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Acta Physica Polonica A

Spin Polarons in Two-Dimensional Systems

J. A. Morkowski

Published Jan 1, 2000• 1 citation
Publisher

Abstract

The problem of motion of holes on a square lattice of antiferromagnetically ordered spins is considered.An overview of the theory of hole dynamics in the antiferromagnetic background is presented.Motion of a single hole is rather well understood both by numerical and analytical methods.For small but finite concentration of holes a treatment analogous to the standard polaron theory is discussed starting with an exact mapping of the t-J Hamiltonian into holon and pseudospin variables.

DOI
10.12693/aphyspola.97.101

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The problem of motion of holes on a square lattice of antiferromagnetically ordered spins is considered.An overview of the theory of hole dynamics in the antiferromagnetic background is presented.Motion of a single hole is rather well understood both by numerical and analytical methods.For small but finite concentration of holes a treatment analogous to the standard polaron theory is discussed starting with an exact mapping of the t-J Hamiltonian into holon and pseudospin variables.
The motion of a single hole in a two-dimensional Heisenberg antiferromagnet (hAF) is studied in a representation where holes are described as spinless fermions (holons) and spins as normal bosons. Assuming long-range AF order the spin dynamics is treated in linear spin-wave theory. The formulation highlights the close relation with the conventional polaron problem. The holon Green's function is calculated self-consistently within the Born approximation using finite-cluster geometries for the numerical solution. As a remarkable result we find close agreement with the spectral function A(k,\ensuremath{\omega}) of a hole calculated by exact diagonalization methods. A(k,\ensuremath{\omega}) is characterized by a narrow quasiparticle (QP) peak at the low-energy side of the spectrum, which is well separated from the incoherent part for large enough J values. A complete characterization of our solution is given, including the spectral weight, the dispersion relation, and effective masses of the QP state. A finite-size-scaling study gives a nonvanishing spectral weight of the QP in the thermodynamic limit for values J/t typical for copper oxide superconductors. Our calculations indicate that the self-consistent Born approximation is a valuable scheme for characterizing the dynamics of a hole in the t-J model, even in the strong-coupling regime.
The motion of a single hole in a two-dimensional triangular antiferromagnet is investigated using the $t\ensuremath{-}J$ model. The one-hole states are described by strings of spin deviations around the hole. Using projection technique the one-hole spectral function is calculated. For large J/tJ/tJ/t we find low-lying quasiparticlelike bands which are well separated from an incoherent background by a gap of order J. However, for small J/tJ/tJ/t this gap vanishes and the spectrum becomes broad over an energy range of several t. The results are compared with self-consistent Born approximation calculations and numerical data.
The motion of a single hole in an arbitrary magnetic background is investigated for the two-dimensional $t\ensuremath{-}J$ model. The wave function of the hole is described within a generalized string picture which leads to a modified concept of spin polarons. We calculate the one-hole spectral function using a large-string basis for the limits of a N\'eel ordered and a completely disordered background. In addition we use a simple approximation to interpolate between these cases. For the antiferromagnetic background we reproduce the well-known quasiparticle band. In the disordered case the shape of the spectral function is found to be strongly momentum dependent, the quasiparticle weight vanishes for all hole momenta. Finally, we discuss the relevance of results for the lowest energy eigenvalue and its dispersion obtained from calculations using a polaron of minimal size as found in the literature.
We present analytic and numerical results for the ground state of a dynamical hole in a quantum Ising antiferromagnet (the t-Jz{J}_{z}Jz​ model) on a two-dimensional square lattice. We find that the ground state has a localized region of reduced N\'eel order associated with the hole, with an energy that is well described by ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{h}}$/t\ensuremath{\approxeq}-3.63+2.93(Jz{\mathit{J}}_{\mathit{z}}Jz​/t)23{)}^{23})23 for 6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$\ensuremath{\lesssim}Jz{\mathit{J}}_{\mathit{z}}Jz​/t\ensuremath{\lesssim}1. This resolves a disagreement in the literature regarding the coefficient of (Jz{J}_{z}Jz​/t)2/3{)}^{2/3})2/3. A simple string picture gives a reasonable description of the extent of the ground-state polaron in this intermediate-coupling regime. Disruption of long-range antiferromagnetic order in the bulk limit is estimated to occur at Jz{J}_{z}Jz​/t\ensuremath{\approxeq}0.3 for a hole-doping fraction of x=(1/16.
An antiferromagnetic spin model (S=1/2) consisting of a chain of octahedra is considered. In a certain parameter regime of the Hamiltonian the exact ground state is a local resonating-valence-bond (RVB) state. We start with the t-J Hamiltonian for this model describing a single hole in the system and derive exact ground and excited states of the Hamiltonian when the hole is static. The local spin distortion around a hole is termed a spin polaron. The dynamics of the hole is studied through construction of exact eigenstates describing spin polarons in extended states. Coherent states for all momentum wave vectors in the chain direction exist for certain spin polarons. In the Nagaoka limit, the RVB polaronic states have energy greater than that of the ferromagnetic state. For exchange interaction J\ensuremath{\ne}0, the RVB states have lower energy. Other exact states obtained include states in which the hole motion is localized. Structural similarity of the present model to the arrangement of Cu spins in La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{CuO}}_{4}CuO4​ is also highlighted.
We investigate the interplay between the formation of a lattice and magnetic polaron in the case of a single hole in the antiferromagnetic background. We present an exact analytical solution of the Holstein $t\ensuremath{-}J$ model in infinite dimensions. The ground-state energy, electron-lattice correlation function, spin bag dimension as well as spectral properties are calculated. The magnetic and hole-lattice correlations sustain each other, i.e., the presence of antiferromagnetic correlations favors the formation of the lattice polaron at lower values of the electron-phonon coupling while the polaronic effect contributes to reduce the number of spin defects in the antiferromagnetic background. The crossover towards a spin-lattice small polaron region of the phase diagram becomes a discontinuous transition in the adiabatic limit.