Antiferromagnetic Spin Background Research Articles

Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction

Unveiling the microscopic origins of quantum phases dominated by the interplay of spin and motional degrees of freedom constitutes one of the central challenges in strongly correlated many-body physics. When holes move through an antiferromagnetic spin background, they displace the positions of spins, which induces effective frustration in the magnetic environment. However, a concrete characterization of this effect in a quantum many-body system is still an unsolved problem. Here we present a Hamiltonian reconstruction scheme that allows for a precise quantification of hole-motion-induced frustration. We access non-local correlation functions through projective measurements of the many-body state, from which effective spin-Hamiltonians can be recovered after detaching the magnetic background from dominant charge fluctuations. The scheme is applied to systems of mixed dimensionality, where holes are restricted to move in one dimension, but SU(2) superexchange is two-dimensional. We demonstrate that hole motion drives the spin background into a highly frustrated regime, which can quantitatively be described by an effective J1–J2-type spin model. We exemplify the applicability of the reconstruction scheme to ultracold atom experiments by recovering effective spin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Our method can be generalized to fully 2D systems, enabling promising microscopic perspectives on the doped Hubbard model.

Doublon-holon pairing mechanism via exchange interaction in two-dimensional cuprate Mott insulators.

Coupling of charge and spin degrees of freedom is a critical feature of correlated electron oxides, as represented by the spin-related mechanism of a Cooper pair under high-T c superconductivity. A doublon-holon pair generated on an antiferromagnetic spin background is also predicted to attract each other via the spin-spin interaction J, similar to a Cooper pair, while its evidence is difficult to obtain experimentally. Here, we investigate such an excitonic effect by electroreflectance spectroscopy using terahertz electric field pulses in undoped cuprates: Nd2CuO4, Sr2CuO2Cl2, and La2CuO4. Analyses of the spectral changes of reflectivity under electric fields reveal that the splitting of odd-parity and even-parity excitons, a measure of doublon-holon binding energy, increases with J. This trend is reproduced by t-J-type model calculations, providing strong evidence of the spin-related doublon-holon pairing. Agreement with the calculations supports the s-wave symmetry of the doublon-holon pair in contrast to the d-wave Cooper pair in doped cuprates.

Ultrafast separation of photodoped carriers in Mott antiferromagnets.

We use inhomogeneous nonequilibrium dynamical mean-field theory to investigate the spreading of photoexcited carriers in Mott insulating heterostructures with strong internal fields. Antiferromagnetic correlations are found to affect the carrier dynamics in a crucial manner: An antiferromagnetic spin background can absorb energy from photoexcited carriers on an ultrafast time scale, thus enabling fast transport between different layers and the separation of electron and holelike carriers, whereas in the paramagnetic state, carriers become localized in strong fields. This interplay between charge and spin degrees of freedom can be exploited to control the functionality of devices based on Mott insulating heterostructures with polar layers, e.g., for photovoltaic applications.

Mechanism of ultrafast relaxation of a photo-carrier in antiferromagnetic spin background

We study the relaxation mechanism of a highly excited charge carrier propagating in the antiferromagnetic background modeled by the $t$-$J$ Hamiltonian on a square lattice. We show that the relaxation consists of two distinct stages. The initial ultrafast stage with the relaxation time $\ensuremath{\tau}\ensuremath{\sim}(\ensuremath{\hbar}/{t}_{0}){(J/{t}_{0})}^{\ensuremath{-}2/3}$ (where ${t}_{0}$ is the hopping integral and $J$ is the exchange interaction) is based on the generation of string states in the close proximity of the carrier. This unusual scaling of $\ensuremath{\tau}$ is obtained by means of the comparison of numerical results with a simplified $t$-${J}_{z}$ model on a Bethe lattice. In the subsequent (much slower) stage, local antiferromagnetic excitations are carried away by magnons. The relaxation time on the two-legged ladder system is an order of magnitude longer due to the lack of string excitations. This further reinforces the importance of string excitations for the ultrafast relaxation in the two-dimensional system.

Mixed singlet‐triplet superconducting state in doped antiferromagnets

AbstractWe analyze symmetry mixing in the superconducting (SC) order parameter of planar cuprates. The behavior of thermal conductivity observed in some systems doped with magnetic impurities or in some systems exposed to external magnetic field seems to indicate that such symmetry mixing takes place. We discuss this phenomenon in the framework of the spin polaron model (SPM). We assume that antiferromagnetic (AF) correlations, which are at least of short range, tend to confine motion of holes which have been created in the AF spin background. The nature of the propagation of quasiparticles which are hole‐like and the nature of the interaction between quasiparticles is determined by a tendency to restore the local AF order. It is known that two holes in the t –J model (tJ M) form bound states with dx 2–y 2 or p‐wave symmetry. The d‐wave bound state has lower energy and is the ground state. The mixing of d‐wave symmetry with p‐wave symmetry takes place in the SC order parameter at some range of finite values of the doping parameter. That range lies at the applicability verge of the SPM, where AF correlation are already very short. On the other hand, these correlations may be strengthened by above mentioned external factors, which seems to explain why symmetry mixing is observed in this case. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Self-localization of holes in a lightly doped Mott insulator

