Double-time Green Research Articles

Magnetic properties of the triangular-lattice multilayer antiferromagnet with single-site anisotropy

The Heisenberg antiferromagnet with single-site anisotropy on the fully frustrated multilayer triangular lattice is investigated by employing the double-time Green's function. The origin of the spin gap is analysed; it is suggested to be closely related to the magnetic anisotropy. The axial and planar susceptibilities and the specific heat are calculated. The theoretical result agrees with that of a Monte Carlo simulation and that of an experiment on the compounds CsMnI3 and CsMnBr3.

Role of Interlayer and Intersite Interactions in Superconducting State in High-Tc Layered Cuprates

We studied the role of interlayer and intersite interactions on transition temperature and specific heat of layered high-Tc cuprates. We used double-time Green's function technique in the spirit of mean field approximation in order to obtain the expressions for hole density, transition temperature, and specific heat. These expressions are found to be dependent on the carrier concentration and intersite and interlayer interactions. The numerical analysis shows that the effect of intersite interaction on transition temperature and specific heat is qualitatively similar to that of interlayer interactions and provides favorable conditions to establish long-range order in the superconducting state.

Magnetic dynamics of bilayer cuprate superconductors

In the present paper, we use the Heisenberg antiferromagnetic model within linear spin-wave theory to study the magnetic dynamics of bilayer antiferromagnets such as ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}.$ The Zubarev's double-time Green's-function formalism has been employed in order to evaluate the expressions for spin-wave dispersion, sublattice magnetization, and specific heat. It has been shown that in these systems, the intrabilayer coupling leads towards a ``spin gap.'' The optical mode is found to contribute significantly to the sublattice magnetization only in the high-temperature regime. In the low-temperature regime, the contribution from the acoustic mode is sensitive to the anisotropy term. We observe that the dipolar anisotropy does not produce the three-dimensional (3D) N\'eel ordering, while the exchange anisotropy is essential to keep 3D N\'eel ordering in these systems. Further, we observe a crossover from 3D to quasi-2D behavior at a certain temperature. The presence of the optic mode does not seem to alter the quasi-2D behavior of these systems in the higher temperature regime. The specific heat is also found to be dependent on the ratio of intrabilayer to in-plane coupling strength (r). These results are compared with the existing results.

Damping of the double giant dipole resonance

A microscopic approach is proposed to the damping of the double giant dipole resonance (DGDR). The double-time Green's function method is used to derive a closed set of coupled equations for the propagation of two-phonon excitation through the field of incoherent nucleon pairs. The analytical expressions for the width and energy shift of the DGDR are obtained. The numerical calculations are performed for ${}^{90}\mathrm{Zr},$ ${}^{90}\mathrm{Sn},$ and ${}^{208}\mathrm{Pb}$ for several characteristics of the DGDR at zero as well as nonzero temperatures T. The results are found in reasonable agreement with existing experimental systematics for the width and energy of the DGDR. As compared to the estimation within the harmonic picture, the anharmonicity leads to a noticeable enhancement of the integrated photoabsorption cross section (IPACS) over the DGDR region. The DGDR width is found to increase sharply with increasing T at $T<~3\mathrm{MeV},$ but goes to a saturation at $T>3\mathrm{MeV}$. The harmonic limit for the DGDR width is restored already at $T>~1.5\mathrm{MeV}.$ It is shown that the IPACS of the DGDR can also be enhanced compared to its harmonic value if it is built on a hot GDR.

Double-time Green’s-function approach to the two-dimensional Heisenberg antiferromagnet with broken bonds

We improved the decoupling approximation of the double-time Green's function theory, and applied it to study the spin-${1\over 2}$ two-dimensional antiferromagnetic Heisenberg model with broken bonds at finite temperature. Our decoupling approximation is applicable to the spin systems with spatial inhomogeneity, introduced by the local defects, over the whole temperature region. At low temperatures, we observed that the quantum fluctuation is reduced in the neighborhood of broken bond, which is in agreement with previous theoretical expectations. At high temperatures our results showed that the quantum fluctuation close to the broken bond is enhanced. For the two parallel broken bonds cases, we found that there exists a repulsive interaction between the two parallel broken bonds at low temperatures.

A comparative study of Heisenberg-like models with and without internal spin fluctuations

A comparative study has been carried out on the magnetic properties of the Heisenberg-like models with and without internal spin fluctuations. A two-spins-per-site Heisenberg-like model is used to mimic the internal spin fluctuations inside atoms. Using the double-time Green's function decoupling method, we have calculated the magnetization and paramagnetic susceptibility of the model Hamiltonians for different atomic spins as functions of the temperature and exchange energies. Our study suggests that the internal spin fluctuations generally reduce the transition temperature, and modify the magnetic behaviours. Unlike the results obtained by using the usual Heisenberg model, our results show that the Curie constant of the two-spins-per-site Heisenberg model depends on the individual moments, rather than on the resultant saturated magnetic moment. The possible physical implication of our result is also discussed.

