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arXiv:1107.4141 · Physical Review B

Computational approach to a doped antiferromagnet: Correlations between two spin polarons in the lightly doped CuO 2 plane

Bayo Lau, Mona Berciu, G. A. Sawatzky

Published Oct 5, 2011• 19 citations
arXivHTMLPDF

Abstract

We extend the methods recently introduced [Phys. Rev. Lett. 106, 036401 (2011)] to investigate correlations between two spin-polarons in a quasi-two-dimensional CuO${}_{2}$ layer. The low-energy wave functions for two doped holes introduced in a half filled CuO${}_{2}$ plane with 32 copper and 64 oxygen sites are calculated explicitly using an efficient yet accurate truncation scheme to model the antiferromagnet background. The energetics and wave functions show that the charges form three spin-polarons and the spin is carried by a disturbance around the three spin-polaron core. The low-energy band results from the competition between the kinetic energy and a local attractive potential, which favors ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ states. Last, we point out features that are expected to be robust for larger systems.

DOI
10.1103/physrevb.84.165102

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Comment on "High-Spin Polaron in Lightly Doped CuO$_2$ Planes"

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In a recent Letter (Phys. Rev. Lett. 106, 036401 (2011)), Lau, et al. investigated the single hole problem in an effective model containing Cu $d$ and O $2p$ orbitals by exact diagonalization on clusters composed of 32 CuO$_2$ unit cells. With full quantum fluctuations due to the antiferromagnetic (AFM) backgroud, they found that spin-polaron solutions with spin 3/2 become lowest energy solutions in certain region of Brillouin zone (BZ), which they claimed no similiar solutions were obtained in other models or approximations before. In this Comment, we would like to point out that such high-spin polaron solutions have been found in our previous Letter (Phys. Rev. Lett. 91, 057001, (2003)) and many of features described by Lau et al. have in fact been seen in our Letter.

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We extend the methods recently introduced [Phys. Rev. Lett. 106, 036401 (2011)] to investigate correlations between two spin-polarons in a quasi-two-dimensional CuO2{}_{2}2​ layer. The low-energy wave functions for two doped holes introduced in a half filled CuO2{}_{2}2​ plane with 32 copper and 64 oxygen sites are calculated explicitly using an efficient yet accurate truncation scheme to model the antiferromagnet background. The energetics and wave functions show that the charges form three spin-polarons and the spin is carried by a disturbance around the three spin-polaron core. The low-energy band results from the competition between the kinetic energy and a local attractive potential, which favors dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ states. Last, we point out features that are expected to be robust for larger systems.
Comment on "High-Spin Polaron in Lightly Doped CuO2_22​ Planes"
In a recent Letter (Phys. Rev. Lett. 106, 036401 (2011)), Lau, et al. investigated the single hole problem in an effective model containing Cu ddd and O 2p2p2p orbitals by exact diagonalization on clusters composed of 32 CuO2_22​ unit cells. With full quantum fluctuations due to the antiferromagnetic (AFM) backgroud, they found that spin-polaron solutions with spin 3/2 become lowest energy solutions in certain region of Brillouin zone (BZ), which they claimed no similiar solutions were obtained in other models or approximations before. In this Comment, we would like to point out that such high-spin polaron solutions have been found in our previous Letter (Phys. Rev. Lett. 91, 057001, (2003)) and many of features described by Lau et al. have in fact been seen in our Letter.
This work is a series of reports on progress in the description of electron-electron and electron-lattice interactions in transition-metal oxides, with an emphasis to the class of high-Tc superconducting cuprates. Combinations of numerical and analytical approaches were devised and developed to study large-scale models, which distinguish cation and anion sites of the realistic lattice structure. The many results range from incremental deviation to significant difference compared to those of the widely-accepted simple models without such distinction. A previously proposed numerical scheme and a perturbation approach were adapted to study the one-dimensional breathing-mode model, which describes a charge carrier interacting with vibrating anions. The effort yielded the first accurate benchmark result for all parameters values of the model. Based on a physical insight about the spin-1/2 Heisenberg antiferromagnet on a two-dimensional square lattice, an octapartite approach was devised to model the low-energy states. The efficiency of the resulting numerical approach was showcased with the explicit solution to a record-breaking 64-spin torus. A spin-polaron model was derived to model holes injected into cuprate's quasi two-dimensional copper-oxygen layer. Total-spin-resolved exact diagonalization was performed for a single fermionic hole in a record-breaking cluster with 32 copper and 64 oxygen sites. The solutions revealed important physics missed by previous studies. The octapartite approach was then developed to solve the spin-polaron model with two extra holes in the same cluster. The accuracy and efficiency of the method were established. Enhanced singlet correlation between two holes was observed. The preliminary results justify the need for an in-depth study.
A CuO chain with one or two holes doped is studied via the two-band Hubbard model in the large-U limit on a finite cluster. The quasiparticle band is Ek{\mathit{E}}_{\mathit{k}}Ek​\ensuremath{\sim}0.87J cos(2ka) with the bottom at ka=\ensuremath{\pi}/2. The quasiparticles are kinks which have the character of three-spin polarons. The copper spin excitations are incommensurate spin waves. The two doped holes repel each other very slightly, in contrast to the slight attraction in the t-J model. Spin-charge separation also occurs.
We study an effective one-dimensional (1-D) orbital $t\text{\ensuremath{-}}J$ model derived for strongly correlated eg{e}_{g}eg​ electrons in doped manganites. The ferromagnetic spin order at half filling is supported by orbital superexchange $\ensuremath{\propto}J$ which stabilizes orbital order with alternating ${x}^{2}\ensuremath{-}{y}^{2}$ and $3{z}^{2}\ensuremath{-}{r}^{2}$ orbitals. In a doped system it competes with the kinetic energy $\ensuremath{\propto}t$. When a single hole is doped to a half-filled chain, its motion is hindered and a localized orbital polaron is formed. An increasing doping generates either separated polarons or phase separation into hole-rich and hole-poor regions, and eventually polarizes the orbitals and gives a metallic phase with occupied $3{z}^{2}\ensuremath{-}{r}^{2}$ orbitals. This crossover, investigated by exact diagonalization at zero temperature, is demonstrated both by the behavior of correlation functions and by spectral properties, showing that the orbital chain with Ising superexchange is more classical and thus radically different from the 1-D spin $t\text{\ensuremath{-}}J$ model. At finite temperature we derive and investigate an effective 1-D orbital model using a combination of exact diagonalization with classical Monte Carlo for spin correlations. A competition between the antiferromagnetic and ferromagnetic spin order was established at half filling, and localized polarons were found for antiferromagnetic interactions at low hole doping. Finally, we clarify that the Jahn-Teller alternating potential stabilizes the orbital order with staggered orbitals, inducing the ferromagnetic spin order, and enhancing the localized features in the excitation spectra. Implications of these findings for colossal magnetoresistance manganites are discussed.
Even though realistic one-dimensional experiments in the field of half-metallic semiconductors are not at hand yet, we are interested in the underlying fundamental physics. In this regard we study a one-dimensional ferromagnetic Kondo lattice model, a model in which a conduction band is coupled ferromagnetically to a background of localized d moments with coupling constant J(H), and investigate the T = 0 phase diagram as a function of the antiferromagnetic interaction J between the localized moments and the band-filling n, since it has been observed that doping of the compounds has led to formation of magnetic domains. We explore the spin-polaron formation by looking at the nearest-neighbour correlation functions in the spin and charge regimes for which we use the density matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.