Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Phonon-induced diamagnetic force and its effect on the lattice thermal conductivity

Abstract

Phonons are displacements of atoms around their rest positions in a crystalline solid. They carry sound and heat, but are not classically associated with magnetism. Here, we show that phonons are, in fact, sensitive to magnetic fields, even in diamagnetic materials. We do so by demonstrating experimentally that acoustic phonons in a diamagnetic semiconductor (InSb) scatter more strongly from one another when a magnetic field is applied. We attribute this observation to the magnetic-field sensitivity of the anharmonicity of the interatomic bonds that govern the probability of phonon–phonon interactions. The displacements of atoms locally affect the orbital motion of valence band electrons, which, in the presence of an external magnetic field, spatially modulates the orbital diamagnetism around the displaced atoms. The spatial gradient in magnetic moment results in an anharmonic magnetic force exerted on the displaced atom. The process is modelled by ab initio calculations that, without the use of a single adjustable parameter, reproduce the observed 12% decrease in the lattice thermal conductivity under a 7 T magnetic field at a temperature of 5.2 K.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Magnetic-field dependence of lattice thermal conductivity in InSb.
Figure 2: Measurements on sample B with reduced thermal conductivity after thermal cycling.
Figure 3: Ab initio calculation of the magnetic moment of frozen phonons in InSb.
Figure 4: Agreement between ab initio theory and experiment.

References

  1. 1

    Harman, T. C. & Honig, J. M. Thermoelectric and Thermomagnetic Effects and Applications (McGraw-Hill, 1967).

    Google Scholar 

  2. 2

    Boona, S. R., Myers, T. C. & Heremans, J. P. Spin caloritronics. Energy Environ. Sci. 7, 885–910 (2014).

    Article  Google Scholar 

  3. 3

    Onose, Y. et al. Observation of the magnon Hall effect. Science 329, 297–299 (2010).

    CAS  Article  Google Scholar 

  4. 4

    Strohm, C., Rikken, G. L. J. A. & Wyder, P. Phenomenological evidence for the phonon Hall effect. Phys. Rev. Lett. 95, 155901 (2005).

    CAS  Article  Google Scholar 

  5. 5

    Morton, I. P. & Rosenberg, H. M. Scattering of phonons by spins at low temperatures. Phys. Rev. Lett. 8, 200–201 (1962).

    CAS  Article  Google Scholar 

  6. 6

    Zhao, L-D. et al. Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 508, 373–377 (2014).

    CAS  Article  Google Scholar 

  7. 7

    Heremans, J. P. The ugly duckling. Nature 508, 327–328 (2014).

    CAS  Article  Google Scholar 

  8. 8

    Nielsen, M. D., Ozolins, V. & Heremans, J. P. Lone pair electrons minimize lattice thermal conductivity. Energy Environ. Sci. 6, 570–578 (2013).

    CAS  Article  Google Scholar 

  9. 9

    Geballe, T. H. & Hull, G. W. in Conference de physique des basses temperatures, Institut international du froid, Paris 460–463 (1955).

    Google Scholar 

  10. 10

    Issi, J-P., Michenaud, J-P. & Heremans, J. P. in Thermal Conductivity 14 (eds Klemens, P. G. & Chu, T. K.) 127–133 (Conference Proceedings, Plenum Press, 1976).

    Book  Google Scholar 

  11. 11

    Berman, R. Thermal Conduction in Solids (Clarendon Press, 1976).

    Google Scholar 

  12. 12

    Price, D. L., Rowe, J. M. & Nicklow, R. M. Lattice dynamics of grey tin and indium antimonide. Phys. Rev. B 3, 1268–1279 (1971).

    Article  Google Scholar 

  13. 13

    Broido, D. A., Ward, A. & Mingo, N. Lattice thermal conductivity of silicon from empirical interatomic potentials. Phys. Rev. B 72, 014308 (2005).

