Magnetic contributions to thermal expansion of transition metals: implications for local moments above Tc

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Abstract
Most transition-metal magnets, although itinerant in nature, do not undergo large volume contractions on passing from the magnetic to the non-magnetic state. Such a contraction might be expected because of the very large internal magnetic pressure which has been calculated to exist in these magnets at zero temperature. By developing the theory of the spontaneous magnetovolume effect in greater generality than previously, the authors show that it is the local magnetic moment which dictates the pressure. A positive pressure also arises from the energy of disordering the moments at high temperature, and a small net expansion from the coupling of magnetic fluctuations to the anharmonic part of the lattice potential. The effects are related to the experimentally measurable specific heat and thermal coefficient of linear expansion. They analyse the data to infer root-mean-square values of the atomic magnetic moments above the Curie (Neel) temperature TC(TN) in Fe, Ni and Cr, and find a remarkably small reduction from the saturation values at T=0. Even in the Invar alloys most of the atomic moment remains above Tc.