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Physics Letters A

Soliton lattice structure of a spin density wave in the one-dimensional t-J model

Vladimir N. Men'shov, Victor V. Tugushev, M. Avignon

Published Mar 1, 2001• 0 citations
Publisher
DOI
10.1016/s0375-9601(01)00056-1

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For a wide range of electron filling we study the spin density wave states in the Hubbard model on a square lattice within a Hartree-Fock approximation. It is shown that the incommensurate helical spin density wave states appear for whole region of the electron filling and, especially, that the commensurate helical spin density wave state with wave vector (π, 0) is stable near the quarter-filling. We examine also the relative stability of the soliton and the vortex lattice states to the helical spin density wave states and obtain the results that near the half-filling case the soliton lattice states are stable states for intermediate interaction strength and that the vortex lattice states do not appear as the stable state, except one particular state with the wind-mill spin structure at the quarter-filling.
Spatially modulated magnetic phases are investigated within the mean field theory for an itinerant electron model, i.e. the Hubbard model on a two-dimensional square lattice. By numerically diagonalizing the Hamiltonian for finite-size systems under a periodic boundary condition, we examine relative stability and physical properties of several possible magnetic states. When the electron fillings are nearly half-full, the diagonally or vertically modulated spin density wave (SDW) state is stabilized over the uniform antiferromagnetic state and a crossover from the vertical to the diagonal states appears. The diagonal or vertical stripe state is characterized by the presence of the midgap band due to the soliton lattice formation inside the main SDW gap, being an insulator. The wave length λ SDW is linearly proportional to the excess carrier concentration. Excess carriers are accommodated in the form of the soliton lattice, forming a charge density wave whose wave length is λ SDW /2.
We study the formation of spin-1 symbiotic spinor solitons in a quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) hyperfine spin F=1 ferromagnetic Bose-Einstein condensate (BEC). The symbiotic solitons necessarily have a repulsive intraspecies interaction and are bound due to an attractive interspecies interaction. Due to a collapse instability in higher dimensions, an additional spin-orbit coupling is necessary to stabilize a quasi-2D symbiotic spinor soliton. Although a quasi-1D symbiotic soliton has a simple Gaussian-type density distribution, novel spatial periodic structure in density is found in quasi-2D symbiotic SO-coupled spinor solitons. For a weak SO coupling, the quasi-2D solitons are of the (-1,0,+1) or (+1,0,-1) type with intrinsic vorticity and multiring structure, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses are angular momenta projections in spin components F_{z}=+1,0,-1, respectively. For a strong SO coupling, stripe and superlattice solitons, respectively, with a stripe and square-lattice modulation in density, are found in addition to the multiring solitons. The stationary states were obtained by imaginary-time propagation of a mean-field model; dynamical stability of the solitons was established by real-time propagation over a long period of time. The possibility of the creation of such a soliton by removing the trap of a confined spin-1 BEC in a laboratory is also demonstrated.