Can the correspondence principle lead to improper relations between the uniaxial magnetic anisotropy constant K and the axial zero-field splitting parameter D for adatoms on surfaces?

Studies of magnetic adatoms on surfaces utilize experimental techniques (scanning tunneling microscopy (STM), inelastic tunneling spectroscopy (ITS) and ab-initio modeling methods. Several fundamental issues involved in these studies, being of utmost importance in view of potential technological applications, are critically examined and elucidated. This includes applications of the correspondence principle and relationships between the notions: magnetic anisotropy (MA), magnetic anisotropy energy (MAE), single-ion anisotropy (SIA), zero-field splitting (ZFS) as well as spin-flip energy of tunneling electrons and energy barrier to magnetization reversal. Proper quantum-mechanical relations between the uniaxial SIA constant K and the axial ZFS parameter D valid for the cases D > 0 and D < 0, as well as integer and half-integer spins, including S = 1/2, are derived. These considerations show that direct equating SIA with ZFS is unwarranted, whereas usage of the correspondence principle to justify such equating proves redundant. So-derived improper relations bear detrimentally on interpretation of STM/ITS and ab-initio results, e.g. for Co(S = 1) and Fe(S = 3/2) on Pt(111) yielding K (aka 'MAE') values differing from those obtained from the proper relations by 100 and 50 percent, respectively. Implications of confusion concerning the basic tenets for S = 1/2 systems, classical versus quantum spin approaches, and applicability of the crucial notions for magnetic adatoms are also discussed.