Synergistic polaron formation in the Hubbard-Holstein model at small doping

We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a 2x2 cluster. Nonlocal antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the nonlocal spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction, the electron-phonon coupling is found to decrease the superconducting transition temperature, due to the reduction in the quasiparticle fraction.     

The spin-peierls critical temperature in an XY quasi-one-dimensional system with nearest and next-nearest neighbour interactions

The mean field critical temperature for the spin-Peierls phase transition in the XY antiferromagnetic chain is obtained for nearest and next nearest neighbour exchange interaction. An increase in T_c is predicted for next nearest neighbour antiferromagnetic exchange and a decrease is obtained for ferromagnetic exchange. This model is applied to the alkali-TCNQ salts, which are treated in the framework of the highly correlated Hubbard model.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Zero-field muon-spin-rotation study of hole antiferromagnetism in low-carrier-density Y1−xCaxBa2Cu3O6

We have studied magnetic correlations in the low-carrier-doping regime of Y_1−xCa_xBa₂Cu₃O₆. Samples with carrier densities p_sh=0.015–0.035 (x=0.03–0.07) were studied in the temperature range 2.6–200 K using the zero-field time differential muon spin rotation (ZF TD μSR) technique. An oscillating signal, of 4.1 MHz (∼300 G) in the low-temperature limit (T→0 K), indicative of antiferromagnetism, was found in each sample. This frequency diminished slightly with increasing Ca concentration. Two distinct regimes of frequency as a function of temperature are separated by a kink, which is interpreted as an independent ordering of the spins of the doped holes. The doped-hole spin-freezing temperature is doping dependent and occurs in the range 20.8–33 K. Even in the low-carrier-density regime, the long-range antiferromagnetic ordering is still strongly frustrated by the spin-glass mechanism through calcium doping. Apparent transitions between the 3D frozen-hole antiferromagnetic state and the spin-glassy state with diffusing holes were observed. Clearly the same magnetic interaction mechanisms are operating in both low-carrier-density (Y,Ca)-123 and (La,Sr)₂CuO₄.     

Magnetic and dynamic properties of the Hubbard model in infinite dimensions

An essentially exact solution of the infinite dimensional Hubbard model is made possible by using a self-consistent mapping of the Hubbard model in this limit to an effective single impurity Anderson model. Solving the latter with quantum Monte Carlo procedures enables us to obtain exact results for the one and two-particle properties of the infinite dimensional Hubbard model. In particular, we find antiferromagnetism and a pseudogap in the single-particle density of states for sufficiently large values of the intrasite Coulomb interaction at half filling. Both the antiferromagnetic phase and the insulating phase above the Néel temperature are found to be quickly suppressed on doping. The latter is replaced by a heavy electron metal with a quasiparticle mass strongly dependent on doping as soon asn<1. At half filling the antiferromagnetic phase boundary agrees surprisingly well in shape and order of magnitude with results for the three dimensional Hubbard model.     

Charge transfer near the Néel temperature in La2CuO4+x

The electrical resistance and the thermoelectric power in the ab plane of a weakly oxygen-doped La₂CuO_4+x crystal (0.001<x<0.007) and its static magnetic susceptibility were studied in the vicinity of antiferromagnetic transition. The electrical resistance and the thermoelectric power behave anomalously near the Néel temperature, indicating that the transport is strongly affected by the establishment of long-range antiferromagnetic order. Analysis of the obtained data allows the conclusion to be drawn that the doping gives rise to a conduction band as a result of the overlap between the wave functions of deep impurity states that are strongly renormalized due to the correlation and polaron effects.     

Spin-wave renormalization by mobile holes in a two-dimensional quantum antiferromagnet

The coupling of antiferromagnetic spin excitations and propagating holes has been studied theoretically on a square lattice in order to investigate the dependence of antiferromagnetic order on hole doping, being of relevance, e.g., for the Cu–3 d⁹ system in antiferromagnetic CuO₂-planes of high-T_c superconductors. An effective Hamiltonian has been used, which results from a 2D Hubbard model (hopping integral t) with holes and with strong on-site Coulomb repulsion U. Bare antiferromagnetic excitations and holes with energies of the same order of magnitude t²/U are interacting via a coupling term being proportional to t and allowing holes to hop by emitting and absorbing spinwaves. In terms of a self-consistent one-loop approximation the renormalization of the spectral function both of holes and antiferromagnetic spin excitations are calculated.     

