Delta chain with anisotropic ferromagnetic and antiferromagnetic interactions

TL;DR

This paper analyzes an anisotropic delta-chain with competing ferromagnetic and antiferromagnetic interactions, revealing flat bands, localized magnons, and unique thermodynamic behaviors depending on anisotropy, bridging ferromagnetic and Ising models.

Contribution

It provides an analytical and numerical study of the anisotropic delta-chain, highlighting the ground state degeneracy and thermodynamic properties across different anisotropy regimes.

Findings

Presence of flat bands and localized magnons at specific interaction values.

Low-temperature specific heat exhibits multiple maxima depending on anisotropy.

Behavior interpolates between ferromagnetic and frustrated Ising models.

Abstract

We consider analytically and numerically an anisotropic spin-$\frac{1}{2}$ delta-chain (sawtooth chain) with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions. For certain values of the interactions a lowest one-particle band becomes flat and there is a class of localized-magnon eigenstates which form a ground state with a macroscopic degeneracy. In this case the model depends on a single parameter which can be chosen as the anisotropy of the exchange interactions. When this parameter changes from zero to infinity the model interpolates between the one-dimensional isotropic ferromagnet and the frustrated Ising model on the delta-chain. It is shown that the low-temperature thermodynamic properties in these limiting cases are governed by the specific structure of the excitation spectrum. In particular, the specific heat has one or infinite number of low-temperature maxima for the small or the large anisotropy parameter, correspondingly. Numerical calculations of finite chains demonstrate that this behavior is generic for definite values of the anisotropy parameter.