Magnetic phase diagram of the spin-1 two-dimensional J1-J3 Heisenberg model on a triangular lattice

Abstract

The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest, $J_1=-(1-p)J,$ $J>0$, and antiferromagnetic third-nearest-neighbor, $J_3=pJ$, exchange interactions is studied in the range of the parameter $0 \leqslant p \leqslant 1$. Mori's projection operator technique is used as a method, which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At $p\approx 0.2$ 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 ${\bf Q = Q^\prime} \approx (1.16, 0)$ at $p\approx 0.31$. With the further growth of $p$ the ordering vector moves along the line ${\bf Q^\prime-Q_c}$ to the commensurate point ${\bf Q_c}=(\frac{2\pi}{3}, 0)$, which is reached at $p = 1$. The final state with an antiferromagnetic long-range order can be conceived as four interpenetrating sublattices with the $120^\circ$ spin structure on each of them. Obtained results are used for interpretation of the incommensurate magnetic ordering observed in NiGa$_2$S$_4$.