We show that lightly doped holes will be self-trapped in an antiferromagnetic spin background at low-temperatures, resulting in a spontaneous translational symmetry breaking. The underlying Mott physics is responsible for such novel self-localization of charge carriers. Interesting transport and dielectric properties are found as the consequences, including large doping-dependent thermopower and dielectric constant, low-temperature variable-range-hopping resistivity, as well as high-temperature strange-metal-like resistivity, which are consistent with experimental measurements in the high-T$_c$ cuprates. Disorder and impurities only play a minor and assistant role here.

Photogenerated holon-doublon cluster states in strongly correlated low-dimensional electron systems

We theoretically investigate the properties of multiphoton excited states in strongly correlated one-dimensional (1D) and two-dimensional (2D) electron systems at half filling using the extended Hubbard model. In the 2D case, we find the photoexcited states where two or more than two holons and doublons are strongly bound, and the cluster of bound holons and doublons coexists with the surrounding antiferromagnetic (AF) spin order, for the realistic Coulomb interaction parameters. The holon-doublon cluster (HDC) states have a unique charge aggregation mechanism originating from the spin-spin interaction in the AF spin background as well as from the direct Coulomb interaction. In the 1D case, the HDC states are destabilized by the spin-spin interaction in contrast to the 2D case. These charge aggregation mechanisms are the outcomes of exotic natures of holons and doublons, and the difference in the mechanism between the 1D and 2D cases is due to the difference in the coupling between spin and charge degrees of freedom. We also calculate the light-induced absorption that enables us to experimentally observe the predicted HDC states.

Cooper pairing and superconductivity in a spin fluctuation model for high-Tc cuprate superconductors

We study the formation of Cooper pairs in high-Tc cuprate superconductors within a spin uctuation model for doped quantum Heisenberg antiferromagnets. The charge of the dopants (chargons) is associated to quantum skyrmion excitations of the Cu++ antiferromagnetic spin background. We then compute the quantum skyrmion e effective interaction potential as a function of doping and temperature in order to study charge pairing. It becomes clear that Cooper pair formation is determined by the competition between the spin uctuations of the Cu++ magnetic ions and the spins of the O-- doped holes (spinons). The superconducting transition occurs when the effective potential allows for skyrmion bound states. Our theoretical predictions for the superconducting phase diagram of La2-x Srx CuO4 and YBa2 Cu3O6+x are in good agreement with experiment.

Relation between flux formation and pairing in doped antiferromagnets

We demonstrate that patterns formed by the current-current correlation function are landmarks which indicate that spin bipolarons form in doped antiferromagnets. Holes which constitute a spin bipolaron reside at opposite ends of a line (string) formed by the defects in the antiferromagnetic spin background. The string is relatively highly mobile, because the motion of a hole at its end does not raise extensively the number of defects, provided that the hole at the other end of the line follows along the same track. Appropriate coherent combinations of string states realize some irreducible representations of the point group C_4v. Creep of strings favors d- and p-wave states. Some more subtle processes decide the symmetry of pairing. The pattern of the current correlation function, that defines the structure of flux, emerges from motion of holes at string ends and coherence factors with which string states appear in the wave function of the bound state. Condensation of bipolarons and phase coherence between them puts to infinity the correlation length of the current correlation function and establishes the flux in the system.

A SELF-CONSISTENT ANALYTIC THEORY OF THE SPIN BIPOLARON IN THE t–J MODEL

The spin bipolaron in the t–J model, i.e., two holes interacting with an antiferromagnetic spin background, is treated by an extension of the self-consistent Born approximation (SCBA), which has proved to be very accurate in the single-hole (spin polaron) problem. One of the main ingredients of our approach is the exact form of the bipolaron eigenstates in terms of a complete set of two-hole basis vectors. This enables us to eliminate the hole operators and to obtain the eigenvalue problem solely in terms of the boson (magnon) operators. The eigenvalue equation is then solved by a procedure similar to Reiter's construction of the single-polaron wave function in the SCBA. As in the latter case, the eigenvalue problem comprises a hierarchy of infinitely many coupled equations. These are brought into a soluble form by means of the SCBA and an additional decoupling approximation, whereupon the eigenvalue problem reduces to a linear integral equation involving the bipolaron self-energy. The numerical solutions of the integral equation are in quantitative agreement with the results of previous numerical studies of the problem. The d-wave bound state is found to have the lowest energy with a critical value J/t| c ≈ 0.4. In contrast to recent claims, we find no indication for a crossover between the d-wave and p-wave bound states.

