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How does crystal field splitting influence the magnetic properties of a coordination compound?

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Structural diagram of the vitamin B12 coenzyme molecule, highlighting its organometallic core with five nitrogen-cobalt bonds and one cobalt-carbon bond at the center, surrounded by complex organic groups. — coordination compound Coordination compounds contain a central metal atom surrounded by nonmetal atoms or groups of atoms, called ligands. For example, vitamin B₁₂ is made up of a central metallic cobalt ion bound to multiple nitrogen-containing ligands.

In coordination chemistry, crystal field theory explains how the arrangement of ligands around a central metal ion causes the five d orbitals to split into groups of different energy levels. This splitting, quantified by the crystal field splitting energy ( $Δ$ ), is the primary factor determining the magnetic properties of the complex.12

The magnetic state of a complex depends on the competition between the splitting energy ( $Δ$ ) and the pairing energy required to place two electrons in the same orbital.13

High-Spin Complexes: When the crystal field is weak, $Δ$ is small. Electrons prefer to occupy separate orbitals to minimize repulsion, resulting in a maximum number of unpaired electrons. These complexes are paramagnetic, meaning they are attracted to a magnetic field.413
Low-Spin Complexes: When the crystal field is strong, $Δ$ is large. Electrons preferentially occupy the lower-energy orbitals, forcing pairing even if higher-energy orbitals are available. This results in fewer unpaired electrons, or even a diamagnetic state if all electrons are paired.413

The strength of this field is dictated by the specific ligands present, which are organized into the spectrochemical series based on their ability to induce splitting.413