Static Spin Correlations Research Articles

RESONANCE MODEL FOR PAIR CORRELATIONS IN HEAVY FERMION SYSTEMS

The free energy and static spin-correlation function of a two site resonance model akin to the single site Schotte model are calculated. Thermodynamic functions are discussed and model parameters are linked to those of the microscopic two site Kondo model.

Static spin correlations in singlet states via triplet overlap integrals

An efficient method for the calculation of static spin-spin correlation matrix elements between singlet states is described. The method uses the property that the site spin operator s XXX p converts a singlet diagram with a line through a site p into a triplet diagram with an arrow through the site p. The method can easily be extended to other spin states as well as to more than two spin correlations. This method would be valuable in cases where charge orthogonality of the VB diagrams alone cannot reduce the computations to a managable extent.

Static and dynamic spin correlations and exchange interactions in Cd 1− xMn xTe

Static and dynamic spin correlations in Cd 0.35Mn 0.65Te were studied by neutron scattering and by computer simulation. We show that it is possible to determine the exchange constant for the nearest neighbors ( J NN) on the basis of inelastic neutron scattering data, and for the next-nearest neighbors ( J NNN) by measuring the anisotropy of the range of static correlations.

Static spin correlations in alternant quantum cell models

Static-spin-correlation functions 4〈${s}_{\mathrm{pz}}$${s}_{\mathrm{qz}}$〉 are evaluated via diagrammatic valence-bond theory for exact states of finite Hubbard, Pariser-Parr-Pople (PPP), and related quantum cell models. Several properties of 〈${s}_{\mathrm{pz}}$${s}_{\mathrm{qz}}$〉 that are independent of intersite potentials ${V}_{\mathrm{pp}\mathcal{'}}$ in the Hartree-Fock (HF) approximation for half-filled alternant systems are shown to be sensitive to correlations in the ground state of N\ensuremath{\le}12 Hubbard and PPP chains. Accurate N\ensuremath{\rightarrow}\ensuremath{\infty} extrapolations are found for near neighbors. The correct ground-state charge density 〈${n}_{p}$〉=1 is a property of half-filled alternant systems and thus not a test of HF or other one-electron approximations. Spin correlations in PPP models with standard molecular parameters and long-range Coulomb interactions are approximately given by on-site interactions of U\ensuremath{\simeq}2\ensuremath{\Vert}t\ensuremath{\Vert} in Hubbard models, although the general semiempirical PPP approach to conjugated molecules is preferable for wide-band systems.

Temperature dependence of the magnetic excitations in gadolinium.

The magnetic excitation spectra of Gd were measured out to the zone boundaries in the and directions over the temperature range from 9 to 320 K. The data were not analyzed because of technical complications, but the data are described remarkably well over the entire q and T range of the experiments by a damped-harmonic-oscillator form for the spectral weight function. The data were parametrized and placed on an absolute basis by an internal calibration using the energy-integrated intensities of the low-temperature spin waves. This parametrization and calibration of the data provide a description of both the static and dynamic spin correlations over this temperature range. Spin-wave peaks are not observed above T/sub c/ in the direction. We attribute this result to the low spin-excitation energies relative to k/sub B/T/sub c/ in this direction.

Low temperature spin wave and domain wall thermodynamics and form factors for the classical easy-plane ferromagnetic chain

Using the steepest descent approach, equivalent to the static limit of the ideal gas phenomenology, we derive low temperature expressions for the free energy and the static spin correlation functions of the classical easy-plane ferromagnetic chain in an in-plane field. At low field the system forms a stable gas spin waves and domain walls. Approaching the critical field for domain wall transition, the domain wall free energy, the longitudinal and transverse in-plane domain wall form factors increase in strength. The transverse in-plane spin wave correlation display damped oscillations and the out-of-plane spin correlations decay exponentially with a growing correlation length. Correspondingly, the out-of-plane form factor increases in intensity. We propose to look for this effect in CsNiF 3 by means of (polarized) neutrons.

Low-temperature spin correlations and spin dynamics in diluted magnetic semiconductors

Neutron scattering measurements of static and dynamic spin correlations in the semimagnetic semiconductor Cd0.35Mn0.65Te are reported and compared to computer simulations for a dilute Heisenberg fcc antiferromagnet that is the model analog of Cd1−xMnxTe.

Magnetic and optical properties of exact PPP states of naphthalene

The Pariser—Parr—Pople (PPP) hamiltonian for naphthalene is solve exactly, to all orders in configuration interaction, using diagrammatic (VB) theory. Standard molecular parameters place the 3B2u, 1B2u, and 1B2a excitations within 0.3 eV of experiment. VB methods for correlated states are extended to the fine-structure constants D and E of the triplet state, which are found to be better than 0.01 cm−1 without any adjustable parameters. Negative spin densities are found at the 9.10 carbons. The weak (f = 0.0005) oscillator strength of the 1B2u transition is related to the absence of electron—hole symmetry on introducing different ionization potential at the 9.10 carbons. The static spin-correlation functions needed for D and E extend the accessible matrix elements over correlated states based on linear combinations of VB diagrams for model hamiltonians with one valence state per site.

