$\gamma -{\mathrm{Fe}}_2{\mathrm{O}}_3$ magnetic nanoparticles, with a very high surface to volume ratio, exhibit both strong exchange anisotropy and magnetic training effect. At the same time high field irreversibility in $M\left(H\right)$ curves and zero field cooled–field cooled (ZFC-FC) processes has also been detected. A low temperature spin-glass-like transition is evidenced at $T_F\approx 42\mathrm{K}$ with strong irreversibility even at $H=55\mathrm{}\mathrm{kOe}$. $T_F\left(H\right)$ evolves following the well known de Almeida–Thouless line $\delta T_F\propto H^{2/3}$. The thermal dependence of the exchange anisotropy field $H_E$ is described by the random-field model of exchange anisotropy. In the framework of this theory, a surface spin-glass layer about 0.6 nm thick is determined.

The amplitude $\Delta \rho (T,H)/\rho$ and temperature $T_M$, where the colossal magnetoresistance (CMR) response of $L_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ manganites are maximum, are found to be controlled by the radius of the lanthanide $\left(L^{3+}\right)$ which modifies the bending of the Mn-O-Mn bond. Increasing the bond distortion lowers $T_M$ and enhances $\Delta \rho (T,H)/\rho$. Enhanced CMR arises from (1) a shift to lower temperatures of $T_M$, (2) a reduced mobility of the doping holes, and (3) an increase of the coupling between itinerant and localized electrons. The resistivity $\rho \left(H\right)$ follows an $\approx {\mathrm{BM}}^2\left(H\right)$ law and the parameter $B$ is also tuned by the Mn-O-Mn bond angle. The narrowing of the electronic bandwidth is the fundamental parameter controlling the observed CMR.

The low-field (LFMR) and high field (HFMR) magnetoresistance response of ceramic ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3$ (LSMO) samples having grain sizes diameters ∅ ranging from 10 μm to 20 nm have been investigated. A limiting LFMR of about ≈30% is obtained for the ∅ ≈0.5 μm but no larger values are obtained by further reduction of the grain size down to the nanometric range. On the contrary, the HFMR progressively rises when reducing the grain size. Magnetic and transport measurements suggest that HFMR originates from the existence of a noncollinear surface layer, having a thickness t that increases when reducing ∅. We have disclosed a clear relationship between the thickness, the intergranular resistance, and the height of the surface energy barrier. In addition, we show that in samples with submicronic grains, there is an intergranular Coulomb gap.