The spin-$\frac{1}{2}$ Heisenberg ferromagnet on the pyrochlore lattice: A Green's function study

TL;DR

This paper investigates the thermodynamic properties of the spin-1/2 Heisenberg ferromagnet on the pyrochlore lattice using Green's function, spin-wave theory, and quantum Monte Carlo, revealing enhanced thermal fluctuations due to frustration.

Contribution

It provides a comparative analysis of pyrochlore and simple cubic lattices, highlighting the impact of frustration on thermal fluctuations in the pyrochlore ferromagnet.

Findings

Thermal fluctuations are more effective in the pyrochlore lattice due to frustration.

Results are consistent across Green's function, spin-wave, and Monte Carlo methods.

Contrasts with simple cubic lattice show mean-field similarity but different fluctuation effects.

Abstract

We consider the pyrochlore-lattice quantum Heisenberg ferromagnet and discuss the properties of this spin model at arbitrary temperatures. To this end, we use the Green's function technique within the random-phase (or Tyablikov) approximation as well as the linear spin-wave theory and quantum Monte Carlo simulations. We compare our results to the ones obtained recently by other methods to corroborate our findings. Finally, we contrast our results with the ones for the simple-cubic-lattice case: both lattices are identical at the mean-field level. We demonstrate that thermal fluctuations are more efficient in the pyrochlore case (finite-temperature frustration effects). Our results may be of use for interpreting experimental data for ferromagnetic pyrochlore materials.