Entropy contributions to explain thermal expansion: thermodynamics of the Invar effect*

The anomalously low thermal expansion observed in some metals, known as the Invar effect, has long been associated with magnetism. Its microscopic underpinnings, however, are still an open scientific question, long after C. E. Guillaume received the 1920 physics Nobel Prize for its discovery. In particular the role of phonons, their contribution to the thermal expansion, and their dependence on magnetism has not been previously quantified. We explore a new method for obtaining the thermal expansion from the pressure dependence of the entropy. By combining two nuclear x-ray scattering techniques, suitable for pressure experiments in diamond-anvil cells, we probe contributions from phonons and spins to the entropy of Fe-Ni Invar. We show that the Invar behavior stems from a competition between phonons and spins, resulting in a cancellation of their entropy contributions. Ab initio phonon calculations reveal a spin-lattice coupling at the root of the Invar anomaly. Such couplings of excitations from phonons and spins go beyond the case of Invar, and could be the cause of the thermal expansion behavior in other magnetic materials.