= Solution
For a partially filled $3d$ shell, <electron>–<electron> Coulomb repulsion and <Hund's rules> first favour particular total <spin> and orbital terms. The <crystal field splitting> is substantial because these orbitals overlap the ligand environment; it normally exceeds the <spin-orbit coupling> and often quenches the orbital moment. Competition between the splitting and the <electron pairing energy> determines high-spin versus low-spin filling. A common hierarchy is Coulomb term energies, then crystal-field and Hund-exchange scales, then <spin>–orbit and weak-field Zeeman energies; the relative sizes of crystal-field splitting and pairing are material-dependent. Hyperfine coupling, if the nucleus carries <spin>, adds a smaller splitting. An isolated ion has no inter-ion exchange ordering field.
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