Sc Lattices Research Articles

Ferromagnetism in thet−t′Hubbard model: Interplay of lattice, band dispersion, and interaction effects studied within a Goldstone-mode preserving scheme

Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy ($1/{\cal N}$) expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the belief that ferromagnetism is a generic feature of the Hubbard model at intermediate and strong coupling provided the DOS is sufficiently asymmetric and strongly peaked near band edge, as for fcc lattice with finite $t'$. For short-wavelength modes, behavior of a characteristic energy scale $\omega^* \sim T_c$ (magnon-DOS-peak energy) is in excellent agreement with the $T_c$ vs. $n$ behavior within DMFT, both with respect to the stable range of densities ($0.20 < n < 0.85$) as well as the optimal density $n=0.65$. However, our finding of vanishing spin stiffness near optimal density highlights the role of long-wavelength fluctuations in further reducing the stable range of densities.

Multipole ordering in f-electron systems

In order to investigate multipole ordering in f-electron systems from a microscopic viewpoint, we study the so-called Γ 8 models on three kinds of lattices, simple cubic (sc), bcc, and fcc, based on a j– j coupling scheme with f-electron hopping integrals through ( ff σ ) bonding. From the Γ 8 model, we derive an effective model for each lattice structure by using the second-order perturbation theory with respect to ( ff σ ) . By further applying mean-field theory to the effective model, we find a Γ 3 g antiferro-quadrupole transition for the sc lattice, a Γ 2 u antiferro-octupole transition for the bcc lattice, and a longitudinal triple- q Γ 5 u octupole transition for the fcc lattice.

Multipole ordering inf-electron systems on the basis of aj−jcoupling scheme

We investigate microscopic aspects of multipole ordering in $f$-electron systems with emphasis on the effect of lattice structure. For this purpose, first we construct $f$-electron models on three kinds of lattices, simple cubic (sc), bcc, and fcc, by including $f$-electron hopping through $(ff\ensuremath{\sigma})$ bonding in a tight-binding approximation on the basis of a $j\text{\ensuremath{-}}j$ coupling scheme. Then, an effective model is derived in the strong-coupling limit for each lattice structure with the use of second-order perturbation theory with respect to $(ff\ensuremath{\sigma})$. By applying mean-field theory to such effective models, we find different types of multipole ordered states, depending on the lattice structure. For the sc lattice, a ${\ensuremath{\Gamma}}_{3g}$ antiferro-quadrupole transition occurs at a finite temperature and, as we further lower the temperature, we find another transition to a ferromagnetic state. For the bcc lattice, a ${\ensuremath{\Gamma}}_{2u}$ antiferro-octupole ordering occurs first, and then a ferromagnetic phase transition follows it. Finally, for the fcc lattice, we find a single phase transition to the longitudinal triple-$\mathbf{q}\phantom{\rule{0.3em}{0ex}}{\ensuremath{\Gamma}}_{5u}$ octupole ordering.

MESOSCOPIC FIELD THEORY OF IONIC SYSTEMS

A mesoscopic field theory for the primitive model of ionic systems with additional, short-range interactions is presented. Generic models in continuum space and with positions of the ions restricted to lattice sites of various lattices are described in detail. We describe briefly the field-theoretic methods and review the foundations of the mesoscopic description. The types of phase diagrams predicted by our theory for different versions of the model are presented and discussed. They all agree with recent simulations. On the quantitative level our theory yields an RPM tricritical-point location on the sc lattice which is in good agreement with the simulation results. Arguments indicating that the critical point in the RPM belongs to the Ising universality class are given.

Magnetic reordering in the vicinity of a ferromagnetic/antiferromagnetic interface

The magnetic arrangement in the vicinity of the interface between a ferromagnet and an antiferromagnet is investigated, in particular its dependence on the exchange couplings and the temperature. Applying a Heisenberg model, both sc(001) and fcc(001) lattices are considered and solved by a mean field approximation. Depending on the parameter values a variety of different magnetic configurations emerge. Usually the subsystem with the larger ordering temperature induces a magnetic order into the other one (magnetic proximity effect). With increasing temperature a reorientation of the magnetic sublattices is obtained. For coupled sc(001) systems both FM and AFM films are disturbed from their collinear magnetic order, hence exhibit a similar behavior. This symmetry is absent for fcc(001) films which, under certain circumstances, may exhibit two different critical temperatures. Analytical results are derived for simple bilayer systems.