Analysis of the first electron-removal states of using polarization dependent angle-resolved photoelectron spectroscopy

The first electron-removal states of the layered cuprate Ba2Cu3O4Cl2 were measured using angle-resolved photoelectron spectroscopy. The symmetry and energy-momentum relations of the lowest-lying states were determined and interpreted in terms of the motion of a single hole in the two different planar Cu-O subsystems of the Cu3O4 plane. One subsystem is antiferromagnetic as in the undoped parent compounds of the high-temperature superconductors and the other is paramagnetic and corresponds to the strongly overdoped case. The data are compared to theoretical results on hole dynamics in two-dimensional antiferromagnetic or paramagnetic spin backgrounds. The lineshape, symmetry and dispersion of the first electron-removal states of Ba2Cu3O4Cl2 can be described in terms of Zhang-Rice singlets within a single band model. The photohole lifetime in the paramagnetic subsystem of the Cu3O4 plane is much smaller than with an antiferromagnetic spin background.

Theory of excitons in the insulatingCu−O2plane

We use a local model to study the formation and the structure of the low-energy charge-transfer excitations in the insulating ${\mathrm{C}\mathrm{u}\ensuremath{-}\mathrm{O}}_{2}$ plane. The elementary excitation is a bound exciton of spin singlet, consisting of a ${\mathrm{Cu}}^{+}$ and a neighboring spin singlet of Cu-O holes. The exciton can move through the lattice freely without disturbing the antiferromagnetic spin background, in contrast to the single hole motion. There are four eigenmodes of excitons with different symmetry. The $p$-wave-like exciton has a large dispersion width. The $s$-wave-like exciton mixes with the $p$ state at finite momentum, and its dipole transition intensity is strongly anisotropic. The model is in excellent agreement with the electron energy-loss spectra in the insulating ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}.$

Orthogonality instability in a planar antiferromagnet with one impurity

We present a study of a model for a single fermion coupled to a planar quantum antiferromagnetic (AFM) spin background via a local Kondo-like coupling. Within the framework of the linear-spin-wave theory and the self-consistent Green's functions formalism we obtain the quasiparticle pole strength vanishing as ϵ 1/2 with the momentum cut-off ϵ ⪡ 1. The wave-function for the ground state is constructed. Using this wave-function we show that the average number of magnons at the position of the impurity is finite and that the distribution of magnons decays as 1/ R at large distances from the impurity.

One spin-polaron problem in the two-dimensional Kondo lattice

Using the spin-polaron concept and the spherically symmetric state for the antiferromagnetic spin background, one-particle motion is studied for the two-dimensional Kondo lattice. The elementary excitations are represented by a Bloch superposition of four one-site electron states: two local states - a bare electron state and a local spin-polaron of small radius -and two states of delocalized polarons which correspond to the coupling of local states to the antiferromagnetic spin wave with momentum Q = ( π, π), so-called Q-polarons. We show that the lowest band of elementary excitations is essentially determined by Q-polaron states in the strongly coupled regime. Taking into account Q-polarons shifts the band bottom from (π,π) to (0,0). The spectral weight of a bare particle in the lowest band states can greatly differ from 1. This may lead to a large Fermi surface for a relatively small particle concentration.

Phase string effect in the t-J model: General theory

We reexamine the problem of a hole moving in an antiferromagnetic spin background and find that the injected hole will always pick up a sequence of nontrivial phases from the spin degrees of freedom. Previously unnoticed, such a stringlike phase originates from the hidden Marshall signs which are scrambled by the hopping of the hole. We can rigorously show that this phase string is nonrepairable at low energy and give a general proof that the spectral weight Z must vanish at the ground-state energy due to the phase-string effect. Thus, the quasiparticle description fails here and the quantum interference effect of the phase string dramatically affects the long-distance behavior of the injected hole. We introduce a so-called phase-string formulation of the t-J model for a general number of holes in which the phase-string effect can be explicitly tracked. As an example, by applying this new mathematical formulation in one dimension, we reproduce the well-known Luttinger-liquid behaviors of the asymptotic single-electron Green's function and the spin-spin correlation function. We can also use the present phase-string theory to justify previously developed spin-charge separation theory in two dimensions, which offers a systematic explanation for the transport and magnetic anomalies in the high-${\mathrm{T}}_{\mathrm{c}}$ cuprates.

Phase String Effect in a Doped Antiferromagnet.

