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

Abstract

We present the high-temperature expansion (HTE) up to 10th order of the specific heat C and the uniform susceptibility χ 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 Padé approximants for the HTE series. For the pyrochlore ferromagnet we use the HTE data for χ to estimate the Curie temperature Tc as a function of the spin quantum number s. We find that Tc 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) ∼ 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.

Stabilization of the tetragonal structure in(Ba1−xSrx)CuSi2O6

“…The data of #2 for the different orientations are fitted with a random-phase approximation (RPA) according to [24] together with a Curie contribution resulting from isolated S = 1 2 impurities (fits are the full green lines). The full orange line corresponds to the expected χm (T ) using high-temperature series expansion (HTSE) [31] with the magnetic coupling constants taken from the DFT calculation, see chapter VI. Inset: χ (T )of #2 (full red circles) together with the data of an undoped single crystal (open cyan circles) for B ⊥c .…”

“…[11] for x = 0 in the tetragonal phase and (ii) a reasonably good agreement between our ab initio-calculated intradimer J 1 and J intra obtained in the previous section. We use a high-temperature series expansion [31] in order to check if the calculated exchange couplings can explain the experimentally measured susceptibility. The values we obtain for the T = 1.5 K neutron structure produce the orange curve in Fig.…”

Barlowite as a canted antiferromagnet: Theory and experiment

“…For the latter orientation the magnetization was measured in fields up to ±5 T. The experimental data have been corrected for the temperatureindependent diamagnetic core contribution of the constituents 26 and the magnetic contribution of the sample holder. By considering the exchange parameters obtained from DFT, we calculated 1/χ mol using 10th-order hightemperature series expansion 23 . The result is shown in Fig.…”

Spin-ordered ground state and thermodynamic behaviors of the spin-32kagome Heisenberg antiferromagnet

“…5, due to the low-lying gapless magnetic excitations. We also include HTSE results [34] at two different parameters Pade [5,5] and Pade [4,6] as comparisons. Both results are consistent with our calculations at high temperatures, while they deviate remarkably from the iPEPS result at relatively low temperatures, revealing the failure of HTSE in that regime.…”

“…In addition, it is still a challenge to accurately calculate the thermodynamic properties at low temperatures for kagome Heisenberg spin systems. The conventional high-temperature series expansion (HTSE) method [34] can effectively capture the nature at high or even intermediate temperatures, but was unable to reliably determine the thermodynamic behavior at low temperature. In this regard, a systematic and accurate study on the spin-3/2 KHAF is quite indispensable.…”