Hubbard model in the ferromagnetic state. Dimer and trimer approach

AbstractWe consider the Hubbard model for the sc lattice which consists of interacting, parallel lying dimer (trimer) planes. Each plane is a collection of equidistant, interacting, parallel lying dimers (trimers). We apply the exact solution of the dimer (trimer) problem after introducing the intrinsic symmetry breaking leading to the ferromagnetic ordering. We present preliminary, test results concerning the phase diagram of the system. In both approximations (dimer and trimer approach) there is a threshold for the ferromagnetic ordering at the Coulomb repulsion U = Ucr. The trimer approach gives a better saturation for the Curie temperature TC vs. U in comparison to the dimer approach. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Localization properties of pure magnetostatic modes in a cubic nanograin

We investigate the dynamical properties of a system of interacting magnetic dipoles disposed in sites of an sc lattice and forming a cubic-shaped sample of size determined by the cube edge length (N-1)a (a being the lattice constant, N representing the number of dipolar planes). The dipolar field resulting from the dipole-dipole interactions is calculated numerically in points of the axis connecting opposite cube face centers (central axis) by collecting individual contributions to this field coming from each of the N atomic planes perpendicular to the central axis. The applied magnetic field is assumed to be oriented along the central axis, magnetizing uniformly the whole sample, all the dipoles being aligned parallelly in the direction of the applied field. The frequency spectrum of magnetostatic waves propagating in the direction of the applied field is found numerically by solving the Landau-Lifshitz equation of motion including the local (nonhomogeneous) dipolar field component; the mode amplitude spatial distributions (mode profiles) are depicted as well. It is found that only the two energetically highest modes have bulk-extended character. All the remaining modes are of localized nature; more precisely, the modes forming the lower part of the spectrum are localized in the subsurface region, while the upper-spectrum modes are localized around the sample center. We show that the mode localization regions narrow down as the cube size, N, increases (we investigated the range of N=21 to N=101), and in sufficiently large cubes one obtains practically only center-localized and surface-localized magnetostatic modes.

Reentrant behavior in the nearest-neighbor Ising antiferromagnet in a magnetic field

Motived by the $H\text{\ensuremath{-}}T$ phase diagram in the bcc Ising antiferromagnetic with nearest-neighbor interactions obtained by Monte Carlo simulation [Landau, Phys. Rev. B 16, 4164 (1977)] that shows a reentrant behavior at low temperature, with two critical temperatures in magnetic field about 2% greater than the critical value ${H}_{c}=8J$, we apply the effective field renormalization group (EFRG) approach in this model on three-dimensional lattices (simple cubic-sc and body centered cubic-bcc). We find that the critical curve ${T}_{N}(H)$ exhibits a maximum point around of $H\ensuremath{\simeq}{H}_{c}$ only in the bcc lattice case. We also discuss the critical behavior by the effective field theory in clusters with one (EFT-1) and two (EFT-2) spins, and a reentrant behavior is observed for the sc and bcc lattices. We have compared our results of EFRG in the bcc lattice with Monte Carlo and series expansion, and we observe a good accordance between the methods.

Unidirectional anisotropy and spin-configurations in ferro/antiferromagnetic exchange coupled layers with FCC(100) and FCC(111) interfaces

In a ferromagnetic (F)/antiferromagnetic (AF) exchange coupled bilayer, we have recently demonstrated by 0 K Monte Carlo simulation using classical nearest neighbor Heisenberg model for an sc lattice system that a typical unidirectional anisotropy can be induced, even for the compensated AF interface, by just assuming a loosely coupled interface within the AF-layer. In this study, we have applied the loosely coupled layer model to FCC(0 0 1) and FCC(1 1 1) AF-interfaces. It has turned out that the model can cause a unidirectional anisotropy for (1 1 1) interfaces, but not for (0 0 1). The unidirectional anisotropy can be attributed to loosely coupled FCC(1 1 1) AF-interface energy, but almost no interface energy is generated in case of FCC(0 0 1) since the nearest-neighbor exchange coupling is canceled out leaving substantially weak exchange coupling between them.

