Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit

We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through a spiral spin configuration with characteristic wave vector Q different in general from the antiferromagnetic wave vector Q _AF, and consider spin fluctuations over and above it within the electronic random-phase (RPA) approximation. We obtain a closed system of equations for the generalized wave vector and frequency dependent susceptibilities, which are equivalent to the ones reported recently by Brenig. We obtain, in addition, analytic results for the spin-wave dispersion relation in the strong-coupling limit of the Hubbard Hamiltonian and find that at finite doping the spin-wave dispersion relation has a hybrid form between that associated with the (localized) Heisenberg model and that associated with the (long-range) RKKY exchange interaction. We also find an instability of the spin-wave spectrum in a finite region about the center of the Brillouin zone, which signals a physical instability toward a different spin- or, possibly, charge-ordered phase, as, for example, the stripe structures observed in the high-T _c materials. We expect, however, on physical grounds that for wave vectors external to this region the spin-wave spectrum that we have determined should survive consideration of more sophisticated mean-field solutions. Received 15 September 2000     

Spin susceptibilities for the Hubbard model in a band approach

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω(Q)=c|Q−(π, π)| near Q∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X″(Q,ω→0) gives the same mode with a peak at Q∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X″(Q,ω→0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector. Zh. éksp. Teor. Fiz. 116, 1058–1080 (September 1999)     

Spin waves and static susceptibility in the weakly doped t-J model

We investigate the spin dynamics in weakly doped high-temperature superconductors. The system is described by the two-dimensional t-J model. Our focus is on the interaction between mobile holes and spin waves. The calculations are based on a recently introduced cumulant method for computing the ground state energy of correlated electronic systems. Contrary to previous works using dynamical quantities like correlation functions or spectral densities our approach contains a static view to the system. This new method treats spin and hole dynamics on the same basis and allows for the calculation of static and dynamical quantities. We present results for spin-wave energies and transverse static susceptibilities for small hole concentrations and various values of t/J. We find a strong renor-malization of the spin-wave energies due to the spin-hole interaction. In agreement with neutron scattering experiments the spin-wave velocity vanishes at a critical hole density of a few percent which is equivalent to the instability of the antiferromagnetic order.     

Surface excitations in magnetic systems with a singlet ground state

We have investigated surface excitations in a system wherein the ionic ground state is a magnetic singlet. The pseudospin formalism is employed to account for the crystal-field and exchange interactions between the ions in a Heisenberg ferromagnet with the singlet-triplet crystal-field-only level scheme. The Hamiltonian was studied in the molecular field approximation to find the possible ground states. Surface excitations for the simple cubic structure were investigated for the (001) surface in the random phase approximation. Analytic expressions have been obtained for the thermodynamic Green functions. For a fully magnetized molecular field ground state, there are in general two bulk bands, the spin-wave and the excitonic. Surface modes were found to exist below the spin-wave band, above the excitonic band and between the bands. The dispersion curves can exist only over one or two limited regions of the two-dimensional wave-vector parallel to the crystal surface.     

Quantum Phase Transition and Local Entanglement in Extended Hubbard Model on Anisotropic Triangular Lattices

Using a mean-field theory based upon Hartree-Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.     

Microscopic study of a spin-orbit-induced Mott insulator in Ir oxides

Motivated by recent experiments of a novel 5d Mott insulator in Sr2IrO4, we have studied the two-dimensional three-orbital Hubbard model with a spin-orbit coupling λ. The variational Monte Carlo method is used to obtain the ground state phase diagram with varying an on-site Coulomb interaction U as well as λ. It is found that the transition from a paramagnetic metal to an antiferromagnetic insulator occurs at a finite U=U(MI), which is greatly reduced by a large λ, characteristic of 5d electrons, and leads to the "spin-orbit-induced" Mott insulator. It is also found that the Hund's coupling induces the anisotropic spin exchange and stabilizes the in-plane antiferromagnetic order. We have further studied the one-particle excitations by using the variational cluster approximation and revealed the internal electronic structure of this novel Mott insulator. These findings are in agreement with experimental observations on Sr2IrO4.     

