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Thus induced anisotropy of Fermi surfaces can nicely be illustrated on Fig. Consider the spin texture in Fig. as a typical example of SOI effect. Exchange splitting due to magnetization oriented horizontally in Fig., effectively acts as a Zeeman energy due to fictitious 'magnetic field' B with the same orientation, see Eq. The states with wave vector k∥B will be shifted upward (downward) in energy because their spin is parallel (antiparallel) to B while the states k∥B remain intact. This k -anisotropic shift in energy can be translated into the splitting of Fermi wave vectors of the two originally degenerate bands.
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Note that once we have set h=0 in Eq., the theoretical AMR depends on the Mn doping x only through the carrier density p [nm-3] =0.22×x [%], because NMn appearing in Eq. drops out in Eq.. This fact should not be taken ad absurdum (NMn →0) because we still assume that the substitutional Mn impurities provide the dominant source of scattering. Presence of other concurrent types of impurities [which is important when we compare the calculated AMR to experiments (Ref.)] will make the AMR depend on the ratio between their concentration and NMn. Nevertheless, this interplay will not simply obey Matthiessen's rule since we deal with anisotropic systems (Ref.).
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Note that once we have set h=0 in Eq., the theoretical AMR depends on the Mn doping x only through the carrier density p [nm-3] =0.22×x [%], because NMn appearing in Eq. drops out in Eq. This fact should not be taken ad absurdum (NMn →0) because we still assume that the substitutional Mn impurities provide the dominant source of scattering. Presence of other concurrent types of impurities [which is important when we compare the calculated AMR to experiments (Ref.)] will make the AMR depend on the ratio between their concentration and NMn. Nevertheless, this interplay will not simply obey Matthiessen's rule since we deal with anisotropic systems (Ref.).
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