Neighbor Antiferromagnetic Interactions Research Articles

Dzyaloshinski–Moriya interactions in the kagomé lattice

The kagomé lattice exhibits peculiar magnetic properties due to its strongly frustated crystallographic structure, based on corner-sharing triangles. For nearest neighbor antiferromagnetic Heisenberg interactions there is no Néel ordering at zero temperature both for quantum and classical spins. We show that, due to the peculiar structure, antisymmetric Dzyaloshinski–Moriya interactions (D·(Si×Sj)) are present in this lattice. In order to derive microscopically this interaction we consider a set of localized d-electronic states. For classical spins systems, we then study the phase diagram (T,D/J) through mean field approximation and Monte-Carlo simulations and show that the antisymmetric interaction drives this system to ordered states as soon as this interaction is non-zero. This mechanism could be involved to explain the magnetic structure of Fe-jarosites.

Moment variations in disordered Co–Mn alloys

The magnetic neutron scattering from Co–Mn alloys in the concentration range between long-range ferromagnetism and antiferromagnetism is analysed using a simple magnetic environment model for itinerant systems with just one magnetic species. 30, 35 and 40 at% Mn alloys at 100 K are magnetically free and display Lorentzian peaks at antiferromagnetic reciprocal lattice points. The magnetic environment model predicts Lorentzian peaks and the variation of peak height and width is well modelled. The peak width is consistent with predominantly first neighbour antiferromagnetic exchange interactions and the peak height compares well with an estimate based on the moment and Neél temperature of face centred cubic manganese.

Doping dependence of electronic excitations in high Tc superconducting cuprates

The single-particle excitation spectrum is studied in the two-dimensional (2D) t–t′ –t′′ –J model with t, t′, t′′ and J being the first, second and third nearest neighbor hopping parameters of carriers and the nearest neighbor antiferromagnetic interaction, respectively, by using the numerically exact diagonalization method of small clusters. For a set of the parameter values, the momentum dependent spectrum is calculated as a function of hole-carrier density. It is found that the calculated results explain the experimental data of angle-resolved photoemission spectroscopy (ARPES) experiments for insulating Sr 2CuO 2Cl 2 and hole-doped Bi2212, both underdoped and overdoped. The spectrum in electron-doped cuprates is also studied. The results indicate that the electronic structure in the insulating parent materials is essentially the same as that in the high T c ones, and that the carrier density and the sign of the charge are the physical parameters to control the physical properties.

Two-dimensional frustrated Heisenberg model: Variational study

The stability of the ferromagnetic phase of the 2D quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnon are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function of new type. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain the accurate estimate of the transition point and to study the character of the phase transition.

Temperature-dependent pitch and phase diagram for incommensurate XY spins in a slab geometry.

Strain-engineered Heisenberg antiferromagnets recently have been produced by controlling the layer thickness of MnSe/ZnTe superlattices. Neutron-scattering studies reveal a spiral that tends to untwist with increasing temperature. To simulate this system, we employ an XY model with nearest- and second-nearest neighbor antiferromagnetic interactions. The bulk mean-field phase diagram has four possible phases, for the full range of the exchange constants. Monte Carlo calculations are performed for a slab geometry, using an algorithm that allows the system to choose incommensurate boundary conditions. The phase diagram is constructed by monitoring the spiral pitch as a function of temperature for a range of exchange constants. For appropriate exchange constants, good agreement is obtained with experiment. From the mean-field phase diagram it appears that strain engineering an NaCl structure in a superlattice configuration might produce a type of spiral phase, and an associated antiferromagnetic-to-spiral phase transition. \textcopyright{} 1996 The American Physical Society.

Oil-Water Interface in the Widom Model: Is It Smooth, Rough or Crumpled?

