• spin Hamiltonian;
  • effective Hamiltonian;
  • spin Hamiltonian parameters;
  • electron magnetic resonance;
  • model Hamiltonian

Based on the relation between quantum mechanical concepts such as effective Hamiltonians (EHs), perturbation theory (PT), and unitary transformations, and phenomenological aspects of spin Hamiltonians (SHs), the present tutorial tries to address the basics of the SH formalism. Using simple physical models and historical important examples, we have reviewed the derivation methods and applications of the SHs for a brief and in-depth description of various sources of anisotropies and interactions such as electronic (EZ), and nuclear Zeeman (NZ), terms, electron-exchange interaction (EE), zero-field splitting (ZFS), spin–spin (SS), spin-orbit (SO), nuclear quadrupole (NQ), and hyperfine couplings (HFCs), in a step-wise manner. In this way, this tutorial is tailored for the graduate students and young researchers who intend to begin their studies in the field of magnetism, electron magnetic resonance (EMR), spectroscopy, and related areas. © 2014 Wiley Periodicals, Inc.