E. R. Priesen Reis, P. Guzman, S. H. Lohaus, A. Lin, C. M. Bernal-Choban, B. Fultz, J. Y. Zhao, G. Shen, M. Y. Hu, E. E. Alp and B. Lavina, Phys. Rev. B 112, 144416 (2025). doi: 10.1103/3c95-rf1b Editor's Suggestion for Oct. 10, 2025.
Synchrotron X-ray diffraction measurements were performed on ^57Fe_68Pd_32 at multiple pressures and two temperatures in a diamond-anvil cell. Between 4 and 11 GPa, the thermal expansion was zero or slightly negative. This pressure-induced Invar effect was studied further with ^57Fe nuclear forward scattering and nuclear resonant inelastic X-ray scattering to obtain information on the pressure-induced changes in both the magnetization and the phonon density of states. Magnetic entropy and phonon entropy were obtained from these results, the latter with additional measurements from inelastic neutron scattering to account for the contributions from Pd atoms. The dependencies of these entropies on pressure gave the magnetic and phonon contributions to thermal expansion. These canceled in the region of pressure-induced Invar behavior, even though they individually increased by more than a factor of 2 below the Curie pressure. The behavior of phonons gives evidence for spin-phonon interactions in Fe_68Pd_32.
A general explanation of the pressure-induced Invar effect
is presented, showing that Invar behavior is typically expected at a pressure P* below a magnetic
transition at pressure P_C. The difference in pressure (P_C - P*) scales with the fractional reduction
in magnetic exchange interaction divided by the average Gruneisen parameter.
C. N. Saunders, V. V. Ladygin, D. S. Kim, C. M. Bernal-Choban, S. H. Lohaus, G. E. Granroth, D. L. Abernathy, and B. Fultz, Phys. Rev. Mater. 9, 024602 (2025). https://doi.org/10.1103/PhysRevMaterials.9.024602
Atomic vibrational dynamics in cuprite, Cu_2O, was studied by inelastic neutron scattering and
molecular dynamics (MD) simulations from 10 K to 900 K. At 300 K, a diffuse inelastic intensity (DII)
appeared in the phonon dispersions, and dominated the spectral intensity at higher temperatures.
Classical MD simulations with a machine learning interatomic potential reproduced general features
of the DII. Better agreement with experiment was obtained with the addition of a stiffer potential at
close approaches of the Cu and O-atoms. The DII originates from random phase shifts of vibrating
O-atoms that have brief (10 fs) anharmonic interactions with neighboring Cu-atoms. The spectrum
of DII gives information about the interaction time of anharmonic interactions between atoms, and
its intensity gives a strength of coupling between vibrating atoms and a thermal bath.
V. V. Ladygin, C. M. Bernal-Choban, C. N. Saunders, D. L. Abernathy, M. E. Manley, B. Fultz, Phys. Rev. M 9, 015002 (2025). DOI: 10.1103/PhysRevMaterials.9.015002
The phenomenon of second harmonic generation (SHG) was found for phonons in anharmonic NaBr by
inelastic neutron scattering. The temperature dependence of this phonon SHG was measured from 300 K to
650 K. At 300 K the second harmonic (SH) is seen as a high-energy branch around 33 meV, nearly independent
of Q. The temperature effective potential (TDEP) method and classical molecular dynamics (MD) simulation
with machine learning interatomic potential were able to reproduce the SH, and showed that SHG occurs with
the flat transverse optical (TO) phonon branch. A classical model of a nonlinear medium explains the intensity
and lifetime of the SH, compared to those of the TO modes. Also successful was a quantum model based on the
Heisenberg-Langevin equation for interacting phonons coupled to a thermal bath, which also predicts a spectral
distribution of the SH. The measured temperature dependence of the intensity of the second harmonic showed
that it follows the Planck distribution of a one-phonon quasiparticle, and not two TO phonons.
Lohaus, SH; Heine, M; Guzman, P; Bernal-Choban, CM; Saunders, CN; Shen, G; Hellman, O; Broido, D; Fultz, B; Nature Physics 19, 1642 (2023) DOI10.1038/s41567-023-02142-z
The anomalously low thermal expansion of Fe-Ni Invar has long been associated with magnetism, but to date, the microscopic underpinnings of the Invar behaviour have eluded both theory and experiment. Here we present nuclear resonant X-ray scattering measurements of the phonon and magnetic entropies under pressure. By applying a thermodynamic Maxwell relation to these data, we obtain the separate phonon and magnetic contributions to thermal expansion. We find that the Invar behaviour stems from a competition between phonons and spins. In particular, the phonon contribution to thermal expansion cancels the magnetic contribution over the 0-3 GPa pressure range of Invar behaviour. At pressures above 3 GPa, the cancellation is lost, but our analysis reproduces the positive thermal expansion measured separately by synchrotron X-ray diffractometry. Ab initio calculations informed by experimental data show that spin-phonon interactions improve the accuracy of this cancellation over the range of Invar behaviour. Spin-phonon interactions also explain how different phonon modes have different energy shifts with pressure.
The iron-nickel alloy Invar has an extremely small coefficient of thermal expansion that has been difficult to explain theoretically. A study of Invar under pressure now suggests that there is a cancellation of phonon and spin contributions to expansion.
Better yet, you can watch the movies instead: Videos of Talks and Presentations
