Thermodynamics of the hyperkagome-lattice $S=1\mathrm{/}2$ Heisenberg ferromagnet

The hyperkagome-lattice $S=1\mathrm{/}2$ Heisenberg ferromagnet is studied by means of the linear spin-wave theory, the double-time temperature Green’s function method, high-temperature expansions series analysis, and quantum Monte Carlo simulations to examine the effect of lattice geometry on the finite-temperature properties. In particular, we have found that the Curie temperature $T_c$ for the hyperkagome-lattice (frustrated lattice) ferromagnet is about $0.33\mathrm{\mid }J\mathrm{\mid }$ that is smaller than $T_c$ for the diamond-lattice (another three-dimensional lattice with the same coordination number 4 but bipartite one) ferromagnet by about $25\mathrm{\%}$.