Thermodynamics of S>=1 ferromagnetic Heisenberg chains with uniaxial single-ion anisotropy

The thermodynamic properties of S>=1 ferromagnetic chains with an easy-axis single-ion anisotropy are investigated at arbitrary temperatures by both a Green-function approach, based on a decoupling of three-spin operator products, and by exact diagonalizations of chains with up to N=12 sites using periodic boundary conditions. A good agreement between the results of both approaches is found. For the S=1 chain, the temperature dependence of the specific heat reveals two maxima, if the ratio of the anisotropy energy D and the exchange energy J exceeds a characteristic value, D/J >7.4, and only one maximum for D/J <7.4. This is in contrast to previous exact diagonalization data for comparably small chains (N <= 7) using open boundary conditions. Comparing the theory with experiments on di-bromo Ni complexes the fit to the specific heat yields concrete values for D and J which are used to make predictions for the temperature dependences of the spin-wave spectrum, the correlation length, and the transverse magnetic susceptibility.