The spin-1 two-dimensional J1-J2 Heisenberg antiferromagnet on a triangular lattice

TL;DR

This study investigates the phase transitions and magnetic ordering in a spin-1 Heisenberg antiferromagnet on a triangular lattice with varying nearest- and next-nearest-neighbor couplings, revealing multiple transitions and incommensurate orderings.

Contribution

It applies Mori's projection operator technique to analyze the entire parameter range, identifying new phases and detailed transition points without assuming magnetic order.

Findings

Four second-order phase transitions identified.

Transition from long-range to short-range order at p≈0.038.

Incommensurate order develops for 0.5<p<0.96.

Abstract

The spin-1 Heisenberg antiferromagnet on a triangular lattice with the nearest- and next-nearest-neighbor couplings, $J_1=(1-p)J$ and $J_2=pJ$, $J>0$, is studied in the entire range of the parameter $p$. 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 four second-order phase transitions are observed. At $p\approx 0.038$ the ground state is transformed from the long-range ordered $120^\circ$ spin structure into a state with short-range ordering, which in its turn is changed to a long-range ordered state with the ordering vector ${\bf Q^\prime}=\left(0,-\frac{2\pi}{\sqrt{3}}\right)$ at $p\approx 0.2$. For $p\approx 0.5$ a new transition to a state with a short-range order occurs. This state has a large correlation length which continuously grows with $p$ until the establishment of a long-range order happens at $p \approx 0.65$. In the range $0.5<p<0.96$, the ordering vector is incommensurate. With growing $p$ it moves along the line ${\bf Q'-Q}_1$ to the point ${\bf Q}_1=\left(0,-\frac{4\pi}{3\sqrt{3}}\right)$ which is reached at $p\approx 0.96$. The obtained state with a long-range order can be conceived as three interpenetrating sublattices with the $120^\circ$ spin structure on each of them.