  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.
