Quantum levels changed the old magnetic picture
Van Vleck used quantum mechanics to connect electric and magnetic susceptibilities with allowed states and transition matrix elements. His 1932 monograph organized this approach for atoms, molecules and solids.
Chemical bonding and crystal fields change the relevant levels. A measured magnetic response therefore contains information about the electronic environment as well as the number of magnetic ions.
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A field can mix states without thermally populating them
A weak magnetic field perturbs the ground state through nearby excited states. The resulting second-order energy shift produces a susceptibility contribution even when thermal populations barely change. Its size depends on both the level gaps and magnetic coupling matrix elements.
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Temperature helps separate contributions
Independent permanent moments often give a strong inverse-temperature contribution over an appropriate range. State mixing can give a much weaker temperature dependence. Interactions, spin–orbit coupling and crystal-field populations can modify both, so a constant signal does not automatically prove a unique mechanism.
Sources: [1]
The spin model offers a restricted starting point
A finite spin chain shows how a specified Hamiltonian changes correlations and dynamics. It omits much of an ion’s orbital and crystal-field structure. The 1977 award groups Van Vleck with Anderson and Mott through electronic structure, while their specific models remain distinct.