Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice

Abstract

We study the zero-temperature phase diagram of the $J_1^{XXZ}$--$J_2^{XXZ}$ Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour ($J_1\equiv 1$) and next-nearest-neighbour ($J_2>0$) bonds. Both bonds have the same $XXZ$-type anisotropy in spin space. The effects on the quasiclassical Néel-ordered and collinear stripe-ordered states of varying the anisotropy parameter $\Delta$ is investigated using the coupled cluster method carried out to high orders. By contrast with the spin-1/2 case studied previously, we predict no intermediate disordered phase between the Néel and collinear stripe phases, for any value of the frustration $J_2/J_1$, for either the $z$-aligned ($\Delta >1$) or $xy$-planar-aligned ($0\le \Delta <1$) states. The quantum phase transition is determined to be first-order for all values of $J_2/J_1$ and $\Delta$. The position of the phase boundary $J_2^c(\Delta )$ is determined accurately. It is observed to deviate most from its classical position $J_2^c=1/2$ (for all values of $\Delta >0$) at the Heisenberg isotropic point ($\Delta =1$), where $J_2^c(1)=0.55\pm 0.01$. By contrast, at the XY isotropic point ($\Delta =0$), we find $J_2^c(0)=0.50\pm 0.01$. In the Ising limit ($\Delta \to \infty$) $J_2^c\to 0.5$ as expected.

20 pages, 5 figures

References in corpus (15)

• Strong Correlations and Magnetic Frustration in the High Tc Iron Pnictides
• Antiferromagnetic superexchange interactions in LaOFeAs
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Possible ferro-spin nematic order in NiGa2S4
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• The quantum $J_1$--$J_1^{\prime }$--$J_2$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model
• The quantum $J_1$-$J_1^{\prime }$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method
• Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: High-order coupled-cluster calculations
• Influence of the spin quantum number $s$ on the zero-temperature phase transition in the square lattice $J$-$J^{\prime }$ model
• Two-dimensional spin-1 frustrated Heisenberg model with valence-bond ground states

Cited by in corpus (16)

• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Magnetism in a family of $S=1$ square lattice antiferromagnets Ni$X_2$(pyz)${}_2$ ($X=$ Cl, Br, I, NCS; pyz = pyrazine)
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
• A frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model
• Ground-state phases of the spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet on the honeycomb lattice
• Magnetic order in spin-1 and spin-3/2 interpolating square-triangle Heisenberg antiferromagnets
• The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB$m$ Approximation Scheme for Lattice Models
• A frustrated quantum spin-${\boldmath s}$ model on the Union Jack lattice with spins ${\boldmath s>1/2}$
• A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer
• The Spin-Half {\it XXZ} Antiferromagnet on the Square Lattice Revisited: A High-Order Coupled Cluster Treatment
• Large-$s$ expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number $s$
• Frustrated Heisenberg antiferromagnet on the honeycomb lattice with spin quantum number $s\ge 1$
• The quantum J_{1}-J_{1'}-J_{2} spin-1/2 Heisenberg antiferromagnet: A variational method study
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model