An effective-medium method: The phonon mechanism of anomaly formation in the magnon spectrum of a finite magnetic superlattice

An effective-medium method is developed and applied to calculate the effect of dynamic magnetoelastic interaction on the spin dynamics of a finite magnetic thin-layer superlattice in the long-wavelength approximation. It is shown that if the intra-and interlayer spin-spin interactions are predominantly due to indirect coupling via the long-range field of quasi-static magnetoelastic strains, then the magnon spectrum of such a superlattice exhibits anomalies which are absent in the usually considered case where collective spin-wave excitations are formed through magnetodipole interaction.     

Correlations and confinement of excitations in an asymmetric Hubbard ladder

Correlation functions and low-energy excitations are investigated in the asymmetric two-leg ladder consisting of a Hubbard chain and a noninteracting tight-binding (Fermi) chain using the density matrix renormalization group method. The behavior of charge, spin and pairing correlations is discussed for the four phases found at half filling, namely, Luttinger liquid, Kondo-Mott insulator, spin-gapped Mott insulator and correlated band insulator. Quasi-long-range antiferromagnetic spin correlations are found in the Hubbard leg in the Luttinger liquid phase only. Pair-density-wave correlations are studied to understand the structure of bound pairs found in the Fermi leg of the spin-gapped Mott phase at half filling and at light doping but we find no enhanced pairing correlations. Low-energy excitations cause variations of spin and charge densities on the two legs that demonstrate the confinement of the lowest charge excitations on the Fermi leg while the lowest spin excitations are localized on the Hubbard leg in the three insulating phases. The velocities of charge, spin, and single-particle excitations are investigated to clarify the confinement of elementary excitations in the Luttinger liquid phase. The observed spatial separation of elementary spin and charge excitations could facilitate the coexistence of different (quasi-)long-range orders in higher-dimensional extensions of the asymmetric Hubbard ladder.     

Spectral functions in the two-dimensional Hubbard model within a spin-charge rotating frame approach

We have performed electronic spectral function calculations for the Hubbard model on the square lattice using recently developed quantum SU(2) × U(1) rotor approach that enables a self-consistent treatment of the antiferromagnetic state. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green’s function in the space-time domain as a product of the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. Consequently, the calculation of the spectral line shapes now reduces to performing the convolution of spin, charge and pseudo-fermion Green’s functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.     

Ground state of the half-filled extended Hubbard model beyond the Hartree-Fock approximation

The local approach for the intraatomic correlation is applied to study the ground state phase diagram of the extended Hubbard model with a half-filled band. The long-range orders are not destroyed by the correlation effect in the limit of weak interaction, though the values of the order parameters are reduced from those of the Hartree-Fock approximation, especially for the antiferromagnetic-state. We find that the antiferromagnetic-charge order phase boundary is only slightly shifted towards the charge ordered state, while the phase boundary between the singlet superconducting and the charge ordered phases remains the same as that derived from the Hartree-Fock approximation.     

Spin-Wave Excitations in Anisotropic Kondo Lattice Model

The spin-wave excitations in anisotropic Kondo lattice model are studied using the spin Green's function. Both the ferromagnetic and antiferromagnetic cases are considered. The equations to determine the spectrum of low-energy excitations are given. The anisotropy gaps are obtained, and the long-wavelength and strong-coupling limits are analyzed.     

Spin-charge density waves in the Hubbard model

The ground state of the Hubbard model in a square lattice is examined in the Hartree-Fock mean field approximation at zero temperature. At small finite hole doping, the system has periodically distributed soliton like structures whose modulations are incommensurate. In a self-consistent way, the Fermi energy can always be located in a gap. The incommensurate states have lower energies than the commensurate antiferromagnetic states calculated at the same filling. These soliton structures persist even when a sizeable nearest neighbor repulsive interaction is included.     

Phase diagram of tetragonal manganites

The phase diagram of La1-xSrxMnO3, as a function of hole doping x and tetragonal distortion c/a, which consists of ferromagnetic (FM), A-, C-, and G-type antiferromagnetic (AF) states, is obtained by the first-principles band structure calculations. Effects of tetragonal distortion on the magnetic ordering are discussed in terms of orbital ordering and anisotropy in the hopping integrals. The general sequence of the magnetic ground states, FM --> A-AF --> C-AF --> G-AF with increasing of x, is also explained based on the instability of FM states with respect to the spin-wave excitations.     

Dual boson approach to collective excitations in correlated fermionic systems

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in the so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to an extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to “bare” RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.     

