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Crystalline anisotropic magnetoresistance with two-fold and eight-fold symmetry in (In,Fe)As ferromagnetic semiconductor

We have investigated the anisotropic magnetoresistance (AMR) of (In,Fe)As ferromagnetic semiconductor (FMS) layers grown on semi-insulating GaAs substrates. In a 10 nm-thick (In,Fe)As layer which is insulating at low temperature, we observed crystalline AMR with two-fold and eight-fold symmetries. In a metallic 100 nm-thick (In,Fe)As layer with higher electron concentration, only two-fold symmetric crystalline AMR was observed. Our results demonstrate the macroscopic ferromagnetism in (In,Fe)As with magnetic anisotropy that depends on the electron concentration. Non-crystalline AMR is also observed in the 100 nm-thick layer, but its magnitude is as small as 10^-5, suggesting that there is no s-d scattering near the Fermi level of (In,Fe)As. We propose the origin of the eight-fold symmetric crystalline anisotropy in (In,Fe)As.