Model of Orbital Populations for Voltage-controlled Magnetic Anisotropy in Transition-metal Thin Films
Voltage controlled magnetic anisotropy (VCMA) is an efficient way to manipulate the magnetization states in nanomagnets, promising for low-power spintronic applications. The underlying physical mechanism for VCMA is known to involve a change in the d-orbital occupation on the transition metal interface atoms with an applied electric field. However, a simple qualitative picture of how this occupation controls the magnetocrystalline anisotropy (MCA) and even why in certain cases the MCA has opposite sign still remains elusive. In this paper, we exploit a simple model of orbital populations to elucidate a number of features typical for the interface MCA and the effect of electric field on it, for 3d transition metal thin films used in magnetic tunnel junctions. We find that in all considered cases including the Fe (001) surface, clean Fe1-xCox (001)/MgO interface and oxidized Fe(001)/MgO interface, the effects of alloying and electric field enhance the MCA energy with electron depletion which is largely explained by the occupancy of the minority-spin dxz,yz orbitals. On the other hand, the hole doped Fe(001) exhibits an inverse VCMA, where the MCA enhancement is achieved when electrons are accumulated at the Fe (001)/MgO interface with applied electric field. In this regime we predict a significantly enhanced VCMA which exceeds 1pJ/Vm. Realizing this regime experimentally may be favorable for a practical purpose of voltage driven magnetization reversal.