Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$

Abstract

We use the rotation-invariant Green's function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the spin-$S$ Heisenberg ferromagnet on the pyrochlore lattice. We examine the excitation spectra as well as various thermodynamic quantities, such as the order parameter (magnetization), the uniform static susceptibility, the correlation length, the spin-spin correlations, and the specific heat, as well as the static and dynamic structure factors. We discuss the influence of the spin quantum number $S$ on the temperature dependence of these quantities. We compare our results for the pyrochlore ferromagnet with the corresponding ones for the simple-cubic lattice both having the same coordination number $z=6$. We find a significant suppression of magnetic ordering for the pyrochlore lattice due to its geometry with corner-sharing tetrahedra.

15 pages, 12 figures

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• Quantum Heisenberg model on a sawtooth-chain lattice: Rotation-invariant Green's function method
• Recursive algorithm for generating high-temperature expansions for spin systems and the chiral non-linear susceptibility
• Thermodynamics of the hyperkagome-lattice $S=1/2$ Heisenberg ferromagnet
• Three-dimensional unfrustrated and frustrated quantum Heisenberg magnets. Specific heat study