Geometrically frustrated Ising-Heisenberg spin model on expanded Kagom\'e lattice

TL;DR

This paper analyzes an exactly solvable Ising-Heisenberg model on an expanded Kagomé lattice, revealing complex phase behavior, frustration effects, and thermodynamic properties through analytical methods.

Contribution

It introduces an exactly solvable Ising-Heisenberg model on the expanded Kagomé lattice and explores its phase diagram and thermodynamic properties.

Findings

Identification of multiple magnetic phases including frustrated and ferrimagnetic phases

Analysis of residual entropy in the frustrated region

Dependence of critical temperature and magnetization on Hamiltonian parameters

Abstract

Here we consider the Ising-Heisenberg model in the expanded Kagom\'e lattice, also known as triangle-dodecagon (3-12) or star lattice. This model can still be understood as a decorated honeycomb lattice. Assuming that the Heisenberg spins are at the vertices of the triangle while other spins are of the Ising type. Thus, this model is equivalent to an effective Kagom\'e Ising lattice, through the decoration transformation technique. Thus this means that the model is exactly solvable so we can study the most relevant properties of this model. Like the phase diagram at zero temperature, exhibiting a frustrated phase, a ferromagnetic phase, a classical ferrimagnetic phase and a quantum ferrimagnetic phase. We observed that Heisenberg spin exchange interaction influences the frustrated phase, but we rigorously verify that the magnitude and origin of the frustration emerge in a similar way to antiferromagnetic Ising Kagom\'e lattice. Likewise, the thermodynamic properties of the model can also be obtained, such as the critical temperature as a dependence of the Hamiltonian parameters and the spontaneous magnetization of the model. Besides, we investigated the entropy of the model, identifying its residual entropy in the frustrated region. Even we analyze the specific heat behavior as a temperature dependence, to deal with the phase transition.