Spin-dependent quantum beating of the conductance oscillations in asymmetric velocity modulated ferromagnetic graphene junction

Abstract

Abstract The mismatch effect of a double Fermi-velocity barrier structures NG/FG 1 /NG/FG 2 /NG junction on the electrically driven SdH-like oscillations of spin-dependent conductance is investigated, where NG is normal graphene and FG 1,2 is the ferromagnetic-gate with Fermi-velocity modulation ξ 1,2 where ξ 1,2 is the Fermi velocity ratio between NG region and FG 1,2 region. The results show that the effect of asymmetry of the double Fermi-velocity barrier structures, the difference value between ξ 1 and ξ 2 cause of the oscillations the spin-dependent quantum beating pattern. Which the beating patterns of the spin transport appeared as a result of the superposition of the two oscillatory components in the double Fermi velocity barriers. In addition, we found that the shifting of the spin-dependent quantum beats of the G ↑ and G ↓ is due to the presence of the exchange field, H, that is, the G ↑ and G ↓ are shifted in the opposite direction. By the difference value of the phase shift can be estimated to be 2H . In case of U + η σ H > > E F which electrons are collimated, the oscillations behaviors show the quantum beating with holding constant amplitude and the period of the beating amplitude depend on the Fermi velocity ratio mismatch in FG regions. These interesting characteristic of spin-dependent quantum transport may identify the effect of Femi-velocity asymmetry on double proximity-induced ferromagnetic graphene structure for making spintronic devices.