Frustrated classical Heisenberg model in 1 dimension with added nearest-neighbor biquadratic exchange interactions

TL;DR

This paper analyzes the ground state phase diagram of a frustrated 1D classical Heisenberg chain with biquadratic interactions, revealing various magnetic phases and a lock-in transition, using an exact analytical method.

Contribution

It provides the first analytical determination of the ground state phases for this frustrated model with biquadratic interactions.

Findings

Identification of ferromagnetic, incommensurate-spiral, and up-up-down-down phases.

Discovery of a lock-in transition at the spiral boundary.

Analytical ground state solutions obtained via the Lyons and Kaplan cluster method.

Abstract

The ground state phase diagram is determined for the frustrated classical Heisenberg chain with added nearest-neighbor biquadratic exchange interactions. There appear ferromagnetic, incommensurate-spiral, and up-up-down-down phases; a lock-in transition occurs at the spiral boundary. The model contains an isotropic version of the ANNNI model; it is also closely related to a model proposed for some manganites. The Luttinger-Tisza method is not obviously useful due to the non-linear weak-constraint problem; however the ground state is obtained analytically by the exact cluster method of Lyons and Kaplan. The results are compared to the model of Thorpe and Blume, where the Heisenberg part of the energy is not frustrated.