  We study a spin structure that arises in a one-dimensional quantum dot with
zero total spin under the action of a charged tip of a scanning probe
microscope in the presence of a weak magnetic field. The evolution of the spin
structure with changing the probe position is traced to show that the movable
probe can be an effective tool to manipulate the spin. The spin structures are
formed when the probe is located in certain regions along the dot due to the
Coulomb interaction of electrons as they are redistributed between the two
sections in which the quantum dot is divided by the potential barrier created
by the probe. There are two main states: spin-polarized and non-polarized ones.
The transition between them is accompanied by a spin precession governed by the
Rashba spin-orbit interaction induced by the electric field of the probe. In
the transition region the spin density changes strongly while the charge
distribution remains nearly unchanged.
