The spin-1 J1-J3 Heisenberg model on a triangular lattice

Abstract

Motivated by the experimental data for NiGa2S4, the spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, J1 = −(1 − p)J and J3 = pJ, J > 0, is studied in the range 0 ≤ p ≤ 1. Mori’s projection operator technique and the Lanczos exact diagonalization are used. Mori’s method retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At pcr ≈ 0.2 the ground state is transformed from the ferromagnetic spin structure into a disordered state, which in its turn is changed to an antiferromagnetic long-range ordered state with the incommensurate ordering vector Q′ ≈ (1.16, 0) at p ≈ 0.31. With growing p the ordering vector moves along the X axis to the commensurate point Qc = (2π/3, 0) which is reached at p = 1. The final state with an antiferromagnetic long-range order can be conceived as four interpenetrating sublattices with the 120° spin structure on each of them. The model is able to describe the state with the incommensurate short-range order observed in NiGa2S4. To verify the used approach the ground state energy and corresponding spin-spin correlations are compared with exact-diagonalization results obtained with the SPINPACK code (the Lanczos exact diagonalization). Results of the two methods are in qualitative agreement.