Gapless Excitation above a Domain Wall Ground State in a Flat-Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and with an extended spiral structure in a deformed flat-band Hubbard model in arbitrary dimensions. We show the uniqueness of the ground state for the half-filled lowest band in a fixed magnetization subspace. The ground states with these structures are degenerate with all-spin-up or all-spin-down states under the open boundary condition. We represent a spin one-point function in terms of local electron number density, and find the domain wall structure in our model. We show the existence of gapless excitations above a domain wall ground state in dimensions higher than one. On the other hand, under the periodic boundary condition, the ground state is the all-spin-up or all-spin-down state. We show that the spin-wave excitation above the all-spin-up or -down state has an energy gap because of the anisotropy     

Interaction between localized moments in dilute alloys: Correlation effects

The effect of including dynamical correlations between electrons of opposite spins in determining the ground state energy of a pair of magnetically interacting impurity atoms in an otherwise normal metal is discussed. It is found that in the ground state of such a system the spins of the magnetic impurity atoms are aligned antiparallel. In other words, the interaction between the localized states is of antiferromagnetic exchange type. This result differs sharply from that predicted by the Hartree-Fock (H-F) theory, in which the ground state of the system can be either ferro- or antiferromagnetic, depending on the energies of the spin up and spin down electrons relative to the Fermi energy. The calculations are performed using many-body Green's function techniques in thet-matrix approximation.     

Antiferromagnetic order in multiband Hubbard models for iron pnictides

We investigate multiband Hubbard models for the three iron 3d t(2g) bands and the two iron 3d e(g) bands in LaOFeAs by means of the Gutzwiller variational theory. Our analysis of the paramagnetic ground state shows that neither Hartree-Fock mean-field theories nor effective spin models describe these systems adequately. In contrast to Hartree-Fock-type approaches, the Gutzwiller theory predicts that antiferromagnetic order requires substantial values of the local Hund's-rule exchange interaction. For the three-band model, the antiferromagnetic moment fits experimental data for a broad range of interaction parameters. However, for the more appropriate five-band model, the iron e(g) electrons polarize the t(2g) electrons and they substantially contribute to the ordered moment.     

Quasi‐particle peak due to magnetic order in strongly correlated electron systems

We study the electron spectral function of the antiferromagnetically ordered phase of the three dimensional Hubbard model, using recently formulated low‐energy theory based on the 2D half‐filled Hubbard model which describes both collective spin and charge fluctuations for arbitrary value of the Coulomb repulsion U. The model then is solved by a saddle‐point approximation within the CP¹ representation for the Neel field. The single‐particle properties are obtained by writing the fermion field in terms of a U(1) phase, Schwinger boson SU(2) fields and a pseudofermion variables. We demonstrate that the appearance of a sharp peak in the electron spectral function in the antiferromagnetic state points to the emergence of the bosonic mode, which is associated with spin ordering.     

Quantum versus Jahn-Teller orbital physics in YVO3 and LaVO3

We argue that the large Jahn-Teller (JT) distortions in YVO3 and LaVO3 should suppress the quantum orbital fluctuation. The unusual magnetic properties can be well explained based on local density approximation + Hubbard U calculations using experimental structures, in terms of the JT orbital. The observed splitting of the spin-wave dispersions for YVO3 in a C-type antiferromagnetic state is attributed to the inequivalent VO2 layers in the crystal structure, instead of the "orbital-Peierls state." Alternative stacking of ab-plane exchange couplings produces the c-axis spin-wave splitting; thus, the spin system is highly three dimensional rather than quasi-one-dimensional. Similar splitting is also predicted for LaVO3, although it is weak.     

Band diagram of spin waves in a two-dimensional magnonic crystal

The dispersion curves of collective spin-wave excitations in a magnonic crystal consisting of a square array of interacting saturated nanodisks have been measured by Brillouin light scattering along the four principal directions of the first Brillouin zone. The experimental data are successfully compared to calculations of the band diagram and of the Brillouin light scattering cross section, performed through the dynamical matrix method extended to include the dipolar interaction between the disks. We found that the fourfold symmetry of the geometrical lattice is reduced by the application of the external field and therefore equivalent directions of the first Brillouin zone are characterized by different dispersion relations of collective spin waves. The dispersion relations are explained through the introduction of a bidimensional effective wave vector that characterizes each mode in this magnonic metamaterial.