Magneto-orientation and quantum size effect in SP-STM conductance in the presence of a subsurface magnetic cluster

The influence of a single magnetic cluster in a non-magnetic host metal on the spin current $\mathbf{j}^{(s)}$ and the charge current $\mathbf{j}$ in the vicinity of a ferromagnetic STM tip is studied theoretically. Spin-flip processes due to electron interaction with the cluster are taken into account. We show that quantum interference between the partial waves injected from the STM tip and those scattered by the cluster results in the appearance of components perpendicular to the initial polarization of the spin current $\mathbf{j}^{(s)}$, which obtain a strongly inhomogeneous spatial distribution. This interference produces oscillations of the conductance as a function of the distance between the contact and the cluster center. The oscillation amplitude depends on the current polarization. We predict a strong magneto-orientational effect: the conductance oscillations may grow, shrink, or even vanish for rotation of the cluster magnetic moment $\mathbf{\mu}_{\mathrm{eff}}$ by an external magnetic field. These results can be used for the determination of the $ \mathbf{\mu}_{\mathrm{eff}}$ for magnetic clusters below a metal surface.