Magnetic short-range order in iron above Tc? Statistical mechanics with many-atom interactions

An effective spin Hamiltonian for iron has been derived previously from electronic structure calculations; there are strong many-atom interactions. The exchange interactions Jij depend on the surrounding magnetic order. We investigate the magnetisation and spin correlation function in iron on this basis in two ways: by fitting the Jij to an analytically soluble Hamiltonian (an extended spherical model) and by Monte Carlo simulation. Short-range manyatom interactions do not lead to substantial short range order in the paramagnetic state; the behaviour closely resembles that of the nearest-neighbour Heisenberg model. The main effect is a slight distortion of the magnetisation curve below TC. Longer range oscillatory pair interactions are needed for short-range order, but are not supported by the electronic structure data. We conclude that calculations of the electronic energy in static configurations do not lead to unusual short range order