Abstract
We investigated the anisotropic magnetoresistance (AMR) effects in ferromagnetic-metal multi-layers stacked on non-magnetic insulators in the context of microscopic theory. We represented this situation with tight-binding models that included the exchange and Rashba fields, where the Rashba field was assumed to originate from spin–orbit interactions as junction effects with the insulator. To describe the AMR ratios, the DC conductivity was calculated based on the Kubo formula. As a result, we showed that the Rashba field induced both perpendicular and in-plane AMR effects and that the perpendicular AMR effect rapidly decayed with increasing film thickness.
Highlights
The anisotropic magnetoresistance (AMR) effect is a phenomenon in which the resistivity in ferromagnetic-metals (FMs) depends on the relative angles between the magnetization direction Mand the charge current J, originating from the interplay between the spin and orbital motion of electrons via the intra-atomic spin–orbit interaction (SOI).[1]
In conventional AMR, the resistivity varies with changes of angle φyx (Fig. 1 (a)) or αxz (Fig. 1 (b)), and the resistivity is invariant to changes of angle θyz (Fig. 1 (c))
In multi-layer systems, space inversion symmetry is broken by the presence of a junction, at which an inner induction electric field perpendicular to the interface acts on the electrons; the electric field induces an additional SOI that is responsible for the perpendicular AMR effect
Summary
The anisotropic magnetoresistance (AMR) effect is a phenomenon in which the resistivity in ferromagnetic-metals (FMs) depends on the relative angles between the magnetization direction Mand the charge current J, originating from the interplay between the spin and orbital motion of electrons via the intra-atomic spin–orbit interaction (SOI).[1]. The anisotropic magnetoresistance (AMR) effect is a phenomenon in which the resistivity in ferromagnetic-metals (FMs) depends on the relative angles between the magnetization direction Mand the charge current J, originating from the interplay between the spin and orbital motion of electrons via the intra-atomic spin–orbit interaction (SOI).[1] Fig. 1 shows the definition of the angles (φyx, αxz, and θyz) characterizing M .
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