Static and dynamic spin correlations in the random one-dimensional antiferromagnetic CsCoxMg1-xCl3

Static and dynamic spin correlations in the random quasi-one-dimensional Ising-like antiferromagnet CsCo0.83Mg0.17Cl3 have been investigated by neutron scattering. The three-dimensional magnetic ordering temperature is strongly suppressed by the presence of impurities. The one-dimensional correlation length tends to a geometric limit at low temperatures in analogy with percolation in higher-dimensional magnetic systems. The quasi-elastic scattering is well described by exact calculations of Szz(Q) for a dilute chain. In addition to the usual spin wave band of the host crystal, the spectrum contains localised modes that arise from the oscillations of spins at the ends of magnetic chains. Their frequency is approximately half that of the host band. Calculations have been made of the weighted contributions to Sxx (Q, omega ) from each randomly occurring length of chain and good agreement with experiment is obtained.

A theory of the properties of anisotropic magnets

Single-ion anisotropy interactions in magnets are notoriously difficult to treat beyond the single-spin-wave approximation, because of the intrinsic important on-site spin correlations. Here the authors propose a Green function decoupling scheme specifically tailored to retain self-consistently the proper static on-site spin correlation functions. The approach is applicable to spins of arbitrary magnitude; the anisotropy contributions do vanish identically for S=1/2, as they should. The magnon interactions arising from exchange terms are treated within the random-phase approximation, and the use of the Dyson-Maleev boson representation limits the accuracy of the results at exceedingly high temperatures. However, the authors find excellent agreement, in some cases greatly improved relative to earlier approximations, with experiments on the prototype uniaxial antiferromagnet FeF2for the temperature dependence of the magnon energies, sublattice magnetisation, parallel susceptibility and spin-flop field up to T approximately=60K approximately=0.76 TN.

Electron paramagnetic resonance of the eclipsed layered compounds NH 3(CH 2) nNH 3CuBr 4 with n = 2, 3, 4

The EPR of the eclipsed layered compounds alkane diammoniumtetrobromocuprate, NH 3(CH 2) n NH 3CuBr 4 with n = 2, 3, and 4 has been studied in the temperature range 113 to 296 K. The angular dependence of the linewidths is explained by the use of the static spin correlations, with emphasis on the extraction of the anisotropies and to confirm the expected departure from two-dimensional magnetism. A discussion of the static spin correlation effects including a possible explanation of the usual linear temperature dependence is included. Comparisons are made to the structurally isomorphic chloride salts.

EPR investigations of the quasi-two-dimensional eclipsed structures of (NH 3(CH 2) nNH 3)CUCl 4 with n = 2, 3, and 4

Electron paramagnetic resonance linewidth measurements as functions of orientation were made on single crystals of the eclipsed, layered series of compounds (NH 3(CH 2) n NH 3)CuCl 4, n = 2, 3, 4, for the temperature range 100 to 333 K. Static spin correlations and antisymmetric exchange contributions are sufficient to explain the orientationally dependent data of the linewidths of the n = 2 and n = 3 compounds of the series, but the n = 4 compound linewidth data require the addition of the secular part of the two-dimensional spin-diffusive effects.

Solitons in magnetic chains: A functional integration approach

The free energies and the static spin correlation functions for the 2π- and π-sine-Gordon systems are calculated from a functional integration approach. The free energies for these systems are rather similar but the soliton contributions to the static two-spin correlation functions can be drastically different. The reasons for these behaviors are discussed, and the nature of the T = 0 phase transitions for the π system is briefly analyzed.

Static Spin Correlations in a Diluted Two-Dimensional Ferromagnet K2CuxZn(1-x)F4 Including the Percolation Vicinity

The static spin correlations in a diluted two-dimensional Heisenberg ferromagnet K 2 Cu x Zn (1- x ) F 4 have been studied. At low temperatures T <3.5 K, the magnetic heat capacity C m ( T ) per mole for Cu 2+ ions in the pure system ( x =1.0) has been revealed to obey the spin wave theory for a two-dimensional Heisenberg ferromagnet with the nearest neighbour exchange constant J / k B =11.4 ±0.4 K. Near the percolation limit ( x p =0.59), the absolute value of C m ( T ) in the same temperature range has been found to agree with the exact solution for the one-dimensional Heisenberg ferromagnet with the same interaction term as in the pure system. The quantities of C m ( T ) for x =0.36 and x =0.26 are discussed in comparison with the theoretical results for the finite size of open chains and closed rings, by taking account of the possible shape of the magnetic clusters presented by the computer generated random system in two dimensions.