Trie interface in trie two-dimensional Ising model with only nearest-neighbour ferromagnetic interactions is known ta be rougir at ail temperatures T > o. Trie Widom model for temary microemulsions is, effectively, a spin-1/2 Ising model with, Dot Orly nearest-neighbour ferromagnetic interactions, but aise specific farther-neighbour antiferromagnetic interactions. We investigate trie effects of these farther-neighbour interactions m the Widom model on the roughening properties of the interface by carrymg eut Monte Carlo simulations. Temary microemulsions are three component mixtures where amphiphilic molecules act as surfactants between oil and water iii. Several lattice models of these systems bave been pro- posed and are similar in spirit to trie lattice gas model for trie liquid-gas transition (2). To our knowledge, trie Widom model (3) is trie simplest among trie lattice models of ternary microemulsions. This is, effectively, a spin-1/2 Ising model with not only nearest-neighbour ferromagnetic interactions, but also with farther neighbour antiferromagnetic interactions of specific type descnbed below. Trie farther-neighbour interactions arise from Widom's prescrip- tion for incorporating trie bending rigidity of trie amphiphilic membrane (a monolayer) formed by trie surfactants at the oil-water interface (4). Trie interface between trie up-spm and down- spin domains in trie two-dimensional Ising model with only nearest-neighbour interactions is known to be rougir at ail non-zero temperatures. Trie atm of this communication is to study trie effects of trie farther-neighbour antiferromagnetic interactions m trie Widom model on trie roughening properties of trie interface. In contrast to trie earlier series expansion study for trie three dimensional Widom model by Kahng et ai. (5) we carry out Monte Carlo Simulation of trie two dimensional Widom model. In trie Widom model trie amphiphilic molecules, as well as trie molecules of oit and water, are assumed to be located on trie nearest-neighbour bonds of a simple cubic lattice. Classical Ising spins are put at each of trie lattice sites and one uses trie convention that each bond between nearest-neighbour (+ +) spin pairs is occupied by a molecule of oil, that between (--) spin pairs is occupied by a molecule of water, and that between anti-parallel nearest-neighbour spin pairs is occupied by a surfactant. Trie Hamiltonian of trie system m ternis of trie Ising spin

Magnetic susceptibility in the spin-Peierls system CuGeO3.

We study numerically, using a one-dimensional Heisenberg model, the spin-Peierls transition in the linear Cu$^{2+}$ spin-1/2 chains in the inorganic compound CuGeO$_3$ which has been recently observed experimentally. We suggest that the magnetic susceptibility, the temperature dependence of the spin gap and the spin-Peierls transition temperature of this material can be reasonably described by including nearest and next nearest neighbor antiferromagnetic interactions along the chain. We estimate that the nearest neighbor exchange parameter J is approximately $160\:\rm K$, and that the next nearest neighbor exchange parameter is approximately $0.36\:\rm J$.

Spin configurations in hexagonal antiferromagnets with competing interactions

The ordered phase of the most part of ABX3 antiferromagnets appears as a stacking of 120°-three sublattice spin layers with alternate spin direction along thec-axis. This configuration is easy to be explained because it is the minimum energy configuration of the Heisenberg hexagonal model with nearest neighbour antiferromagnetic interaction. However we show that moderate competitive interactions between in plane next nearest and third nearest neighbours stabilize incommensurate spin configurations. This gives some insight into the unexplained spin configuration observed in RbMnBr3 by elastic neutron scattering experiment.

Geometrically-frustrated magnetism on triangular and tetrahedral lattices

The combination of simple, nearest neighbor antiferromagnetic interactions and certain lattice symmetries leads to phenomena known broadly as frustration. In such systems, the formation of a collinear magnetic structure cannot occur at low temperature. The material may undergo a phase transition to an unusual magneticallyordered state, or it may not undergo a conventional transition at all-entering a glass-like state as the temperature is lowered. This paper will review recent work, mostly from neutron scattering studies, on three such magnetic materials. CsMnBr3 and CsCoBr3 are XY-like and Ising-like stacked-triangular lattice antiferromagnets, respectively. Both undergo magnetic phase transitions with interesting properties due to the presence of geometricalfrustration within the triangular layers. TD2Mo2O7 is a pyrochlore antiferromagnet, in which the magnetic moments reside on a network of corner-sharing tetrahedra. This material enters a magnetic glass-like state at low temperature.

