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

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.