Sign inversion of the radiation-induced plastic effect in C60 single crystals upon the SC-FCC phase transition

A reversible variation in the microhardness of C60 single crystals induced by low-dose β irradiation is found to change sign in the vicinity of the phase transition at Tc=250–260 K. Radiation hardening is observed at T Tc. The kinetic characteristics of the β-induced variation in the microhardness of C60 and its recovery to the initial value are studied in the temperature range 170–350 K. Both processes are found to be thermally activated. The activation energies are determined and are shown to be different for sc and fcc lattices.

Unidirectional anisotropy and spin-configurations in ferro/antiferromagnetic exchange coupled layers with FCC(1 0 0) and FCC(1 1 1) interfaces

Abstract In a ferromagnetic (F)/antiferromagnetic (AF) exchange coupled bilayer, we have recently demonstrated by 0 K Monte Carlo simulation using classical nearest neighbor Heisenberg model for an sc lattice system that a typical unidirectional anisotropy can be induced, even for the compensated AF interface, by just assuming a loosely coupled interface within the AF-layer. In this study, we have applied the loosely coupled layer model to FCC(0 0 1) and FCC(1 1 1) AF-interfaces. It has turned out that the model can cause a unidirectional anisotropy for (1 1 1) interfaces, but not for (0 0 1). The unidirectional anisotropy can be attributed to loosely coupled FCC(1 1 1) AF-interface energy, but almost no interface energy is generated in case of FCC(0 0 1) since the nearest-neighbor exchange coupling is canceled out leaving substantially weak exchange coupling between them.

The ground-state phase diagrams of the spin-3/2 Ising model

The ground-state spin configurations are obtained for the spin-3/2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. The calculated ground-state phase diagrams are presented on diatomic lattices, such as the square, honeycomb and sc lattices, and triangular lattice in the ( Δ/ z| J|, K/| J|) and ( H/ z| J|, K/| J|) planes.

Quantum spin liquid and antiferromagnetism

A spin liquid concept for the Heisenberg Hamiltonian (spin s=1/2) with antiferromagnetic exchange interactions between nearest neighbors is developed. The spin liquid is described by the Green’s function method in the framework of a second-order theory. Equations are presented for the self-consistent calculation of the parameters of the system and its thermodynamic properties at all temperatures. A description of the spin system in the sc and bcc lattices is proposed wherein it is treated as a spatially homogeneous spin liquid with a condensate and with a singlet ground state. It is shown that the modulus of the “staggered” magnetization is expressed uniquely in terms of a condensate at a boundary point of the Brillouin zone and is the long-range order parameter. The existence region in temprature of the ordered state of the spin liquid with a condensate (T&amp;lt;T0) is wider than the existence region of the two-sublattice antiferromagnetism (T0&amp;lt;TN, where TN is the Néel temperature), while the energy is lower. For T&amp;gt;T0 the system passes into an ordinary spin liquid state.

Glass transition in systems without static correlations: a microscopictheory

We present a first step toward a microscopic theory for the glass transition insystems with trivial static correlations. As an example we have chosenN infinitely thin hardrods with length L,fixed with their centres on a periodic lattice with lattice constanta. Startingfrom the N-rodSmoluchowski equation we derive a coupled set of equations for fluctuations of reducedk-roddensities. We approximate the influence of the surrounding rods on the dynamics of a pairof rods by introduction of an effective rotational diffusion tensor D(Ω1, Ω2)and in this way we obtain a self-consistent equation for D.This equation exhibits a feedback mechanism leading to a slowing down ofthe relaxation. It involves as an input the Laplace transform υ0 (l/r)at z = 0,l = L/a,of a torque–torque correlator of an isolated pair of rods with distanceR = ar. Ourequation predicts the existence of a continuous ergodicity-breaking transition at a criticallength lc = Lc /a.To estimate the critical length we perform an approximate analytical calculation of υ0 (l/r)based on a variational approach and obtain lcvar ∼ = 5.68,4.84 and 3.96 for an sc, bcc and fcc lattice. We also evaluate υ0 (l/r) numericallyexactly from a two-rod simulation. The latter calculation leads to lcnum ∼ = 3.45,2.78 and 2.20 for the corresponding lattices. Close tolcthe rotational diffusion constant decreases as D(l) ∼ (lc − l)γ withγ = 1and a diverging timescale tϵ ∼ |lc − l|−δ, δ = 2, appears. Onthis timescale the t-and l-dependenceof the one-rod density is determined by a master function depending only on t/tϵ. Incontrast to present microscopic theories our approach predicts a glass transitiondespite the absence of any static correlations.

