Effective spin quantum numbers in iron, cobalt and nickel

The known macroscopic data for the temperature dependence of the normalized spontaneous magnetization, m(s)(T), of iron, cobalt and nickel are reconsidered and compared with our normalized zero-field hyperfine field data, h(hf)(T), obtained by Mossbauer spectroscopy or nuclear magnetic resonance. It is observed that for all three metals h(hf)(T) is not proportional to m(s)(T) and systematically smaller than m(s)(T). This is attributed to smaller magnetic interactions in the domain walls compared to the volume of the domains. The temperature dependence of m(s)(T) and h(hf)(T) can be described in the whole range 0 < T < T-C by a few temperature power functions with analytical changes (crossovers) at the intersections of these functions. Below the critical power law, m(s) similar to (T-C - T)(beta), further power functions of the absolute temperature according to m(s)(T) = A - cT(epsilon), follow. From the observed rational exponents epsilon it can be concluded whether the effective spin is integer or half-integer. Using additionally the known data for the saturation magnetic moments and the effective paramagnetic Bohr magneton numbers it is suggested that for nickel the effective spin is S = 1/2 for T --> 0 but S = 1 for higher temperatures including the paramagnetic phase. For iron and cobalt the corresponding values are S = 3/2 and 2. (C) 2003 Elsevier B.V. All rights reserved.