Magnetic order in a spin-1/2 interpolating kagome-square Heisenberg antiferromagnet

Abstract

The coupled cluster method is applied to a spin-half model at zero temperature ($T=0$), which interpolates between Heisenberg antiferromagnets (HAF's) on a kagome and a square lattice. With respect to an underlying triangular lattice the strengths of the Heisenberg bonds joining the nearest-neighbor (NN) kagome sites are $J_1\ge 0$ along two of the equivalent directions and $J_2\ge 0$ along the third. Sites connected by $J_2$ bonds are themselves connected to the missing NN non-kagome sites of the triangular lattice by bonds of strength $J_1^{\prime }\ge 0$. When $J_1^{\prime }=J_1$ and $J_2=0$ the model reduces to the square-lattice HAF. The magnetic ordering of the system is investigated and its $T=0$ phase diagram discussed. Results for the kagome HAF limit are among the best available.

21 pages, 8 figures

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• 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
• Spin-1/2 $J_1$-$J_2$ Heisenberg model on a cross-striped square lattice
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• Frustrated Heisenberg antiferromagnet on the honeycomb lattice with spin quantum number $s\ge 1$
• Frustration induced noncollinear magnetic order phase in one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions
• 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
• Emergence of magnetic long-range order in kagome quantum antiferromagnets