We have developed an ab initio framework for calculating parameters of a high-temperature magnetic Hamiltonian. In the adiabatic approximation, this includes transverse and longitudinal magnetic excitation spectra on equal footing. The exchange interaction parameters of the Hamiltonian for bcc Fe and fcc Ni are determined from constrained local spin-density approximation calculations. Finite temperature magnetic properties of the resulting model Hamiltonian are then investigated by a Monte Carlo simulation technique. The calculated Curie temperatures and paramagnetic susceptibilities are in good agreement with experimental data for both metals. We demonstrate that the temperature-induced longitudinal spin fluctuations are important for high temperature properties such as susceptibility and magnetic specific heat.
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