The spiral spin state in a zigzag spin chain system

TL;DR

This paper analyzes the conditions under which spiral spin states are the ground states in a zigzag spin chain with various interactions, using a transformation approach and matrix theorems, highlighting the role of Dzyaloshinskii-Moriya interaction.

Contribution

It introduces a method connecting spiral and fully polarized states via a unitary transformation to identify ground state conditions in complex spin systems.

Findings

Dzyaloshinskii-Moriya interaction influences spiral pitch angle.

The method applies to coupled chains and 2D lattices.

Results are comparable with experimental data.

Abstract

We considered a spin chain with nearest neighbor and next nearest neighbor exchange interactions, anisotropic exchange interaction and Dzyaloshinskii-Moriya interaction. The conditions of the spiral spin state as the ground state were analyzed. Our method was to build the connection between the spiral state and the fully polarized state with a unitary transformation. Under this transformation, anisotropic exchange interaction and Dzyaloshinskii-Moriya interaction can be transformed to each other. Then we used positive semi-definite matrix theorem to identify the region of fully polarized state as the ground state for the transformed Hamiltonian, and it is the region of spiral spin state as the ground state of the original Hamiltonian. We also found that the effect of Dzyaloshinskii-Moriya interaction is important. Its strength is related to the pitch angle of spiral spins. Our method can be applied to coupled spin chains and two dimensional triangular lattice systems. The result can be compared with experiment data.