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We report the evolution of crystallographic structure, magnetic ordering andelectronic transport in thin films of full-Heusler alloy Co$_2$MnSi depositedon (001) MgO with annealing temperatures ($T_A$). By increasing the $T_A$ from300$^\circ$C to 600$^\circ$C, the film goes from a disordered nanocrystallinephase to $B2$ ordered and finally to the $L2_1$ ordered alloy. The saturationmagnetic moment improves with structural ordering and approaches theSlater-Pauling value of $\approx 5.0 \mu_B$ per formula unit for $T_A$ =600$^\circ$C. At this stage the films are soft magnets with coercive andsaturation fields as low as $\approx$ 7 mT and 350 mT, respectively. Remarkableeffects of improved structural order are also seen in longitudinal resistivity($\rho_{xx}$) and residual resistivity ratio. A model based upon electronictransparency of grain boundaries illucidates the transition from a state ofnegative $d\rho/dT$ to positive $d\rho/dT$ with improved structural order. TheHall resistivity ($\rho_{xy}$) derives contribution from the normal scatteringof charge carriers in external magnetic field, the anomalous effect originatingfrom built-in magnetization and a small but distinct topological Hall effect inthe disordered phase. The carrier concentration ($n$) and mobility ($\mu$) havebeen extracted from the high field $\rho_{xy}$ data. The highly ordered filmsare characterized by $n$ and $\mu$ of 1.19$\times$ 10$^{29}$ m$^{-3}$ and 0.4cm$^2V^{-1}s^{-1}$ at room temperature. The dependence of $\rho_{xy}$ on$\rho_{xx}$ indicates the dominance of skew scattering in our films, whichshows a monotonic drop on raising the $T_A$. The topological Hall effect isanalyzed for the films annealed at 300$^\circ$C.

Structural ordering driven anisotropic magnetoresistance, anomalous Hall resistance and its topological overtones in full-Heusler Co2MnSi thin films