Magnetization and susceptibility of the two-spin Heisenberg model

To take the intra-site spin magnitude fluctuation into account, the usual one-spin per site Heisenberg Hamiltonian is extended to two interacting spins per site. We have studied the magnetization and susceptibility of the model Hamiltonian as function of temperature and coupling constants using the double-time Green's function method. In contrast to the one-spin per site Heisenberg Hamiltonian where the Curie constant depends only on the resultant saturated magnetic moment, our results show that Curie constant of the two-spin per site Heisenberg model depends rather on the individual moments. Thus, the Curie constant can have finite value even when the resultant saturated magnetic moment vanishes. The possible physical implication of our result is also discussed.

Role of interlayer interactions on transition temperature in high- Tc cuprate superconductors

The effect of interlayer interactions on transition temperature in high- T c layered superconductors has been studied using a one-band two-layer tight binding Hamiltonian with intra- and interlayer attractive interactions. The double-time Green's function technique is employed and higher-order Green's functions are linearized by using a mean field decoupling approximation. The expressions for the transition temperature ( T c) and excitonic type interlayer correlation ( γ c) are obtained. It is shown that interlayer interactions play an important role in the enhancement of T c in high- T c cuprates. We have also explained the relevance of our results in high- T c layered superconductors having two layers per unit cell under externally applied pressure.

Effect of interlayer interaction in high-T c cuprate superconductors

We have studied the role of interlayer attractive interaction in a high-Tc system having two layers per unit cell. The single band two-layer tight binding model Hamiltonian is considered and the double time Green's function technique is applied within the mean field approximation. The expressions for the hole density, transition temperature, and intra- and interlayer order parameters are obtained which are found to be dependent on the interlayer interaction and other parameters appearing in the Hamiltonian. The numerical analysis shows that the coupling of the charge carriers (holes) between the layers provides better conditions for the stabilization of long-range order and high superconducting transition temperature in layered superconductors. It is also observed that superconductivity is confined to a narrow region of hole concentration and the single particle tunneling suppresses the transition temperature.

Effect of an interband interaction on narrow-band superconductivity.

The effect of an interband interaction (${\mathit{U}}_{\mathit{s}\mathit{d}}$) on narrow-band superconductivity in the presence of weak hybridization has been studied by extending the Anderson lattice Hamiltonian. We have employed Zubarev's double-time Green's-function technique and used a mean-field decoupling scheme to obtain the self-consistent expressions for the transition temperature (${\mathit{T}}_{\mathit{c}}$) and interband correlation parameter (${\ensuremath{\gamma}}_{\mathit{c}}$). The ${\mathit{T}}_{\mathit{c}}$ is found to be dependent on both the interband interaction and on the strength of the hybridization between s- (or p-) and d-band electrons (within a two-band model). We have shown that the interband interaction (${\mathit{U}}_{\mathit{s}\mathit{d}}$) plays qualitatively the same role as that of hybridization (V). Finally, we have explained the relevance of our results in transition metals or electron-doped high-${\mathit{T}}_{\mathit{c}}$ superconductors under externally applied pressure.

Comment on "Effect of fractons and magnons on the resistivity of dilute ferromagnets"

The double-time Green's-function decoupling scheme used by Li, Tian, and Jiang [Phys. Rev. B 47, 11 905 (1993)] is non-self-consistent and non-moment-preserving. When replaced by a self-consistent, moment-preserving decoupling scheme, important differences arise. In particular, the results presented by Li et al. for a system of spin S and spin coupling constant ${\mathit{J}}_{\mathit{i}\mathit{j}}$ are, instead, appropriate for a system with spin S/2 and spin coupling constant 2${\mathit{J}}_{\mathit{i}\mathit{j}}$.

Spin Waves in a Surface-Diluted Quantum Spin system11The project supported by the State Key Laboratory of Magnetism, Institute of Physics of Chinese Academy of Sciences.

A theoretical investigation of the effects of surface dilution on spin waves in a semi-infinite transverse Ising model (TIM) is presented. Within the framework of the double-time Green's function theory, the local density of spin-wave states is obtained by the application of the cluster-Bethe-lattice (CBL) method. Numerical calculations of paramagnetic phases reveal that surface dilution will lead to appearance of the localized spin-wave states whose frequencies are bulk independent while the corresponding density of states is a function of the exchange interactions. Increase of the bulk exchange interactions between the surface and the bulk spins tends to diminish the localized spin-wave states. Dependence of the local density of states on the concentration p of the magnetic atoms is similar with that in a three-dimensional infinite TIM which has been discussed in our previous paper.

