A study of long range order in certain two-dimensional frustrated lattices

TL;DR

This paper investigates long-range magnetic order in two-dimensional frustrated lattices, analyzing quantum corrections and the effects of interactions, magnetic fields, and Dzyaloshinskii-Moriya interactions using linear spin-wave theory.

Contribution

It provides analytical insights into how DM interactions and additional couplings influence order stability in frustrated 2D lattices.

Findings

DM interaction stabilizes long-range order

Nearest-neighbour interactions are insufficient to suppress fluctuations

Additional interactions make the excitation spectrum dispersive

Abstract

We have studied the Heisenberg antiferromagnets on two-dimensional frustrated lattices, triangular and kagome lattices using linear spin-wave theory. A collinear ground state ordering is possible if one of the three bonds in each triangular plaquette of the lattice becomes weaker or frustrated. We study spiral order in the Heisenberg model along with Dzyaloshinskii-Moriya (DM) interaction and in the presence of a magnetic field. The quantum corrections to the ground state energy and sublattice magnetization are calculated analytically in the case of triangular lattice with nearesr-neighbour interaction. The corrections depend on the DM interaction strength and the magnetic field. We find that the DM interaction stabilizes the long-range order, reducing the effect of quantum fluctuations. Similar conclusions are reached for the kagome lattice. We work out the linear spin-wave theory at first with only nearest-neighbour (nn) terms for the kagome lattice. We find that the nn interaction is not sufficient to remove the effects of low energy fluctuations. The flat branch in the excitation spectrum becomes dispersive on addition of furthet neighbour interactions. The ground state energy and the excitation spectrum have been obtained for various cases.