Green's function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: stacked square versus stacked kagom\'e lattice

TL;DR

This paper uses Green's function theory to analyze thermodynamic properties of quasi-two-dimensional spin-half Heisenberg ferromagnets on stacked square and kagomé lattices, highlighting the impact of frustration on critical temperature and magnetization.

Contribution

It introduces a Green's function approach to compare thermodynamic behaviors of stacked square and kagomé lattices, emphasizing frustration effects at finite temperatures.

Findings

Lower critical temperature for stacked kagomé lattice due to frustration.

Reduced magnetization at finite temperatures in kagomé lattice.

Short-range order persists above critical temperature.

Abstract

We consider the thermodynamic properties of the quasi-two-dimensional spin-half Heisenberg ferromagnet on the stacked square and the stacked kagom\'e lattices by using the spin-rotation-invariant Green's function method. We calculate the critical temperature $T_C$, the uniform static susceptibility $\chi$, the correlation lengths $\xi_\nu$ and the magnetization $M$ and investigate the short-range order above $T_C$. We find that $T_C$ and $M$ at $T>0$ are smaller for the stacked kagom\'e lattice which we attribute to frustration effects becoming relevant at finite temperatures.