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Physical review. B, Condensed matter

Formation of ferromagnetic clusters around holes in the two-dimensionalt-Jmodel

Jörg Sabczynski, Michael Schreiber, A. Sherman

Published Jul 1, 1993• 19 citations
Publisher

Abstract

In the spin-wave approximation the energy spectrum of one-hole states of the two-dimensional t-J model is considered in the parameter range 0.01\ensuremath{\le}J/t\ensuremath{\le}1, where J is the exchange constant and t the hopping-matrix element. Attention is focused on single-particle states (in contrast to hole-magnon continua) that form energy bands characterized by different values of the z component of the total spin ${\mathit{S}}_{\mathit{z}}$, corresponding to ferromagnetically ordered regions of different size around the hole. For an infinite lattice, the shapes and relative positions of the lowest bands are computed by means of the Lanczos method. The formation process of the ferromagnetically ordered region in the one-hole ground state is discussed. It is connected with a characteristic dependence of the band energy on J/t for different ${\mathit{S}}_{\mathit{z}}$. The shapes of the magnon cloud around the hole and the point symmetries of the eigenfunctions are determined for various points in the Brillouin zone and for different bands of interest.

DOI
10.1103/physrevb.48.543

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A motion of a hole in a two-dimensional antiferromagnet is considered in the framework of the #-J model.A temperature dependence of the lowest energy band is calculated for the range T/t £ 0.1 where T and ¢ are the temperature and the hopping constant, respectively.For the exchange constant J= J. =~0 .52 f the lowest energy is shown to be degenerate along the boundaries of the magnetic Brillouin zone.For J < J, the lowest energy is achieved in the points q = (£n/2,+n/2) while for larger J, @ е points (+n,o), (0,%n) of the Brillouin zone.The critical value is independent on 7. А perceptible dependence of the quasiparticle energy on Tis observed for Т »203 J

Proceedings of the Estonian Academy of Sciences Physics Mathematics•Jan 1, 1994•0 citations
In the spin-wave approximation the energy spectrum of one-hole states of the two-dimensional t-J model is considered in the parameter range 0.01\ensuremath{\le}J/t\ensuremath{\le}1, where J is the exchange constant and t the hopping-matrix element. Attention is focused on single-particle states (in contrast to hole-magnon continua) that form energy bands characterized by different values of the z component of the total spin Sz{\mathit{S}}_{\mathit{z}}Sz​, corresponding to ferromagnetically ordered regions of different size around the hole. For an infinite lattice, the shapes and relative positions of the lowest bands are computed by means of the Lanczos method. The formation process of the ferromagnetically ordered region in the one-hole ground state is discussed. It is connected with a characteristic dependence of the band energy on J/t for different Sz{\mathit{S}}_{\mathit{z}}Sz​. The shapes of the magnon cloud around the hole and the point symmetries of the eigenfunctions are determined for various points in the Brillouin zone and for different bands of interest.
Exact many-body states of square clusters up to 18 sites (with periodic boundary conditions) are investigated in order to study the dynamics of one or two holes in the t-J model. Our method takes full advantage of the translation, rotation, and reflection symmetries of the cluster. Using a modified Lanczos algorithm, we calculate the lowest state of all the different space-group representations and its total spin as well as its spin and hole correlations. For a single hole, at intermediate J/t values, the magnetic, kinetic energies, and staggered magnetization follow J/t power-law behaviors with size-dependent exponents. A binding energy of order J between two holes appears for sufficiently large J/t(\ensuremath{\ge}0.25). One-hole and two-hole calculations give different results regarding the stability of the Nagaoka state (against the singlet state) when J/t\ensuremath{\rightarrow}0. Energy expectation values of variational resonating-valence-bond states are calculated exactly and optimized. Significant overlaps with the exact states are found for any symmetry.
We have studied hole states on square lattices with 8, 10, 16, 18, and 20 sites by exactly diagonalizing the single-hole t-J model with twisted boundary conditions in the whole Brillouin zone. The bottom of the hole band is found to be extremely flat and anisotropic. The hole effective mass is highly anisotropic and enhanced in a quantum antiferromagnet. The momentum of a hole in the ground state is not located at high-symmetry points such as (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0), or (0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}). They are strongly lattice-size dependent and weakly parameter J/t (t is the hopping constant and J is the exchange constant) dependent. As the lattice size increases, the momentum of the ground state approaches the zone face center (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).
The behavior of the Drude weight is studied in the small-J/t regime of the t-J model by Lanczos diagonalizations of small clusters with arbitrary boundary conditions and a small number of holes. Although the total spin of the ground state in the J/t\ensuremath{\rightarrow}0 limit depends strongly on the boundary conditions, the Drude weight exhibits a rather universal behavior and indicates a sharp transition around J/t\ensuremath{\sim}0.1 for a hole concentration of \ensuremath{\sim}10%. This crossover is interpreted as a paramagnetic-ferromagnetic transition. For J/t larger than the crossover value, the Drude weight is somehow constant (and reduced by a factor \ensuremath{\sim}3 compared to the case of free holes), suggesting that coherent transport is almost insensitive to the variation of the antiferromagnetic correlation length. At small J/t (and finite doping), the exact nature of the ferromagnetic phase is still uncertain, since both fully polarized state or spin-polaron gas are found in small clusters depending on the boundaries.
The hole spectral function of the t-J model on a two-dimensional semi-infinite lattice is calculated using the spin-wave and non-crossing approximations. In the case of small hole concentrations and strong correlations, t >> J, several near-boundary site rows appear to be depleted of holes. The reason is a deformation of the magnon cloud, which surrounds the hole, near the boundary. The hole depletion leads to a more complicated spectral function in the boundary row in comparison with its bulk shape. This is connected with a maximum related to the underlying row, which reveals itself in the boundary spectrum.
In a t-J model on a chain, an additional next-nearest-neighbor hopping term destroys the complete spin-charge separation at J/t\ensuremath{\ll}1 and induces the formation of stable spin-polarized S>0 states. The properties of a single ferromagnetic polaron are investigated by the exact diagonalization of small systems and by the approximative treatment of an effective model, describing a spinless fermion coupled to the spin background. Both methods give consistent results on the critical Jc{\mathit{J}}_{\mathit{c}}Jc​ for the polaron formation on the increase of the spin S and the polaron size with decreasing J. A very large enhancement of the polaron mass with increasing S is observed. Systems with a finite concentration of holes are also studied within the same framework. Analytical considerations indicate on the bound many-hole states and consequently on phase-separated regions in the phase diagram.
A motion of a hole in a two-dimensional antiferromagnet is considered in the framework of the #-J model.A temperature dependence of the lowest energy band is calculated for the range T/t £ 0.1 where T and ¢ are the temperature and the hopping constant, respectively.For the exchange constant J= J. =~0 .52 f the lowest energy is shown to be degenerate along the boundaries of the magnetic Brillouin zone.For J < J, the lowest energy is achieved in the points q = (£n/2,+n/2) while for larger J, @ е points (+n,o), (0,%n) of the Brillouin zone.The critical value is independent on 7. А perceptible dependence of the quasiparticle energy on Tis observed for Т »203 J