Based on the $t\ensuremath{-}J$ model, it is shown that a hole moving on an antiferromagnetic spin background always induces a phase-string effect. Such a previously unnoticed phase string is revealed by explicitly tracking the Marshall sign and can be rigorously shown to be nonrepairable at low energy. Its quantum interference can drastically modify the long-wavelength behavior of the doped hole, leading to a vanishing spectral weight $Z$ at the ground-state energy. Implication for finite doping is also discussed.

Intermediate-coupling theory of the spin polaron in the t-J model.

The spin polaron in the t-J model, i.e., a hole dressed by a cloud of virtual magnons of the antiferromagnetic spin background, is treated within the framework of intermediate-coupling theory. To this end the original t-J model is first reformulated in terms of spinless fermions and bosons by means of the generalized Dyson-Maleev representation (DMR). The latter may be regarded as the natural extension of the ordinary DMR of pure (undoped) spin systems to the case where holes are present, and is similar to the one originally proposed by Schmitt-Rink, Varma, and Ruckenstein. The reformulated t-J model, which is reminiscent of the Fr\"ohlich Hamiltonian, is then subjected to a series of unitary transformations, analogous to those employed by Lee, Low, and Pines in their treatment of the Fr\"ohlich polaron. Our approach yields an approximate quasiparticle energy E(k) as well as the corresponding eigenvector. To explore the range of validity of the theory presented here, the analytic expressions are then further analyzed for intermediate (J/t=0.4) and strong (J/t=0.08) coupling, where special attention is paid to the quasiparticle bandwidth W. The intermediate-coupling result for E(k) is in excellent agreement with the dispersion curve recently obtained by Dagotto and co-workers by means of a Green function Monte Carlo method. Surprisingly, even in the strong-coupling range the bandshape remains qualitatively correct.The bandwidth W is rather accurate for weak coupling (J/t\ensuremath{\gtrsim}3), as expected, and still reasonable in the intermediate range 0.4\ensuremath{\lesssim}J/t\ensuremath{\le}3, where it deviates from the correct values by some 10--20 %. Our theory fails, however, to describe the proper behavior of W in the strong-coupling regime. This shows that the limitations of our approach manifest themselves in the bandwidths rather than in the shapes of the dispersion curves. Our conclusion is that intermediate-coupling theory is appropriate for J/t\ensuremath{\gtrsim}0.4, whereas a genuine strong-coupling theory is required for all other cases. \textcopyright{} 1996 The American Physical Society.

Freezing electronic correlations by polaronic instabilities in doped La2NiO4.

In doped Mott-Hubbard insulators, the electron-phonon interaction and strong Coulomb repulsion can reinforce each other to stabilize small polarons, domain walls, and charge-density waves. We discuss how the electron-phonon coupling stabilizes domain-wall states in an antiferromagnetic spin background for small doping, and promotes coupled spin- and charge-density wave transitions at larger doping, and we explain why this coupling is more important in the nickelate than in the cuprate. We discuss our results in the light of recent experiments on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{NiO}}_{4+\mathit{y}}$.

Lattice- and spin-polaronic defects in antiferromagnetic halogen-bridged transition-metal chain compounds.

The results of many-body modeling are reported for polaronic defect excitations in the nickel-based halogen-bridged chain compounds, exemplified by NiBr. One-electron band structures and Raman scattering amplitudes, for electron and hole polarons and bipolarons, triplet excitons, negative, neutral, and positive solitons, are qualitatively described. A singlet exciton is found to be unstable with our model parameters, due to the large on-site Hubbard repulsion. Most significantly, the local defect excitations exhibit a substantial lattice distortion relative to the undistorted antiferromagnetic spin background. The stoichiometric lattice symmetry is therefore broken locally, resulting in Raman activity, which is unexpected on the basis of the stoichiometric ground-state symmetry.

Fermions in an antiferromagnet with generalized Berry phases.

Starting with the spin-fermion model we construct an effective field theory for holes moving in a slowly varying antiferromagnetic (AF) spin background. The fast magnetic modes are integrated out by performing the trace over the spin degrees of freedom within an expansion in generalized Berry phases. Then the continuum limit is taken both in the order-parameter field as well as in the fermionic variables, where the whole band structure with minima at wave vectors ${\mathbf{k}}_{\mathrm{min}}$=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) is replaced by parabolic bands centered at those k points. The influence of the fluctuating antiferromagnetic background on the motion of the holes is taken into account by introducing a local and time-dependent spin reference frame for the fermions via an SU(2) rotation of the fermionic spinor. This transformation leads to an effective action for charge carriers minimally coupled to a vector gauge field whose fluctuations are controlled by the ${\mathit{CP}}^{1}$ model. An alternative representation in the laboratory reference frame gives a coupling of spin- and fermionic currents that was previously obtained by Shraiman and Siggia for the t-J model.