Structure and magnetic properties of Sn1−xMnxO2

The microstructure and magnetic properties have been investigated systematically for Sn_1−xMn_xO₂ polycrystalline powder samples with x=0.02-0.08 synthesized by a solid-state reaction method. X-ray diffraction revealed that all samples are pure rutile-type tetragonal phase and the cell parameters a and c decrease monotonously with the increase in Mn content, which indicated that Mn ions substitute into the lattice of SnO₂. Magnetic measurements revealed that all samples exhibit room temperature ferromagnetism. Furthermore, magnetic investigations demonstrate that magnetic properties strongly depend on doping content, x. The average magnetic moment per Mn atom decreases with increase in the Mn content, because antiferromagnetic super-exchange interaction takes place within the neighbor Mn³⁺ ions through O²⁻ ions for the samples with higher Mn doping. Our results indicate that the ferromagnetic property is intrinsic to the SnO₂ system and is not a result of any secondary magnetic phase or cluster formation.     

Fragmentation of bands and Fermi surfaces in cuprate stripe phases

The band structure and evolution of the Fermi surfaces of stripe phases were studied using the t-t′-U Hubbard model in the mean field approximation. The appearance of quasi-one-dimensional “impurity” subbands caused by the localization of particles on domain walls inside the Hubbard gap is confirmed. Among vertical stripe phases parallel to y bonds, the Y₈ and Y₄ structures with distances l = 8a and 4a between domain walls were found to be stable. Fermi surface segments in antinodal or nodal directions were shown to correspond to an “ impurity” band or the main band related to the entire antiferromagnetic domain region. This is a probable explanation of the difference in the properties of ARPES spectra at different Fermi surface regions observed for La_2?xSr_xCuO₄. It was shown for the Y₈ structure that the topology of the Fermi surface changed and an isotropic pseudogap opened at the point corresponding to a p = 1/8 doping level. Attempts at relating this property to the anomalous suppression of T _c in LSCO at p = 1/8 encountered difficulties. The low dispersion of the impurity band and the wide gap separating it from the lower Hubbard band in diagonal stripe phases formed at p < 0.05 create prerequisites for the existence of the insulating state at nonzero doping.     

Kinematic spin-fluctuation mechanism of high-temperature superconductivity

We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands, there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electron kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators, which results in the kinematic spin-fluctuation pairing mechanism for V ? W. The theory is based on the Mori projection technique in the equation of motion method for the Green’s functions in terms of the Hubbard operators. The doping dependence of the superconductivity temperature T _c is calculated for various values of U and V.     

Magnetization in the two-dimensional Hubbard model: a numerical study

The Projector Quantum Monte Carlo method is used to study the two-dimensional Hubbard model with generalized boundary conditions at half-filling. The convergence of the algorithm depends strongly on the initial trial state. Spin-density waves provide an excellent trial state for the case of weak and of strong correlations. This choice of a trial state with broken symmetry allows us to calculate directly the staggered (or sublattice) magnetization m ₀ as a function of the on-site repulsion U. The use of general boundary conditions strongly reduces finite size effects in m ₀.     

Effect of Ca doping on the magnetic properties of Nd0.5Sr0.5MnO3 studied by electron spin resonance

The magnetic properties of Ca-doped Nd_0.5Sr_0.5MnO₃ have been studied by electron spin resonance (ESR) and dc magnetization measurements. The antiferromagnetic order and charge order are found to occur separately at T_N=200 K and T_co=150 K, respectively. Compared to the undoped Nd_0.5Sr_0.5MnO₃, the ferromagnetic correlations are suppressed by doping of the small Ca²⁺ ion. In addition, the antiferromagnetic transition temperature is enhanced to 200 K, which can be explained by an increase of superexchange interaction between Mn³⁺ and Mn⁴⁺ ions as their distance decreases.     

Optical conductivity of spin/lattice polarons in underdoped copper oxides

Optical and spectral properties of carriers in the presence of strong antiferromagnetic correlations and interacting with optical phonon modes are analyzed using Dynamical Mean Field Theory. We interpret the mid-infrared band in σ(ω) in term of mixed spin lattice polaronic excitations which arise from the stabilization of the lattice polaron due to the antiferromagnetic correlations. We compare our results with experimental data in NCCO showing that the doping and temperature dependences of the optical conductivity in this compound is naturally reproduced within a spin/lattice polaronic model.     

Hartree-Fock theory of spiral magnetic order in the 2-d Hubbard model

The magnetic order in the 2-d Hubbard model is investigated within Hartree-Fock theory. For the class of states with uniform particle density and spiral arrangement of spins the phase diagram is obtained by minimizing the free energy. At zero temperature and large Hubbard interactionU there is a continuous transition from the antiferromagnetic solution at half filling over a spiral state of increasing wavelength along the diagonal of the lattice to the ferromagnetic state at doping _c 2t/U. At finite temperatureT, the antiferromagnetic state remains stable for doping smaller than _AF 2T/U. For intermediate values ofU and finite doping there exists also a phase with a spiral wave vector of the form Q=(Q, ).     

Mott physics, sign structure, ground state wavefunction, and high-T c superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-T _c superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang-Doucot-Anderson (LDA) wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi statistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature ??strange metal phase?? of the doped Mott insulator.     

