Surface supported single magnetic atoms, the so-called
"single-atom magnets", open new opportunities in a quest for
the ultimate size limit of magnetic information storage.
Initially, the research mainly focused on 3d-atoms on surfaces,
but none of them were found magnetically stable above 0.3 K.
Very recently, the attention was turned to the rare-earth (RE)
atoms, culminating in the experimental discovery of magnetically
stable Ho atom on MgO(001) substrate [1], and Dy atom on
graphene/Ir(111)[2].
     We address the electronic and magnetic character of RE atoms
on metal substrate making use of  a combination of the density
functional theory (DFT) with the exact diagonalization (ED)
of Anderson impurity model. The spin and orbital magnetic
moments of Ho@Pt(111)[3] and Dy@Ir(111)[4] are evaluated and
compared with experimental XMCD data. The magnetic anisotropy
energy is estimated, and the magnetic stability is discussed.
The role of 5d-4f interorbital exchange polarization in modification
of the 4f-shell energy spectrum is emphasized.

[1] F. Donati et al., Science 352, 318 (2016).
[2] R. Baltic et al., Nano Lett. 16, 7610 (2016).
[3] A. B. Shick, D. S. Shapiro, J. Kolorenc, A. I. Lichtenstein,
     Sci. Rep. 7, 2751 (2017).
[4] A. B. Shick, and A. I. Lichtenstein, submitted to the
JMMM special issue in memory of A. J. Freeman (2017).