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How do unpaired electrons affect the magnetic properties of transition-metal compounds?

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A color-coded periodic table of the elements displays each element's symbol and atomic number, with categories such as alkali metals, noble gases, halogens, transition metals, and actinoid elements distinguished by different background colors. — transition metal Modern version of the periodic table of the elements (printable).

In transition-metal compounds, the magnetic properties are fundamentally determined by the number of unpaired electrons within the partially filled d orbitals. Because electrons possess spin, each unpaired electron contributes a permanent magnetic dipole moment, which serves as the building block for the substance's overall magnetic behavior.123

The number of unpaired electrons is governed by the competition between two factors: the tendency of electrons to occupy separate orbitals to minimize repulsion, and the tendency to occupy lower-energy orbitals. In chemical compounds, surrounding ligands cause the d orbitals to split into different energy levels.41

High-spin configurations: When the energy difference (splitting) between orbital subsets is small, electrons occupy separate orbitals to maximize total spin, resulting in a higher number of unpaired electrons and a larger magnetic moment.42
Low-spin configurations: When the splitting is large, electrons preferentially pair up in lower-energy orbitals, reducing the number of unpaired electrons and the resulting magnetic moment.4

Once the number of unpaired electrons is established, the total magnetic moment is calculated by accounting for both spin-angular momentum and orbital-angular momentum.4