As long as there is a percolating conducting path connecting all parts of your porous sphere, I don't see any reason why the spins would tunnel through a barrier.

I am almost certain that magnetically a 'solid magnetic nano-sphere' fundamentally differs from a 'mesoporous magnetic nano-sphere'. In my considered opinion, the former behaves more like a giant atom (with a sizeable diamagnetic susceptibility), whereas the latter more like a piece of solid. In particular, the magnetic response of a 'mesoporous magnetic nano-sphere' is more difficult to know a priori.

@ Christian Binek: The question is explicitly about properties of individual spheres, implying that one is to consider the case below the percolation threshold.

@Christian Binek and @Behnam Farid: In literature I have found that the porosity affects the Magnetic susceptibility of metal oxide layers. So, can I expect the same kind of phenomenon in case of nanomaterials?

@Kakoli Bhattacharya As I indicated above, I have no doubt that porosity brings about significant physical change; considering a 'solid magnetic nano-sphere', which to me appears like a giant atom, porosity turns it into a solid-like object, an assembly of many smaller atoms -- ideally, while the former has a continuous rotational symmetry group, like a conventional atom, the latter has at best a discrete one; this fundamental difference in the underlying symmetry, will necessarily have physical consequences (the energy spectra of the two, and the degeneracies of the levels, are fundamentally different). Incidentally, what you have found in the literature seems to support my viewpoint.

I have no doubt either that there are substantial differences. I just cannot see the spin tunneling to happen. The question whether the nanoparticle can be considered a superspin as Behnam describes it or not can be clearly answered. It depends on the magnetic properties of the material. Specifically, the interplay between exchange and anisotropy. These parameters determine the width of a domain wall. If the wall width in bulk material would be larger than the size of the nanoparticle then the particle will be a single-domain particle. Otherwise it will subdivide into magnetic domains. That has been heavily investigated and is the basis for superparamagnets. As I mentioned earlier, it will also matter if your particle is insulating or conducting. If it is conducting I would expect that porosity will heavily affect the eddy current distribution and thus the response on an applied field. In other words that will affect the susceptibility. Also, when introducing porosity you increase the number of spins which do not see the complete bulk coordination even much further. At some point your material will pretty much be only surface. Certainly it will be extremely different from bulk and also very different from a solid nanosphere.

At high porosity (or even at low porosity) one very likely will have a spin glass, where tunnelling amongst various metastable spin configurations are the all-important processes at low temperatures.