Variational tests of current order parameters in the Hubbard model

Variational tests are performed for current order parameters as probable sources of the pseudogap normal state of cuprates. The calculations are carried out based on the states with correlations of the valence bond type whose formation can induce in principle both the superconducting order of the d symmetry and current phases. It is shown for the t-t′-U Hubbard models with a large value of U(～8t) and the Hubbard splitting of the conduction band that (1) phases of alternating charge and longitudinal spin currents cannot be realized and (2) transverse spin currents are not compatible with the superconducting order and they could exist against the normal-state background only within a very narrow doping region near the optimal one. This region does not correspond to the region of existence of a pseudogap in cuprates, which refutes the above-mentioned hypothesis of the pseudogap origin. The requirements to the parameters of models for which the consideration of correlations of the valence bond type yields a reasonable phase curve. The existence of current phases in the t-t′-U-V Hubbard models with a strong interaction (V>0.25t) of particles in neighboring sites is predicted when the d-superconductivity is completely suppressed.     

Spin polarization in V(001) slabs

We discuss the onset of layered antiferromagnetic structure in very thin V(001) slabs in terms of the exchange integral J. We use a self-consistent real-space tight-binding method in the unrestricted Hartree-Fock approximation to the Hubbard Hamiltonian. Antiferromagnetic structures occur more readily, i.e. at smaller J values, than ferromagnetic structures. When both paramagnetic and antiferromagnetic solutions are present (for a J value greater than a critical value J_c), the layered antiferromagnetic solutions are always stable. The bilayer is found to be antiferromagnetically polarized; for three layer slabs two types of antiferromagnetic solution are obtained. Our results display the variety of possible magnetic behavior in metallic films and give some insight into the controversial situation on V(001) surface.     

Peculiarity of interrelation between electronic and magnetic properties of HTSC cuprates associated with short-range antiferromagnetic order

We report on the results of measurements of anisotropic resistivity of RBa₂Cu₃O_{6 + x} (R = Tm, Lu) high-temperature superconducting single crystals in a wide range of doping levels, indicating a nontrivial effect of magnetic order on the electronic properties of cuprates. In particular, our results visually demonstrate the crossover from the state with moderate anisotropy of resistivity ρ _c /ρ _ab ～ 30 to a strongly anisotropic state with ρ _c /ρ _ab ～ 7 × 10³ upon cooling as well as upon a decrease in the hole concentration in the CuO₂ planes. It is also shown that anisotropy is sensitive to the magnetic state of CuO₂ planes and attains its maximum value after the establishment of the long-range antiferromagnetic order. The results are discussed in the framework of the theory based on the t-t′-t″-J model of CuO₂ layers taking into account strong electron correlations and short-range magnetic order. In this theory, anomalies of spin correlators and Fermi surface topology for a critical hole concentration of p* ≈ 0.24 are demonstrated. The concentration dependence of the charge carrier energy indicates partial suppression of energy due to the emergence of a pseudogap at p < p*. This theory explains both the experimentally observed sensitivity of anisotropy in conductivity to the establishment of the antiferromagnetic order and the absence of anomalies in the temperature dependence of resistivity ρ _ab (T) in the vicinity of the Néel temperature.     

The effect of Fe doping on structural, magnetic and electrical transport properties of CaMn1−xFexO3 (x=0-0.35)

A comprehensive study of the effect of Fe doping on CaMnO₃ is carried out by means of experiments on the structural, transport conduction, and magnetic properties of CaMn_1−xFe_xO₃ (0≤x≤0.35). With a sol-gel process for sample preparation, Fe is substituted for Mn up to x=0.35. This substitution substantially brings out the lattice expansion and gradually suppresses the antiferromagnetism. For x=0.08 and 0.10 in particular, the magnetization curves with a field-cooled mode under the field of 1 kOe behave as those of a ferrimagnetic-like system and present low-temperature negative magnetization. For x≥0.15, the negative magnetization phenomenon disappears, and a ferromagnetic component coexists with an antiferromagnetic one, but the antiferromagnetic interaction still dominates in these compounds. Electrical transport measurements show insulating behavior for all compositions. Fe doping, even at a level as low as x=0.02, can cause a marked resistivity increase in the temperature range studied. Further increasing the Fe content causes the resistivity to gradually decrease due to the increasing carrier presence.     

Effects of ion doping on magnetism of antiferromagnetic nanoparticles

Based on the Heisenberg model including single-ion anisotropy and using a Green's function technique we have studied the influence of doping effects on magnetization M, Neel temperature T_N and coercive field H_c of antiferromagnetic nanoparticles. We have shown that the experimentally obtained room temperature magnetization M is due to surface or/and doping effects in antiferromagnetic nanoparticles.