Magnetization processes in nanocrystalline gadolinium

The thermal decline in magnetization, M(T), at fixed magnetic field (H) under 'zero-field-cooled' (ZFC) and 'field-cooled' (FC) conditions, the time evolution of ZFC magnetization, M(ZFC)(t), at fixed temperature and field, M(H) hysteresis loops/isotherms, and ac susceptibility have been measured on polycrystalline Gd samples with average grain sizes of d = 12 and 18 nm. The irreversibility in magnetization, M(irr), occurring below a characteristic temperature that reduces with increasing H, is completely suppressed above a grain-size-dependent threshold field, H*. At low fields (H ≤ 100 Oe), M(irr)(T), like the coercive field, H(c)(T), exhibits a minimum at ∼16 K and a broad peak at ∼50 K before going to zero at T ≃ T(C) (Curie temperature). At fixed temperature (T < T(C)) and field (H ≪ H*), where M(irr) is finite, M(ZFC) has a logarithmic dependence on time. The magnetic viscosity (S) at H = 1 Oe and T ≤ 290 K is independent of the measurement time above ∼2 ms but for t < 2 ms it is strongly time-dependent. S(T) peaks at T ≃ T(C) for H = 1 Oe. A magnetic field reduces the peak height and shifts the peak in S(T) to lower temperatures. All the above observations are put on a consistent theoretical footing within the framework of a model in which the intra-grain magnetizations overcome the energy barriers (brought about by the intra-grain and grain-boundary/interfacial magnetic anisotropies) by the thermal activation process. These field- and temperature-dependent energy barriers, that separate the high-energy metastable (ZFC) state from the stable minimum-energy (FC) state, are independent of time for t ≳ 2 ms and have a very broad distribution. We show that the shape anisotropy plays a decisive role in the magnetization reversal process, and that the magnetocrystalline and magnetostatic fluctuations, prevalent in the grain-boundary and interfacial regions, govern the approach-to-saturation of magnetization in nanocrystalline Gd.