Optical absorption and static spin correlation functions in the one-dimensional ferromagnet CsNiF3

The authors report the temperature dependence (1.6<T<25K) of the zeroth and first moments of the absorption line due to the 3A2g to 3T2g( Gamma 3) excitonic transition in the one-dimensional easy-plane ferromagnet CsNiF3. They have found a linear dependence of its position (or of the first moment) on the temperature, a quite unusual behaviour which is claimed to be due to its 1D character. The authors have calculated these moments in terms of one- and two-ion static spin correlation functions. In particular, the linear shift of the first moment with temperature is qualitatively well explained. They discuss quantitatively their results in the light of 1D-Heisenberg, X Y or easy-plane models.

Spin correlations of a dilute two-dimensional Heisenberg ferromagnet near the percolation limit

We have studied the static spin correlations in the quasi-two-dimensional Heisenberg system K 2Cu x Zn 1- x F 4 near the critical percolation concentration. The temperature dependence of the correlation length can be described reasonably well by a classical model without adjustable parameter.

The spin correlation in a ferromagnet with random anisotropy

A computer simulation technique has been used to study the static spin correlation in a ferromagnet with random magnetic anisotropy. An effective anisotropy constant which enables us to express the spin correlation by the domain wall equation was calculated for various values of single-ion anisotropy constant. Allowing the spin tunnelling or not makes a significant difference in the high anisotropy region. The energy of a relaxed domain wall was calculated and it was shown that the domain wall energy approached to zero in the Ising limit, suggesting the instability of the ferromagnetic remanent state. The ground state can be obtained by creating reverse domains in the ferromagnetic state, and should be classified as the spin-glass state. The temperature dependence of the coercivity of the amorphous magnet was explained by the theory developed for highly anisotropic crystalline magnets.

Boundary effects on static spin correlation functions in the isotropicX—Y chain at zero temperature

In this work the static spin correlation of an isotropicX—Y-chain with free ends at zero temperature is dealt with. Following the method of Lieb, Schultz, Mattis the problem is reduced to the evaluation of a determinant of the Cauchy type. With regard to the transverse correlation function we find a change from aR −3/4 to aR −1/2 behavior if the correlated spins move away from the boundary at fixed mutual distanceR.

Antisymmetric and anisotropic exchange in ferromagnetic copper(II) layers

The theory of exchange narrowing is extended in systems with large isotropic ${J}_{0}$ to include static spin correlations and antisymmetric exchange. Both contribute to the unusual temperature-dependent, exchange-narrowed EPR linewidth $\ensuremath{\Delta}H(T)$ in $\mathrm{Cu}X_{4}^{}{}_{}{}^{2\ensuremath{-}} (X=\mathrm{Cl},\mathrm{Br})$ salts based on ferromagnetic layers of $s=\frac{1}{2}$ copper(II) sites. Single-crystal EPR data are presented for Pt${(\mathrm{N}{\mathrm{H}}_{3})}_{4}$Cu${\mathrm{Cl}}_{4}$ and for 1-3-propanediammonium-Cu${\mathrm{Cl}}_{4}$ as a function of temperature and crystal orientation. In both salts, $\ensuremath{\Delta}H(T)$ is shown to be dominated by corrections to ${J}_{0}$, with the antisymmetric exchange larger than the symmetric anisotropic term. Single-crystal EPR provides a novel general approach for finding the magnitude and orientation of the vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{d}}$ for antisymmetric exchange. Antisymmetric contributions to $\ensuremath{\Delta}H(T)$ are not enhanced by spin diffusion in low-dimensional systems when the paramagnetic sites are at inversion centers. The different role of static spin correlations for symmetric and antisymmetric perturbations accounts without adjustable parameters for the angular anisotropy of $\ensuremath{\Delta}H(T)$. The residual temperature dependence of the effective exchange frequency is not understood and probably involves various kinds of phonon modulation.

Wavelength-dependent fluctuations in classical paramagnets in a magnetic field. II. Dynamical properties

For pt.I see ibid., vol.9, p.3639 (1976). A description of the dynamic response of a classical paramagnet to a time and spatially varying perturbation is formulated, which takes into account coupling between the magnetization and energy densities induced by an applied magnetic field. The coupling is manifested implicitly, via thermodynamic quantities which enter the theory, and this aspect is included fully by a renormalization of the energy density. There is also an explicit modification of the dynamical equations, which is studied within the context of a generalized Langevin equation, using the formulation proposed by Mori. It is shown that a judicious choice of dynamical variables enables one to identify dynamical effects resulting from the coupling and, in particular, modifications to the frequency and width of a collective mode. In order to illustrate the consequences of this formalism, results are presented of explicit calculations for one-dimensional ferro- and antiferromagnetically coupled classical Heisenberg magnets, for which all static spin correlation functions of interest can be calculated exactly.