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 $0⩽p⩽1$. 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 $\mathbf{Q}={\mathbf{Q}}^{\prime }\approx (1.16,0)$ at $p\approx 0.31$. With the further growth of $p$ the ordering vector moves along the line ${\mathbf{Q}}^{\prime }-{\mathbf{Q}}_{\mathbf{c}}$ to the commensurate point ${\mathbf{Q}}_{\mathbf{c}}=(\frac{2\pi }{3},0)$, 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${}_4$.

18 pages, 6 figures, accepted for publication in Physics Letters A

References in corpus (2)

• First-Order Transition to Incommensurate Phase with Broken Lattice Rotation Symmetry in Frustrated Heisenberg Model
• Incommensurate Phase of a Triangular Frustrated Heisenberg Model Studied via Schwinger-Boson Mean-Field Theory

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• Incommensurate Short-Range Order in $S=1$ Triangular Lattice Ising Antiferromagnet
• Magnetic spiral order in the square-lattice spin system (CuBr)Sr${}_2$Nb${}_3$O${}_{10}$
• Exact diagonalization study of the spin-1 two-dimensional $J_1$-$J_3$ Heisenberg model on a triangular lattice
• Magnetic properties of the spin-1 two-dimensional $J_1-J_3$ Heisenberg model on a triangular lattice