The application of the effect of magneto-resistance in magneto-electronics, field sensors and random access memory elements and others created a huge interest on the studies of the magnetic and transport properties of the magnetic material realized in low dimensions. The interplay between magnetization and localization is central to the behavior of many artificially tailored materials and has given rise to phenomena such as giant magneto-resistance in metallic multi-layers, spin polarons in high Tc superconductors and skyrmion in two dimensional electron gases in semiconductors. At low temperatures, transport measurements in ferromagnetic materials indicate remarkable modification of the quantum correction to the 2D magneto-conductivity in the weakly localized regime, and negative magneto-resistance (MR) at high field suggesting suppression of weak electron localization (WEL) and spin disorder scattering. Moreover, the observation of anisotropic magneto-resistance (AMR) and anomalous Hall effect in ferromagnets emphasizes the importance of spin-orbit scattering in the transport properties of the low-dimensional ferromagnetic material. In order to get a better understanding regarding the transport properties of the ferromagnetic materials we will study the magneto-conductivity of a two-dimensional ferromagnet in presence of elastic scattering as well as spin-orbit scattering. Here we will provide a general description of the electronic transport in ferro-magnets for arbitrary direction of magnetization and magnetic field. By means of the diagrammatic perturbation technique, an analytical results for the magneto-conductivity has been obtained as a function of the magnetization and characteristic relaxation times due to elastic, inelastic and spin-orbit scattering. The result shows a strong dependence of the orientation of the magnetization with respect to the plane of the system on the conductivity. Depending on the orientation and strength of the magnetization and the coupling of the electronic spin with the magnetization both negative and positive magneto-resistance has been predicted. In addition, it is shown that, in order to explain the experimental variation of the conductivity in thin ferromagnetic films [1], electron-electron interaction and domain wall scattering must be considered.
