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 [Formula: see text] correction to identify the mechanism behind the electric-field modulation, via [Formula: see text]-[Formula: see text] domain-wall motion, of the anisotropic magnetoresistance (AMR) ratio in [Formula: see text]/[Formula: see text] heterostructures. The effects of [Formula: see text] (BTO) electric polarization in the [[Formula: see text]], [[Formula: see text]], and [[Formula: see text]] directions on the [Formula: see text]/[Formula: see text] and [Formula: see text]/[Formula: see text] 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 [Formula: see text]-terminated interface inhibits the [[Formula: see text]] polarization. Through the [Formula: see text]-[Formula: see text] domain-wall motion, interface hybridized 3[Formula: see text] states shift in energy and change the minority-spin density of states at the Fermi level, modifying the AMR through the [Formula: see text] component. A discussion of the results based on the Campbell–Fert–Jaoul model with [Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text] scattering is provided. The electronic states of [Formula: see text] 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 [Formula: see text]-[Formula: see text] domain-wall motion in [Formula: see text]/[Formula: see text] heterostructures.