Lattice models of ionic systems

A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye–Hückel theory with ion-pairing and dipole–ion solvation, specific calculations being performed for three-dimensional lattices. As for continuum electrolytes, low-density results for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices indicate the existence of gas–liquid phase separation. The predicted critical densities have values comparable to those of continuum ionic systems, while the critical temperatures are 60%–70% higher. However, when the possibility of sublattice ordering as well as Debye screening is taken into account systematically, order–disorder transitions and a tricritical point are found on sc and bcc lattices, and gas–liquid coexistence is suppressed. Our results agree with recent Monte Carlo simulations of lattice electrolytes.

Extended Hubbard Model in the Dimer Representation. II. Lattice Hamiltonian in the Large U Limit

We consider the extended Hubbard model for the single cubic lattice and rewrite it in the form of interacting dimers, using the exact solution of the dimer problem. We analytically derive the second quantization form of the dimer Hamiltonian eliminating from the considerations unoccupied dimer energy levels in the large U limit (it is the only assumption). The resulting dimer Hamiltonian written with the use of the Hubbard operators and spin operators contains three terms, visualizing explicitly competing magnetic interactions (ferromagnetic, antiferromagnetic) as a generalization of the t-J model. The presented, nonperturbative method, can in principle be applied to the cluster of any size (e.g. one central atom and z its nearest neighbours). The use of the projection technique can further be applied in the case of a crystal to obtain the second quantization form of the extended Hubbard model for the sc lattice in the large U limit.

Extended Hubbard Model in the Dimer Representation. I. Dimer Hamiltonian in the Large U Limit

We consider the extended Hubbard model for the single cubic lattice and rewrite it in the form of interacting dimers, using the exact solution of the dimer problem. We analytically derive the second quantization form of the dimer Hamiltonian eliminating from the considerations unoccupied dimer energy levels in the large U limit (it is the only assumption). The resulting dimer Hamiltonian written with the use of the Hubbard operators and spin operators contains three terms, visualizing explicitly competing magnetic interactions (ferromagnetic, antiferromagnetic) as a generalization of the t-J model. The presented, nonperturbative method, can in principle be applied to the cluster of any size (e.g. one central atom and z its nearest neighbours). The use of the projection technique can further be applied in the case of a crystal to obtain the second quantization form of the extended Hubbard model for the sc lattice in the large U limit.

A proposed damage gradient model for the sequentialdisordering induced in Sc-Ni multilayers by ion irradiation

An abnormal sequential disordering process was observed in Sc-Nimultilayers upon room temperature 200 keV xenon-ion irradiation:the Ni lattice became unstable and entered an amorphous state fasterthan the Sc lattice did. Since there was negligible difference inmutual solid solubility and no significant difference in meltingpoint between the two metals, this abnormal process was attributedto the fact that the damage density in the Ni layer was calculatedto be about 2-3 times that in the Sc. A damage gradient model wasthus proposed in which the Sc atoms diffused much faster along anuphill damage gradient towards the Ni layer than vice versa,resulting in the Ni lattice exceeding its critical solid solubilityand collapsing into a disordered state faster than the Sc lattice.

Low-temperature orientational ordering and possible domain structures in C60 fullerite

Based on a simple model for the ordering of hexagons on a square planar lattice, an attempt is made to consider the possible structure of C60 fullerite in its low-temperature phase. It is shown that hexagons representing fullerenes oriented along the C3 axes of the sc lattice can be ordered into an ideal structure with four nonequivalent molecules in the unit cell. Then the energy degeneracy for the rotation of each hexagon by π/3 around its C3 axis leaves the translational and orientational order in this structure but leads to a random distribution of π/3 rotations and hence to an “averaged” unit cell with two molecules. However, the most relevant structural defects are not these intrinsic “misorientations” but some walls between domains with different sequences of the above-mentioned two (nonideal) sublattices. Numerical estimates are made for the anisotropic intermolecular potential, showing that the anisotropy is noticeably smaller for molecules in walls than in domains.

Quantum statistical approach to Debye-Waller factor in EXAFS: application to monatomic fcc systems.

Temperature dependence of the Debye-Waller factors in EXAFS is studied for monatomic fcc lattice by use of the perturbation approach in terms of temperature Green's function. We apply the theory to the temperature dependence of EXAFS for Kr and Ni crystals. Furthermore we make a comparison among sc, bcc and fcc lattices for the present ab initio calculations.