Spin populations in one-dimensional alternant spin systems: A theoretical approach

Spin-density maps, deduced from polarized neutron diffraction experiments, for both the pair and chain compounds of the system Mn2+Cu2+ have been reported recently. These results have motivated us to investigate theoretically the spin populations in such alternant mixed-spin systems. In this paper, we report our studies on the one-dimensional ferrimagnetic systems (S-A,S-B)(N) where hi is the number of AB pairs. We have considered all cases in which the spin Sri takes on allowed values in the range I to 7/2 while the spin S-B is held fixed at 1/2. The theoretical studies have been carried out on the isotropic Heisenberg model, using the density matrix renormalization group method. The effect of the magnitude of the larger spin SA On the quantum fluctuations in both A and B sublattices has been studied as a function of the system size N. We have investigated systems with both periodic and open boundary conditions, the latter with a view to understanding end-of-chain effects. The spin populations have been followed as a function of temperature as well as an applied magnetic field. High-magnetic fields are found to lead to interesting re-entrant behavior. The ratio of spin populations P-A-P-B is not sensitive to temperature at low temperatures.

Temperature dependence of the dielectric constant of diamond

The temperature dependence of the dielectric constant of diamond has been measured over the temperature range 50-2OO"c. The value of E-ldc dT over this range is + 1 x 10-j. Details of the method of measuring the temperature coefficient of dielectric constant are also given. The magnitude and sign of c-ldc, dT for diamond has been theoretically calculated using Maxwell's relationship and Kramers-Heisenberg theory. The agreement between theoretical and experimental values is extremely good.

Noncommutativity and Some of Its Present-Day Developments

This masters thesis explores some of the most recent developments in noncommutative quantum field theory. This old theme, first suggested by Heisenberg in the late 1940s, has had a renaissance during the last decade due to the firmly held belief that space-time becomes noncommutative at small distances and also due to the discovery that string theory in a background field gives rise to noncommutative field theory as an effective low energy limit. This has led to interesting attempts to create a noncommutative standard model, a noncommutative minimal supersymmetric standard model, noncommutative gravity theories etc. This thesis reviews themes and problems like those of UV/IR mixing, charge quantization, how to deal with the non-commutative symmetries, how to solve the Seiberg-Witten map, its connection to fluid mechanics and the problem of constructing general coordinate transformations to obtain a theory of noncommutative gravity. An emphasis has been put on presenting both the group theoretical results and the string theoretical ones, so that a comparison of the two can be made.

On the unreasonable effectiveness of Gutzmer's formula

In this article we plan to demonstrate the usefulness of `Gutzmer's formula' in the study of various problems related to the Segal-Bargmann transform. Gutzmer's formula is known in several contexts: compact Lie groups, symmetric spaces of compact and noncompact type, Heisenberg groups and Hermite expansions. We apply Gutzmer's formula to study holomorphic Sobolev spaces, local Peter-Weyl theorems, Paley-Wiener theorems and Poisson semigroups.

Isobaric electrical resistance along the critical line in nickel: An experimental test of universality

High-precision measurement of the electrical resistance of nickel along its critical line, a first attempt of this kind, as a function of pressure to 47.5 kbar is reported. Our analysis yields the values of the critical exponents α=α’=-0.115±0.005 and the amplitude ratios ‖A/A’‖=1.17±0.07 and ‖D/D’‖=1.2±0.1. These values are in close agreement with those predicted by renormalization-group (RG) theory. Moreover, this investigation provides an unambiguous experimental verification to one of the key consequences of RG theory that the critical exponents and amplitudes ratios are insensitive to pressure variation in nickel, a Heisenberg ferromagnet.

Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered one-dimensional bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet La-2(Zn,Mg)(x)Cu1-xO4.

Investigations on Bi2CuO4: a quasi-one-dimensional oxide system

The potential of Bi2CuO4 as the first oxide system to show a linear-chain magnetic behaviour is examined. Electron diffraction studies do not resolve the previously reported ambiguity regarding its space group. The magnetic susceptibility data at high temperatures are best fitted to a uniform antiferromagnetic spin-1/2 Heisenberg chain. At low temperatures, however, neither the uniform nor the alternating Heisenberg antiferromagnetic model fits the data. Magnetic susceptibility data over the entire temperature range can be fitted if one assumes dimeric units with a nearly degenerate second singlet state close to the ground state, these states being separated from an excited triplet state by an energy gap. A simple heuristic model of a dimer that gives such an energy level spectrum is examined.

Synthesis, structure and magnetic properties of the polyoxovanadate cluster Zn-2(NH2(CH2)(2)NH2)(5)]{Zn(NH2(CH2)(2)NH2)(2)}(2){V18O42(H2O)\ ]center dot xH(2)O (x similar to 12), possessing a layered structure

A hydrothermal reaction of a mixture of ZnCl2, V2O5, ethylenediamine and water gave rise to a layered poly oxovanadate material. clusters. These clusters, with all the vanadium ions in the +4 state, are connected together through Zn(NH2(CH2)(2)NH2)(2) linkers forming a two-dimensional structure. The layers are also separated by distorted trigonal bipyramidal [Zn-2(NH2(CH2)(2)NH2)(5)] complexes. The Structure, thus, presents a dual role for the Zn-ethylenediamine complex. The magnetic susceptibility studies indicate that the interactions between the V centres in I are predominantly antiferromagnetic in nature and the compound shows highly frustrated behaviour. The magnetic properties are compared to the theoretical calculations based oil the Heisenberg model, in addition to correlating to the structure. Crystal data for the complexes are presented.

