Some of the most relevant finite-size and surface effects in the magnetic and transport properties of magnetic fine particles and granular solids are reviewed. The stability of the particle magnetization, superparamagnetic regime and the magnetic relaxation are discussed. New phenomena appearing due to interparticle interactions, such as the collective state and non-equilibrium dynamics, are presented. Surface anisotropy and disorder, spin-wave excitations, as well as the enhancements of the coercive field and particle magnetization are also reviewed. The competition of surface and finite-size effects to settle the magnetic behaviour is addressed. Finally, two of the most relevant phenomena in the transport properties of granular solids are summarized namely, giant magnetoresistance in granular heterogeneous alloys and Coulomb gap in insulating granular solids.

We have used the unique spatial sensitivity of polarized neutron and soft x-ray beams in reflection geometry to measure the depth dependence of magnetization across the interface between a ferromagnet and an antiferromagnet. The net uncompensated magnetization near the interface responds to applied field, while uncompensated spins in the antiferromagnet bulk are pinned, thus providing a means to establish exchange bias.

We have analyzed magnetization measurements in a series of composition-related Ni-Mn-Ga shape-memory alloys. It is shown that the magnetocaloric effect in the vicinity of the martensitic transition mainly originates from two different contributions: (i) magnetostructural coupling on the mesoscopic scale between the magnetic moments and the martensitic variants, which is also responsible for the magnetic shape-memory effect and (ii) the microscopic spin-phonon coupling which gives rise to the shift of the transition temperature with the applied magnetic field. The relative importance of these two contributions has been shown to vary with composition, which is suitably expressed through the average number of valence electrons per atom $e/a.\mathrm{}$ In alloys with a large difference between the Curie and martensitic transition temperatures $(e/a\simeq 7.5),$ mesoscopic coupling is dominant and a negative giant magnetocaloric effect (increase of temperature by adiabatic demagnetization) is induced at moderate applied fields. In contrast, in alloys when these temperatures are very close to one another $(e/a\simeq 7.7),$ the microscopic coupling is the most relevant contribution and gives rise to a positive giant effect.