Incommensurate Single-Angle Spiral Orderings of Classical Heisenberg Spins on Zigzag Ladder Lattices

TL;DR

This paper presents exact solutions for classical Heisenberg spins on zigzag ladder lattices, revealing incommensurate spiral orderings driven by geometrical frustration, characterized by a single angle and interaction signs.

Contribution

It introduces a simple cluster method to rigorously solve the ground-state problem and uncovers single-angle spiral orderings caused by lattice geometry.

Findings

Incommensurate spiral orderings arise from geometrical frustration.

Orderings are determined by a single angle and interaction signs.

Solutions are obtained exactly for 2D and 3D zigzag ladder lattices.

Abstract

Exact and rigorous solutions of the ground-state problem for the classical Heisenberg model with nearest-neighbor interactions on two- and three-dimensional lattices composed of zigzag (triangular) ladders are obtained in a very simple way, with the use of a cluster method. It is shown how the geometrical frustration due to the presence of triangles as structural units leads to the emergence of incommensurate spiral orderings and their collinear limits. Interestingly, these orderings are determined by a single angle (along with the signs of the interactions between neighboring spins); therefore, the term "single-angle spiral orderings" is proposed.