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant Gf reverse similar, equals 1038 GN (GN being the Newtonian constant) and a cosmological term λf ƒ;μν (ƒ;μν is strong gravity metric and λf not, vert, similar 1028 cm− is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature not, vert, similar10−14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length not, vert, similar2 × 10−14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-Image particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.

Descriptions of operators in quantum mechanics

The problem of expressing a general dynamical variable in quantum mechanics as a function of a primitive set of operators is studied from several points of view. In the context of the Heisenberg commutation relation, the Weyl representation for operators and a new Fourier-Mellin representation are related to the Heisenberg group and the groupSL(2,R) respectively. The description of unitary transformations via generating functions is analysed in detail. The relation between functions and ordered functions of noncommuting operators is discussed, and results closely paralleling classical results are obtained.

Molecular ferromagnetism in C60·TDAE

C60·TDAE = tetrakis(dimethylamino)ethylene) with a Tc of not, vert, similar 16K is probably the best example of an organic molecular ferromagnet known to date. Based on ESR studies, we demonstrate that C60·TDAE is a quasi one-dimensional spin one-half Heisenberg ferromagnet, with the C60 units being entirely responsible for the magnetism. C60-C60 interactions responsible for superconductivity in alkali metal doped C60 seem to be essential for the magnetism of C60·TDAE as well.

Magnetism, exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS3 is a layered antiferromagnet (T N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate5 T 2g ground state of the Fe2+ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ?=?i [?(L iz 2 ?2)+|?|L i .S i ]?? ij J ij S i .S j . The crystal field trigonal distortion parameter ?, the spin-orbit coupling ? and the isotropic Heisenberg exchange,J ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for ?/k=215.5 K; ?/k=166.5 K;J nn k=27.7 K; andJ nnn k=?2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT N=122 K for FePS3, which is remarkably close to the observed value of theT N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS3, for which the high temperature series expansion susceptibility is available.

Magnetic Raman scattering from 1D antiferromagnets

We study Raman scattering from 1D antiferromagnets within the Fleury-Loudon scheme by applying a finite temperature Lanczos method to a 1D spin-half Heisenberg model with nearest-neighbor (J(1)) and second-neighbor (J(2)) interactions. The low-temperature spectra are analyzed in terms of the known elementary excitations of the system for J(2) = 0 and J(2) = 1/2. We find that the low-T Raman spectra are very broad for \J(2)/J(1)\ less than or equal to 0.3. This broad peak gradually diminishes and shifts with temperature, so that at T > J(1) the spectra are narrower and peaked at low frequencies. The experimental spectra for CuGeO3 are discussed in light of our calculations.

Regular versus alternating (FeS4)(n) chains: Magnetism in KFeS2 and CsFeS2

We report crystal magnetic susceptibility results of two S = 1/2 one-dimensional Heisenberg antiferromagnets, KFeS2 and CsFeS2. Both compounds consist of (FeS4)(n) chains with an average Fe-Fe distance of 2.7 Angstrom. In KFeS2, all intrachain Fe-Fe distances are identical. Its magnetic susceptibility is typical of a regular antiferromagnetic chain with spin-spin exchange parameter J = -440.7 K. In CsFeS2, however, the Fe-Fe distances alternate between 2.61 and 2.82 Angstrom. This is reflected in its magnetic susceptibility, which could be fitted with J = -640 K, and the degree of alternation, alpha = 0.3. These compounds form a unique pair, and allow for a convenient experimental comparison of the magnetic properties of regular versus alternating Heisenberg chains.

Spin state and exchange in the quasi-one-dimensional antiferromagnet KFeS2

We report the optical spectra and single crystal magnetic susceptibility of the one-dimensional antiferromagnet KFeS2. Measurements have been carried out to ascertain the spin state of Fe3+ and the nature of the magnetic interactions in this compound. The optical spectra and magnetic susceptibility could be consistently interpreted using a S = 1/2 spin ground state for the Fe3+ ion. The features in the optical spectra have been assigned to transitions within the d-electron manifold of the Fe3+ ion, and analysed in the strong field limit of the ligand field theory. The high temperature isotropic magnetic susceptibility is typical of a low-dimensional system and exhibits a broad maximum at similar to 565 K. The susceptibility shows a well defined transition to a three dimensionally ordered antiferromagnetic state at T-N = 250 K. The intra and interchain exchange constants, J and J', have been evaluated from the experimental susceptibilities using the relationship between these quantities, and chi(max), T-max, and T-N for a spin 1/2 one-dimensional chain. The values are J = -440.71 K, and J' = 53.94 K. Using these values of J and J', the susceptibility of a spin 1/2 Heisenberg chain was calculated. A non-interacting spin wave model was used below T-N. The susceptibility in the paramagnetic region was calculated from the theoretical curves for an infinite S = 1/2 chain. The calculated susceptibility compares well with the experimental data of KFeS2. Further support for a one-dimensional spin 1/2 model comes from the fact that the calculated perpendicular susceptibility at 0K (2.75 x 10(-4) emu/mol) evaluated considering the zero point reduction in magnetization from spin wave theory is close to the projected value (2.7 x 10(-4) emu/mol) obtained from the experimental data.