Equation of motion for the Green's function in anharmonic solids.

We discuss the double-time Green's-function approach for the phonon-phonon interaction in anharmonic solids. Using a certain interpretation of the phonon operators, the crystal Hamiltonian may be rewritten in a compact form. The equation of motion for the Green's function is tremendously simplified with this formalism. The self-energy can be obtained in a very simple way, to any desired perturbation order. Our results reproduce the corresponding terms of the available literature results, which are limited to the fourth order in the perturbation parameter.

Mean-field Green's-function theory of the two-sublattice Ising model in a transverse field.

Double-time Green's functions are used within a mean-field treatment of the two-sublattice Ising model in a transverse field. In contrast to previous treatments, a correct version of the spectral theorem is used to obtain a correct mean-field treatment for all spin. In particular, the dielectric constant is obtained for S=1. The results are markedly different from those of earlier treatments and are readily extended to four-sublattice models.

Comment on "Undetermined-constant method in the boson Green's-function theory"

The apparent fundamental inconsistency in the behavior of double-time Green's functions and the correlations related to them by the spectral theorem claimed by Zhang and Qin [Phys. Rev. A 36, 915 (1987)] is shown to arise from the use of an incorrect version of the spectral theorem. The ``method of undetermined constants'' constructed by Zhang and Qin to remove this apparent inconsistency is not an intrinsic characteristic of the boson Green's-function method. Rather, it is unnecessary and leads to incorrect results in both systems considered by Zhang and Qin, i.e., the mean-field transverse Ising model and the symmetrically decoupled zero-field Heisenberg model. Use of the correct spectral theorem is shown to remove the inconsistency. Correct treatments based on the correct spectral theorem of the models considered by Zhang and Qin are also presented.

Self-consistent generalized random-phase approximation for spin systems.

A generalized random-phase approximation (RPA) for decoupling the double-time Green's functions (DTGF) equations of motion of spin systems is developed. The decoupling parameters are chosen by fixing the moments of both the commutator and anticommutator decoupled spectral functions, thus establishing a well-defined relationship between the approximation scheme and the fundamental properties of DTGF. It is shown that the standard RPA must be supplemented by a condition on correlations to provide a well-defined, complete approximation scheme. The procedure is demonstrated by application to the fully anisotropic S=1/2 Heisenberg model in a field.

The shift of the curie temperature due to spin-phonon interaction

By means of the method of double-time Green's functions with Callen's decoupling scheme an expression for the energy of a spin-phonon interaction system was derived. Using this result a formula for the shift of the Curie temperature due to spin-phonon interaction was obtained.

A General Approach to Deriving the Statistical Distribution Function

In this paper a general approach to obtaining the statistical distribution function is given. In the specific case of free field, the statistical distribution functions are derived under a basis set of general commutation relations by using the double–time Green's functions in the first, second and third order decoupling approximations respectively.

Green's-function theory of the spin-1 exchange-interaction model of ferromagnetism.

Double-time Green's functions are used to study dipolar and biaxial ordering in the presence of a uniaxial field for the spin-1 exchange interaction model of ferromagnetism. The decoupling of the Green's function equations of motion hierarchy is based upon the identification of the members of the spin-1 basis operator set whose diagonal susceptibilities diverge in the ordered phase as the statistically independent members of the basis set. In contrast to standard double-time Green's function techniques, the results are unambiguous and the result for the critical temperature in the vanishing field limit compares very favorably with the high-temperature series expansion result.

Infrared lattice absorption in anharmonic crystals with impurities

The dielectric susceptibility and infrared absorption in anharmonic crystals, containing randomly distributed substitutional defects, is theoretically investigated, with the use of double time Green's function technique and modified Kubo formalism. The study uses cubic, quartic, anharmonic and defect terms in the Hamiltonian along with the second order terms in the dipole moment expansion. Mass change as well as force constant change between impurity and host lattice atoms, are taken into account. The total lattice absorption in such crystals is the sum of the terms depending on the first and second order dipole moments, respectively. The dominant first order term can be further separated into the diagonal and nondiagonal contributions. The nondiagonal contribution, being small, vanishes in the absence of substitutional impurities. The diagonal term is discussed in detail and can be written as a sum of the contributions, namely anharmonic, defect dependent, and a cross term contribution, involving both anharmonic and defect parameters simultaneously. It is shown that this cross term contribution to the absorption coefficient is finite and will show up in experiments.