Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin S

We use a second-order rotational invariant Green's-function method (RGM) and the high-temperature expansion (HTE) to calculate the thermodynamic properties of the kagome-lattice spin-S Heisenberg antiferromagnet with nearest-neighbor exchange J. While the HTE yields accurate results down to temperatures of about T/S(S + 1) similar to J, the RGM provides data for arbitrary T >= 0. For the ground state we use the RGM data to analyze the S dependence of the excitation spectrum, the excitation velocity, the uniform susceptibility, the spin-spin correlation functions, the correlation length, and the structure factor. We found that the so-called root 3 x root 3 ordering is more pronounced than the q = 0 ordering for all values of S. In the extreme quantum case S = 1/2, the zero-temperature correlation length is only of the order of the nearest-neighbor separation. Then we study the temperature dependence of several physical quantities for spin quantum numbers S = 1/2,1.....7/2. As S increases, the typical maximum in the specific heat and that in the uniform susceptibility are shifted toward lower values of T/S(S + 1), and the height of the maximum is growing. The structure factor 8(q) exhibits two maxima at magnetic wave vectors q = Q(i), i = 0,1, corresponding to the q = 0 and root 3 x root 3 state. We find that the root 3 x root 3 short-range order is more pronounced than the q = 0 short-range order for all temperatures T >= 0. For the spin-spin correlation functions, the correlation lengths, and the structure factors, we find a finite low-temperature region 0 <= T < T* approximate to a/S(S + 1), a approximate to 0.2, where these quantities are almost independent of T.