Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

TL;DR

This paper presents an exactly solvable model of a sawtooth chain with mixed Ising and Heisenberg bonds, revealing ground state phases, magnetization plateaus, and a new stabilization mechanism for the 1/4 magnetization plateau.

Contribution

It introduces an exact solution for the sawtooth chain with lattice distortions and uncovers a novel mechanism for stabilizing the 1/4 magnetization plateau.

Findings

Ground state phase diagrams with magnetization plateaus at 0, 1/4, and 1/2.

Exact formulas for bond distortions in various ground states.

Identification of a new mechanism stabilizing the 1/4 magnetization plateau.

Abstract

An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling to lattice distortion for Heisenberg bonds is considered in the magnetic field. Using the direct transfer-matrix formalism an exact description of the thermodynamic functions is obtained. The ground state phase diagrams for all regions of parameters values containing phases corresponding to the magnetization plateaus at $M=0,1/4$ and 1/2 have been obtained. Exact formulas for bond distortions for various ground states are presented. A novel mechanism of magnetization plateau stabilization corresponding to $M=1/4$ state is reported.