---
title: "Van Vleck’s susceptibility: excited states influence a quiet magnet"
description: "How can virtual changes of quantum state contribute to magnetization?"
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[Magnetism, disorder and topological response](https://sandboxphysics.com/stories/condensed-matter/#magnetism)

Materials · Measurements · Explanation

# Van Vleck’s susceptibility: excited states influence a quiet magnet

How can virtual changes of quantum state contribute to magnetization?

Sandbox Physics · 2026-10-23

Nobel contribution: 1977-1

1. Specify atomic or ionic levels
2. Apply a weak magnetic field
3. Mix states and change populations
4. Compare susceptibility with temperature

Susceptibility depends on level separations, magnetic matrix elements and the local environment; it is not a simple count of free spins.

## 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.

Sources: [1]

## 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.

Sources: [1]

## 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.

Sources: [1] [2]

Continue with the physics

## Try the related models

### [Quantum spin dynamics](https://sandboxphysics.com/labs/quantum-spin-chain-quench/)

Follow correlations after changing a spin-chain Hamiltonian.

A finite dynamical chain does not by itself establish the thermodynamic Haldane gap or a measured ferrite structure.

## Sources and reading notes

1. [Van Vleck: Quantum mechanics, the key to understanding magnetism (1977)](https://www.nobelprize.org/uploads/2018/06/vleck-lecture.pdf)

   Quantum levels and matrix elements connect susceptibility to chemical and crystal environments.

2. [Nobel Prize in Physics 1977: official award](https://www.nobelprize.org/prizes/physics/1977/summary/)

   Official attribution and award year. The observation or theoretical paper may be much earlier.

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