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


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.

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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.


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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.

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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.

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Correspondence to Joseph P. Heremans.

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The authors declare no competing financial interests.

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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).

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