Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin-s Heisenberg models with arbitrary exchange patterns: Application to pyrochlore and kagome magnets

TL;DR

This paper develops a 10th-order high-temperature expansion method for Heisenberg models with arbitrary exchange patterns and spins, applying it to pyrochlore and kagome magnets to analyze susceptibility and specific heat.

Contribution

The authors introduce a C++ algorithm for high-order series expansion of Heisenberg models and apply it to complex lattices, providing new insights into magnetic properties across different spin values.

Findings

Curie temperature for pyrochlore ferromagnets is lower than for simple cubic lattices.

Susceptibility shows weak dependence on spin quantum number at certain temperatures.

Specific heat maximum shifts to lower temperatures as spin quantum number increases.

Abstract

We present the high-temperature expansion (HTE) up to 10th order of the specific heat C and the uniform susceptibility \chi for Heisenberg models with arbitrary exchange patterns and arbitrary spin quantum number s. We encode the algorithm in a C++ program which allows to get explicitly the HTE series for concrete Heisenberg models. We apply our algorithm to pyrochlore ferromagnets and kagome antiferromagnets using several Pad\'e approximants for the HTE series. For the pyrochlore ferromagnet we use the HTE data for \chi to estimate the Curie temperature T_c as a function of the spin quantum number s. We find that T_c is smaller than that for the simple cubic lattice, although both lattices have the same coordination number. For the kagome antiferromagnet the influence of the spin quantum number s on the susceptibility as a function of renormalized temperature T/s(s+1) is rather weak for temperatures down to T/s(s+1) \sim 0.3. On the other hand, the specific heat as a function of T/s(s+1) noticeably depends on s. The characteristic maximum in C(T) is monotonously shifted to lower values of T/s(s+1) when increasing s.