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Phonon Softening due to Melting of the Ferromagnetic Order in Elemental Iron

Qiang Han, Turan Birol, and Kristjan Haule
Phys. Rev. Lett. 120, 187203 – Published 4 May 2018
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    Abstract

    We study the fundamental question of the lattice dynamics of a metallic ferromagnet in the regime where the static long-range magnetic order is replaced by the fluctuating local moments embedded in a metallic host. We use the ab initio density functional theory + embedded dynamical mean-field theory functional approach to address the dynamic stability of iron polymorphs and the phonon softening with an increased temperature. We show that the nonharmonic and inhomogeneous phonon softening measured in iron is a result of the melting of the long-range ferromagnetic order and is unrelated to the first-order structural transition from the bcc to the fcc phase, as is usually assumed. We predict that the bcc structure is dynamically stable at all temperatures at normal pressure and is thermodynamically unstable only between the bcc-α and the bcc-δ phases of iron.

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    • Received 19 May 2017
    • Revised 3 January 2018

    DOI:https://doi.org/10.1103/PhysRevLett.120.187203

    © 2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    FerromagnetismPhononsStructural properties
    1. Physical Systems
    Elemental materials
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Qiang Han1, Turan Birol2, and Kristjan Haule1

    • 1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA
    • 2Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA

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    Vol. 120, Iss. 18 — 4 May 2018

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    Images

    • Figure 1
      Figure 1

      (a) The electronic free energy per atom versus V of a cubic unit cell. (b) The temperature dependence of the ordered ferromagnetic moment of bcc iron using both the density-density (“Ising”) and the rotationally invariant (“full”) Coulomb interaction form. (c) The single-particle spectral function of the bcc-α phase at 300 K (the majority and minority spectra are plotted in blue and red, respectively).

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    • Figure 2
      Figure 2

      Phonon spectrum at a low temperature (T=300  K), in the paramagnetic bcc-α phase (T=1.125Tc) and in the paramagnetic bcc-δ phase (T=1800  K) evaluated at experimental lattice constants. The dots correspond to the experimental data from Refs. [11, 66, 67] at 300 K, 1.125Tc, and T=1743  K, respectively.

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    • Figure 3
      Figure 3

      (a) The calculated phonon dispersions in the bcc-α phase below and above the Curie temperature at an experimental equilibrium volume. (b) Phonons in the metastable paramagnetic bcc phase, but at a constant volume (experimental volume at T=Tc).

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    • Figure 4
      Figure 4

      The change of the phonon frequencies for representative modes with the temperature calculated by DFT+DMFT (red dots) compared to experimental data (green triangle). The dashed blue lines denote the change predicted by the quasiharmonic model: ωqh(T)=ω300 K(1−γth)(VT−V300 K/V300 K), where ω300 K is the calculated value of the phonon frequency at 300 K, VT is the experimental volume of the unit cell at temperature T, and γth is the thermal Grüneisen parameter, approximated by a constant value of 1.81, as suggested in Refs. [12, 68].

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    • Figure 5
      Figure 5

      (a) The total energy computed along the Bain crystallographic transition from the bcc to the fcc phase in the FM state. Note that at T=1547  K the FM and PM phases are indistinguishable. (b) The ordered ferromagnetic moment along the same path.

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