Theoretical study of a localized quantum spin reversal by the sequential injection of spins in a spin quantum dot

This is a theoretical study of the reversal of a localized quantum spin induced by sequential injection of spins for a spin quantum dot that has a quantum spin. The system consists of ``electrode/quantum well(QW)/dot/QW/electrode" junctions, in which the left QW has an energy level of conduction electrons with only up-spin. We consider a situation in which up-spin electrons are sequentially injected from the left electrode into the dot through the QW and an exchange interaction acts between the electrons and the localized spin. To describe the sequentially injected electrons, we propose a simple method based on approximate solutions from the time-dependent Schr$\ddot{\rm o}$dinger equation. Using this method, it is shown that the spin reversal occurs when the right QW has energy levels of conduction electrons with only down-spin. In particular, the expression of the reversal time of a localized spin is derived and the upper and lower limits of the time are clearly expressed. This expression is expected to be useful for a rough estimation of the minimum relaxation time of the localized spin to achieve the reversal. We also obtain analytic expressions for the expectation value of the localized spin and the electrical current as a function of time. In addition, we found that a system with the non-magnetic right QW exhibits spin reversal or non-reversal depending on the exchange interaction.