Lattice gas and spin ordering on stacked triangular lattices

Mean field theory is used to determine the highest temperature ordered phases of lattice gas and spin systems on stacked triangular lattices. The authors include nearest neighbour repulsive or antiferromagnetic interactions and map out the ordered phases as a function of interactions out to fifth neighbours. They show that the type of stacking, .AAA., .ABAB. (hexagonal close packed), .ABCABC. (cubic closed packed), has a profound effect on the nature of the ordering. For .ABAB. and .ABCABC. stacking the inter-plane interactions can compound the frustration within the planes resulting in phase diagrams dominated by incommensurate order just below the critical temperature. Comparison with relevant experimental lattice gas and magnetic systems is made.

2-dimensional magnetism of hydroxy Mn- and Fe-mica intercalations

The two dimensional magnetism in a triangular lattice of hydroxy Mn- and Fe-mica intercalations has been investigated. The Fe-mica intercalation containing more than 8 wt%Fe shows an XY type ferrimagnetism with the ordering temperature of about 10 K. It is revealed by Mössbauer spectroscopy that only Fe 3+ is responsible for the ferrimagnetic ordering in the Fe-mica intercalation, although Fe 2+ ions coexist. The Mn-mica intercalation is most likely a Heisenberg type magnet with a near neighbour antiferromagnetic interaction, and a magnetic ordering is not found at least down to 4.2K. The M(M = Mn, Fe, Co and Ni) dependence of the 2-dimensional magnetic properties of the M-mica intercalations is discussed.

Incommensurate magnetic phases in doped high Tc compounds

An effective spin hamiltonian has been presented to describe the effect of doping with holes the half filled band of a Hubbard model. Doping generates second and third neighbor antiferromagnetic interactions leading to frustration. We show that this hamiltonian yields modulated phases when the hole concentration exceeds a critical value. The antiferromagnetic and spiral phases meet at a Lifshitz point. Quantum fluctuations and thermal effects for the resulting phase diagram are treated à la Chakravarty et al. Recent neutron experiments on La2−xSrxCuO4 by Birgeneau et al displaying 3D incommensurate magnetic structures can be explained within our model. The influence of the incommensurate state on the mobility of the holes is considered.

Consistent Solutions of BCS-Gap Equation for the Hole-Pairing Mechanism by the Exchange of Soft-Magnons in a Frustrated Heisenberg Square-Lattice System

The pairing mechanism for doped holes to d 3 z 2 - r 2 orbitals of Cu 2+ ions on a CuO 2 plane is proposed so as to make clear the property of superconducting phases of high- T c superconductors where coexistence of the antiferromagnetic ordering has been recently reported. The pairing is made by the exchange of antiferromagnetic magnons for d x 2 - y 2 spins on CuO 2 plane. Here, the frustration introduced by the second nearest neighbor antiferromagnetic exchange interaction between Cu 2+ ions plays an significant role. The BCS-type gap equation is derived and self-consistent solutions are obtained numerically for various symmetries. Among them, the gaps for s and d x y symmetries are discussed in detail. By the essential contribution of the frustration, the gap can be formed even for the intermediate coupling region.

Theoretical and Experimental Study of Alternating (Classical Spin)/(Quantum System) Isotropic Ferrimagnets

Abstract Compounds containing well isolated complex magnetic chains are now available from inorganic and molecular chemistry. Interpreting their magnetic behavior generally requires specific models. We describe here a general analytic solution for a large class of such compounds. The model concerns isotropic chains, where a single moment which may be treated classically, alternates with a composite system of quantum spins. It is applied to to the magnetic properties the one-dimensional compound MnCu2(bapo)(H2O)4.2H2O, (where bapo = N,N′-bis(oxamatol,3-propylene)oxamido), within which one may observe ‒MnII-CuII-CuII-MnII‒ sequences with nearest neighbor antiferromagnetic interactions. The results appear to be consistent with independant estimates of MnII-CuII and CulI-CuII exchange interations involving similar paths.

The 3D Z 3 spin model and the deconfinement transition in QCD: A problem of universality

We study the three-dimensional three-state Potts Z 3 model. We add a second nearest neighbour interaction to the usual first neighbour interaction term. We measure the correlation length by using a source technique. We find that when considering a small second neighbour antiferromagnetic interaction the phase transition has a large correlation length, linearly increasing with the lattice size, for sizes up to 16 2×48. Such a critical behaviour is very similar to the one that the APE Collaboration observed in the case of the deconfining transition of the finite temperature SU(3) gauge theory. We underscore the similarities in the behavior of the two systems.

