Temperature dependence of the spontaneous magnetization of body-centred-cubic bulk iron, amorphous iron and thin iron films

It is shown that the thermal decrease of the spontaneous magnetization of iron differs characteristically depending on the preparation conditions. In all cases, the deviations from saturation at absolute zero can be accurately described by a single temperature power term Tε which holds up to several hundreds of kelvins. The empirical exponents are ε=2 for crystalline bulk iron, ε=3/2 for amorphous iron as well as for isotropic (crystalline) two-dimensional iron films, but ε=5/2 for inhomogeneous (pseudomorphic) monatomic layers. In crystalline films which are sufficiently thick (∼100-300 nm) to allow the excitation of standing spin waves, the T2 bulk law is confirmed for the uniform precession mode, but for states with a periodically modulated magnetization due to spin wave resonance, a T3/2 dependence holds. For ultrathin iron films with more than three atomic layers, a thermodynamic crossover from T3/2 to T2 is observed at higher temperatures. This is indicative of a dimensionality change of the relevant interactions from 2 to 3. Crystalline and amorphous bulk iron also exhibit a crossover, but only for the amplitude and not for the exponent of the Tε law. This is assumed to be caused by the thermal variation of the magnetic interaction strength. All observed empirical exponents ε fit into a recently proposed scheme of universality classes for the low-temperature behaviour of the order parameter in materials with half-integer spin quantum number and three-, two-and one-dimensional interactions. It can therefore be concluded that the thermodynamics of iron is like that of an insulating material with s=1/2. (author)