is due to the Coulomb mechanism. The SSH model is implicitly taking into account the nearest neighbour exchange interac­ tion. The Franck-Condon band gap is mostly determined by the nearest neighbour exchange interaction. The IBu excited state is excitonic. The exciton binding energy is estimated for the effective Coulomb potential with the screened long range part. It is not large owing to very small effective mass of electron and hole. To explain the observed I Bu excitation energy, the short range part of the effective Coulomb potential must be screened by about half compared to the one in small conjugate molecules. The condition for splitting of the exciton into a zwitter­ ionic pair of charged solitons is discussed.

Theory of Electronic Structures and Lattice Distortions in Polyacetylene and Itinerant Peierls Systems. I: UHF Transfer Matrix Method Adapted to the Long Range Coulomb Interaction and UHF States in Regular Bond Alternated Lattice

We develop in this series a theory of itinerant Peierls systems that mainly aims to study polyacetylene. In order to investigate roles of the long range Coulomb interaction in electronic structures and lattice distortions in a Peierls system, we develop a transfer matrix technique adapted to the. unrestricted Hartree·Fock (UHF) approximation. The method makes it pos­ sible to calculate UHF states and equilibrium lattice geometries in a lattice with any aperiodic structure due to the presence of solitons. Applying the method, we obtain the UHF states in the case of regular lattice that may become the HF ground state. There are at least eight such UHF states which are distinguished by the long range orders in the spin and charge densities and the bond orders. The nearest neighbour exchange interaction is responsible to produce such plentiful UHF states. We calculate the bond alternation potential and the band gap in trans polyacetylene using paramet­ rizations of the Hamiltonian and the elastic potential that are able to well reproduce spectra and equilibrium geometries of small conjugated hydrocarbons. The bond alternation potential is very sensitive to the strength of the nearest neighbour Coulomb interaction. The Coulomb potential with fast damping prevents the bond alternation. The band gap is much larger than the energy 2 eV of the lowest absorption band as long as the Coulomb interaction in poly­ acetylene is similar to that in small conjugated hydrocarbons, suggesting the excitonic nature of the absorption band. We make also an illustrative calculation for an itinerant spin Peierls system with an antiferromagnetic spin order as well as a lattice dimerization.

Excitons in a semi-infinite insulator in the tight-binding approximation

The non-local susceptibility is calculated for a semi-infinite, simple cubic insulator with two narrow bands: the conduction ( alpha ) band and valence ( beta ) band. The electrons in the conduction band and the holes in the valence band hop between nearest-neighbour atoms only. The interactions between electron-hole pairs on the same lattice site and on nearest-neighbour lattice sites are also included. As a model for the surface the authors ignore interactions between electron-hole pairs on opposite sides of a plane which bisects the crystal but contains no atoms itself. The hopping integrals of the electrons and holes across this plane are neglected as well. It is shown that the Coulomb interaction between two electron-hole pairs on the same lattice site never produces excitons (bound electron-hole pairs). Excitons are produced by the nearest-neighbour exchange interaction. The equation of motion of the exciton green function is solved analytically. Under suitable conditions, surface excitons localised on the surface of the insulator may be produced.

On the ferromagnetic phase breakdown of a two-dimensional Ising model with competing interactions

The authors study a quenched random Ising magnet with nearest-neighbour exchange interactions jij=+or-J on a square lattice at T=0. A new-type effective field approach beyond mean field-approximation is used in order to obtain an estimate for the critical antiferro-magnetic bond concentration pc at which the ferromagnetic phase breaks down. The result is in quite good agreement with Bethe, Monte Carlo and replica method calculations. The Edwards-Anderson order parameter q within the authors formulation is also obtained. They found that both the magnetisation and q vanish at the same value pc=1/6.

Hyperfine and super-exchange interactions in M 2CuX 4.2H 2O compounds

The ground state of the magnetic copper ion and the transfer of unpaired spin to the ligands is described taking into account the influence of the crystalline field and the partly covalent bonding with three inequivalent pairs of ligands. Experimentally determined (super) hyperfine interactions of all nuclei, electronic g tensor and crystal field parameters form the data on which the analysis of the covalency is based. A discussion of the super-exchange mechanisms and exchange paths in these compounds is given. From this analysis the nearest-neighbour exchange interactions are estimated in close agreement with experimental values.

The frequency moments for an anisotropic paramagnet with exchange-bond dilution in the high-temperature limit

The low-order frequency moments omega n (n=0, 2, 4, 6) of the spin correlation function for a Heisenberg paramagnet with bond dilution are calculated at infinite temperature. The calculations are for a model in which the three cartesian components of the exchange between each pair of atoms can fluctuate independently. The results are for general spin but are restricted to nearest-neighbour exchange interactions.

Nmr and Mössbauer Effect Studies on Diluted Heisenberg Ferromagnets and Spin-Glasses: EuxSr1−xS

ABSTRACTThe systematic variations of experimentally determined exchange and hyperfine (h.f.) interactions between Eu2+ ions are compared firstly within the EuX (X=0,S,Se,Te) series of compounds and secondly in the magnetic dilution system EuxSr1−xS. Reasonably relations can be established between the individual nearest and next nearest neighbour exchange interactions (J1,J2 ) and the transferred h.f. interactions (ΔB1 , ΔB2 ), respectively, by considering their variations with the Eu–Eu distances (R1,R2). Using these results, the measured mean hyperfine field, BI(x), and the ferromagnetic saturation h.f. field, B↑↑ (x), of the EuxSr1−xS system can be related reasonably well to the ferro- and paramagnetic phase boundaries, Tc(x) and θ (x), respectively.

The order parameter and induced susceptibility ofc a magnetic of a magnetic field dependent ising model

Abstract Abstract. A two-dimensional Ising model with nearest neighbour exchange interactions among electrons, in the field of a finite intensity, is investigated. By including interactions along a given direction into the structure of the transfer matrix, we pass over from the direct lattice space to the pseudo-spin space. A field dependent unitary transformation in the pseudo-spin space is applied in order to evaluate the partition function exactly. There are two important consequences of the general field dependence of the partition function: (a) The order parameter undergoes a finite discontinuity at the transition temperature; and (b) The induced susceptibility discovers a logarithmic singularity just below the transition temperature. Neither consequence seems to conform with an existing theory of a two-dimensional ferromagnet.

Magnetic responses to the spin-peierls transition in the Ising chain with the next-nearest neighbour interactions

The initial magnetic susceptibility and the specific heat of a one-dimensional Ising spin system interacting with a single phonon of harmonic lattice are studied. Both the nearest and next nearest-neighbour exchange interactions are taken into considerations. The statistical mechanics of the spin system is calculated exactly, and a self-consistent equation for the induced lattice distortion is obtained.

Magnetic properties of (Ti1-xVx)2O3(0<x<1): spin glass and metallic antiferromagnetism

Susceptibility measurements performed on (Ti1-x Vx)2O3 single crystals between 4.2 and 300K for the whole concentration range of x<1 are reported. The spin-glass regime extends into a mictomagnetic regime for x<60%. At higher V concentration (x<0.95), an antiferromagnetic phase is found with Neel temperatures ranging between 10 and 50K. The antiferromagnetic transition is corroborated by high-field magnetisation measurements and by electrical resistivity and lattice parameters studies, both showing anomalies at TN. The dependence of the Curie temperature, the initial reversible susceptibility and the remanent magnetisation is well accounted for by a competition between long-range RKKY couplings, predominantly ferromagnetic in this material, and direct nearest-neighbour antiferromagnetic exchange interactions.