Superconductivity in correlated wavefunctions

We discuss variational approaches to the one band Hamiltonian in the projected subspace. This Hamiltonian has a kinetic energy term for charge degree of freedom and nearest neighbor antiferromagnetic spin-spin interactions. We show that the projected d-wave BCS state (RVB-wavefunction) is a quantum spin liquid. This is done with results from numerical evaluation of the wavefunction, renormalized mean field theory and results from exact diagonalization of small systems. Off half-filling, this wavefunction leads to superconductivity with an order parameter which has d-symmetry.

The 2×1 and 2×2 Structures on a Triangular Lattice

Phase transitions of the triangular Ising model in a field with nearest and second nearest neighbor antiferromagnetic interactions with couplings, - J and - J /2, respectively, are studied by the interfacial free energy method, by the mean field approximation, by the transfer matrix and phenomenological renormalization methods and by the Monte Carlo simulation. At low temperatures and at fields weaker than the lower critical field h c1 the system takes the 2 × 1 structure, and at fields between h c1 and the upper critical field h c2 it takes the 2×2 structure. Between the 2×1 and 2×2 phases near the field h c1 , a partial disordered phase, in which a part of the sublattices are in disorder, is found. Specific heat shows no divergence, when the partial disordered phase changes to other phases.

The Spin Wave Theory in Antiferromagnetic Heisenberg Model on Face Centered Cubic Lattice

The classical ground states of face centered cubic lattice with nearest neighbor antiferromagnetic Heisenberg interactions are shown to have continuous degeneracy. The spin wave theory removes the degeneracy and determines the ground state, in which the energy E g and spin reduction are calculated. E g is also obtained by calculating the lowest energy of finite size systems and extrapolating to infinite lattice. Both results are in fairly good agreement with each other. Finally it is concluded that the sublattice long range order exists.

\(\sqrt{3}\times\sqrt{3}\) Structure on the Triangular Lattice

An Ising model with nearest neighbor antiferromagnetic and next nearest neighbor ferromagnetic interactions is studied by the phenomenological renormalization method. The phase transition to the \(\sqrt{3}\times\sqrt{3}\) structure is of the second order for weak fields, and the critical exponents \(y_{\text{T}}{\cong}1.2\) and \(\eta{\cong}0.30\) are consistent with the conjectured values of the 3-state Potts model. Beyond a tricritical point the transition becomes of the first order for strong fields. The tricritical exponent \(y_{\text{T,t}}{\cong}1.73\) and \(\eta_{\text{t}}{\cong}0.21\) are also in agreement with the 3-state Potts tricritical values y T,t 3P =12/7 and η t 3P =4/21. The XY-like phase transition at zero fields, which was obtained by the Monte Carlo simulations, is not found in the present calculation.

An Ising ferromagnet with an antiferromagnetic surface layer: A simple model for magnetic surface reconstruction

Simple cubic Ising lattices are studied by Monte Carlo simulation, using a thin film geometry (usually 40 atomic layers thick), with nearest neighbour ferromagnetic exchange J in the bulk and nearest neighbour antiferromagnetic interaction J s between surface spins. Applying a technique of preferential sampling in the surface layers, we investigate the ordering for a variety of values of J s J and for various temperatures. For J s AF < J s < − 0.25 J (where J s AF ≈ − 2.01 J) ferromagnetic ordering occurs at a higher temperature than the antiferromagnetic surface ordering, while for − 0.25 J < J s no antiferromagnetic long range order is possible. For J s < J s AF the surface transition occurs at a higher temperature than the bulk transition. We also study the magnetization profile of the film and find it is hardly affected by the antiferromagnetic ordering in its surface: the system between the surface layers behaves just as a ferromagnet with unchanged interactions at the surfaces. Likewise the antiferromagnetic order in the surface is only affected very little by the underlying layers becoming ferromagnetic, and hence such a system would be a very good approximation for a strictly two-dimensional Ising antiferromagnet. Consequently the multicritical point J s J s AF , T = T cb where surface and bulk order simultaneously is interpreted as a decoupled multicritical point. Extensions to surfaces of isotropic magnets ( XY and Heisenberg model) are discussed qualitatively.