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The anomalously low thermal expansion of Fe-Ni Invar has long been associated with magnetism, but to date, the microscopic underpinnings of Invar behavior have eluded both theory and experiment. Here, we present nuclear resonant X-ray scattering measurements of the phonon and magnetic entropy 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 behavior 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 behavior. 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 behavior. Spin-phonon interactions also explain how different phonon modes have different energy shifts with pressure.
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Resonant thermal Hall effect of phonons coupled to dynamical defects
We present computations of the thermal Hall coefficient of phonons scattering off a defect with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon–defect coupling is proportional to the phonon lifetime and has a “side-jump” interpretation. Consequently, the thermal Hall angle is independent of the phonon lifetime. The contribution to the thermal Hall coefficient is at resonance when the phonon energy equals a defect-level spacing. Our results are obtained for three different defect models, which apply to different correlated electron materials. For the pseudogap regime of the cuprates, we propose a model of phonons coupled to an impurity quantum spin in the presence of quasistatic magnetic order with an isotropic Zeeman coupling to the applied field and without spin–orbit interaction.
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- Award ID(s):
- 2002850
- PAR ID:
- 10482004
- Publisher / Repository:
- National Academy of Science
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 119
- Issue:
- 46
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2215141119
