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

We report the evolution of crystallographic structure, magnetic ordering and electronic transport in thin films of full-Heusler alloy Co$_2$MnSi deposited on (001) MgO with annealing temperatures ($T_A$). By increasing the $T_A$ from 300$^\circ$C to 600$^\circ$C, the film goes from a disordered nanocrystalline phase to $B2$ ordered and finally to the $L2_1$ ordered alloy. The saturation magnetic moment improves with structural ordering and approaches the Slater-Pauling value of $\approx 5.0 μ_B$ per formula unit for $T_A$ = 600$^\circ$C. At this stage the films are soft magnets with coercive and saturation fields as low as $\approx$ 7 mT and 350 mT, respectively. Remarkable effects of improved structural order are also seen in longitudinal resistivity ($ρ_{xx}$) and residual resistivity ratio. A model based upon electronic transparency of grain boundaries illucidates the transition from a state of negative $dρ/dT$ to positive $dρ/dT$ with improved structural order. The Hall resistivity ($ρ_{xy}$) derives contribution from the normal scattering of charge carriers in external magnetic field, the anomalous effect originating from built-in magnetization and a small but distinct topological Hall effect in the disordered phase. The carrier concentration ($n$) and mobility ($μ$) have been extracted from the high field $ρ_{xy}$ data. The highly ordered films are characterized by $n$ and $μ$ of 1.19$\times$ 10$^{29}$ m$^{-3}$ and 0.4 cm$^2V^{-1}s^{-1}$ at room temperature. The dependence of $ρ_{xy}$ on $ρ_{xx}$ indicates the dominance of skew scattering in our films, which shows a monotonic drop on raising the $T_A$. The topological Hall effect is analyzed for the films annealed at 300$^\circ$C. ......