Origin of anisotropic magnetoresistance tunable with electric field in $Co2FeSi$/$BaTiO3$ multiferroic interfaces

We report a first-principles investigation based on density functional theory with the Hubbard $U$ correction to identify the mechanism behind the electric-field modulation, via $a$-$c$ domain-wall motion, of the anisotropic magnetoresistance (AMR) ratio in $Co2FeSi$/$BaTiO3$ heterostructures. The effects of $BaTiO3$ (BTO) electric polarization in the [$001$], [$001¯$], and [$01¯0$] directions on the $FeSi$/$TiO2$ and $CoCo$/$TiO2$ interface terminations are taken into account. We show that the response of the interface geometric and electronic properties to the BTO polarization depends on the interface termination. For instance, the pinning of atoms at the $FeSi$-terminated interface inhibits the [$001$] polarization. Through the $a$-$c$ domain-wall motion, interface hybridized 3$dyz$ states shift in energy and change the minority-spin density of states at the Fermi level, modifying the AMR through the $α=ρ↓ρ↑$ component. A discussion of the results based on the Campbell–Fert–Jaoul model with $s$-$s$ and $s$-$d$ scattering is provided. The electronic states of $Co2FeSi$ inner layers remained mostly unchanged upon the transition between the ferroelectric domains, which indicates that long-range magnetoelastic effects have a negligible influence on the AMR ratio. Hence, the results indicate that interface bonding effects are the origin of the electric-field modulation of the AMR via $a$-$c$ domain-wall motion in $Co2FeSi$/$BaTiO3$ heterostructures.