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Surface supported single magnetic atoms, the so-called "single-atom magnets", open new opportunities in a quest for t
he ultimate size limit of magnetic information storage. Initially, the research mainly focused on 3d-atoms on surfaces.
Recently, the attention was turned to the 4f-atoms, culminating in the experimental discovery of magnetically stable Ho atom
on MgO(001) substrate, and Dy atom on graphene/Ir(111).

I address the electronic and magnetic character of 4f-atoms on metal and Graphene substrate making use of a combination
of the DFT+U with the exact diagonalization of Anderson impurity model (DFT+U+ED). The spin and orbital magnetic moments
of Dy@Ir(111) and Dy/Graphene/Ir(111) 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.

Laser manipulation of quantum particles, such as atoms, ions, and molecules, underpins much of modern physics. Electrons, too, can be coherently controlled by light. In this work, we study electron-laser interaction in free space and find that the conventional description based on the effective (ponderomotive) potential requires significant modification. We demonstrate laser-based phase manipulation of the electron wave function by performing interferometric experiments in a transmission electron microscope (TEM) and capture TEM images of the light wave. We then utilize the laser-induced phase shift to realize a nearly ideal phase plate for Zernike phase contrast TEM, solving a long-standing problem and addressing the challenge of dose-efficient interrogation of radiation-sensitive specimens. The laser phase plate is widely expected to advance the TEM studies of protein structure and cell organization.