Advances in Lanthanide Single-Ion Magnets

We present an overview of the investigation methods of lanthanide-based single-ion magnet. The electronic structure of lanthanide ions is described in the picture of electron-electron interaction, spin-orbit coupling, and ligand-field effects. The ligand-field Hamiltonian is introduced in cooperation with equivalent operator method. In the part of experimental methods, we review the advanced methods of the angle-resolved magnetometry measurement and magnetic resonance spectroscopy on lanthanide ions. In the part of theoretical approaches, we describe the lanthanide-ion electron-density distribution anisotropy using the multipole-moment model, which is able to qualitatively describe the magnetic anisotropy behavior of various lanthanide ions. We introduce three approaches of determining ligand-field parameters. Additionally, we review four series of well-investigated lanthanide single-ion magnets.