    Article  Google Scholar 

  14. 14

    Sparks, P. W. & Swenson, C. A. Thermal expansions from 2 to 40 K of Ge, Si, and four III–V compounds. Phys. Rev. 163, 779–790 (1967).

    CAS  Article  Google Scholar 

  15. 15

    Cetas, T. C., Tilford, C. R. & Swenson, C. A. Specific heats of Cu, GaAs, GaSb, InAs, and InSb from 1 to 30 K. Phys. Rev. 174, 835–844 (1968).

    CAS  Article  Google Scholar 

  16. 16

    Puri, S. M. & Geballe, T. H. Phonon drag in n-type InSb. Phys. Rev. 136, A1767–A1774 (1964).

    Article  Google Scholar 

  17. 17

    Hudgen, S., Kastner, M. & Fritzsche, H. Diamagnetic susceptibility of tetrahedral semiconductors. Phys. Rev. Lett. 33, 1552–1555 (1974).

    Article  Google Scholar 

  18. 18

    Nolting, W. & Ramakanth, A. Quantum Theory of Magnetism (Springer, 2009).

    Book  Google Scholar 

  19. 19

    Olguín, D., Cardona, M. & Cantarero, A. Electron–phonon effects on the direct band gap in semiconductors: LCAO calculations. Solid State Commun. 122, 575–589 (2002).

    Article  Google Scholar 

  20. 20

    Dewhurst, J. K. et al. Elk FP-LAPW code, version 2.2.9 (2004); http://elk.sourceforge.net

  21. 21

    Sharma, S. et al. Comparison of exact-exchange calculations for solids in current-spin-density- and spin-density-functional theory. Phys. Rev. B 76, 100401 (2007).

    Article  Google Scholar 

  22. 22

    Heremans, J., Michenaud, J-P., Shayegan, M. & Dresselhaus, G. Magnetostriction and deformation potentials in graphite. J. Phys. C 14, 3541–3546 (1981).

    CAS  Google Scholar 

  23. 23

    Michenaud, J-P., Heremans, J., Shayegan, M. & Haumont, C. Magnetostriction of bismuth in quantizing magnetic fields. Phys. Rev. B 26, 2552–2559 (1982).

    CAS  Article  Google Scholar 

  24. 24

    Souvatzis, P., Eriksson, O. & Katsnelson, M. I. Anomalous thermal expansion in α-titanium. Phys. Rev. Lett. 99, 015901 (2007).

    CAS  Article  Google Scholar 

  25. 25

    Akgöz, Y. C. & Saunders, G. A Space-time symmetry restrictions on the form of transport tensors: I. Galvanomagnetic effects. J. Phys. C 8, 1387–1396 (1975).

    Article  Google Scholar 

  26. 26

    Hass, M. & Henvis, B. W. Infrared lattice reflection spectra of III–V compound semiconductors. J. Phys. Chem. Solids 23, 1099–1104 (1962).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

The experiments were supported as part of the ARO MURI under award number W911NF-14-1-0016, US AFOSR MURI under award number FA9550-10-1-0533 (H.J.) and the NSF grant CBET-1133589 (J.P.H., R.C.M.). The theoretical work was supported by the NSF MRSEC program under grant DMR 1420451, as well as an allocation of computing time from the Ohio Supercomputing Center. We acknowledge help from Z. Yang and useful discussions with S. Barnes.

Author information

Affiliations

Authors

Contributions

The experiments were designed and carried out by H.J. and J.P.H., the theory by J.P.H., W.W., R.C.M., S.R.B., N.A. and O.D.R., and all DFT computations by N.A., O.D.R. and W.W. All contributed to the integration between theory and experiment, and in writing the manuscript.

Corresponding author

Correspondence to Joseph P. Heremans.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 2997 kb)

Supplementary Movie 1

Supplementary Movie 1 (MP4 2170 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jin, H., Restrepo, O., Antolin, N. et al. Phonon-induced diamagnetic force and its effect on the lattice thermal conductivity. Nature Mater 14, 601–606 (2015). https://doi.org/10.1038/nmat4247

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing