  We theoretically investigate the local density of states (LDOS) probed by a
STM tip of ferromagnetic metals hosting a single adatom and a subsurface
impurity. We model the system via the two-impurity Anderson Hamiltonian. By
using the equation of motion with the relevant Green functions, we derive
analytical expressions for the LDOS of two host types: a surface and a quantum
wire. The LDOS reveals Friedel-like oscillations and Fano interference as a
function of the STM tip position. These oscillations strongly depend on the
host dimension. Interestingly, we find that the spin-dependent Fermi wave
numbers of the hosts give rise to spin-polarized quantum beats in the LDOS.
While the LDOS for the metallic surface shows a damped beating pattern, it
exhibits an opposite behavior in the quantum wire. Due to this absence of
damping, the wire operates as a spatially resolved spin filter with a high
efficiency.
