Research ArticleMATERIALS SCIENCE

Multiple structural transitions driven by spin-phonon couplings in a perovskite oxide

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Science Advances  30 Jun 2017:
Vol. 3, no. 6, e1700288
DOI: 10.1126/sciadv.1700288
  • Fig. 1 Structural and magnetic properties of energetically competitive polymorphs in bulk BiFeO3 and BiCoO3.

    (A) rhombohedral R3c (R), (B) orthorhombic Pbnm (Embedded Image), and (C) tetragonal P4mm (Embedded Image). Patterns of O6 octahedra rotations are expressed in Glazer’s notation (30). The c/a aspect ratio of pseudocubic lattice parameters is approximately 1 for the Embedded Image and Embedded Image phases, whereas it is about 1.3 for the so-called super-tetragonal Embedded Image structure. Sketches of the lowest-energy spin configurations and exchange constants for a Heisenberg spin model of each phase are also shown.

  • Fig. 2 P-T phase diagram of bulk BCO calculated from first principles.

    (A) SP coupling effects are considered in the calculation of quasi-harmonic free energies. Multiple T-induced multiferroic phase transitions occur in the region colored in yellow. (B) Fixed magnetic spin order (corresponding to the lowest-energy spin arrangement) is imposed in the calculation of quasi-harmonic free energies. Experimental data from Belik et al. and Oka et al. (6, 7) corresponding to FE-to-PE (dots) and AFM-to-PM (triangle) phase transitions are shown for comparison.

  • Fig. 3 Analysis of SP couplings in the Embedded Image and Embedded Image phases of BCO.

    Vibrational frequency shifts between AFM and FM spin configurations calculated at the reciprocal lattice point Γ, Δω = ωAFM − ωFM, are shown as a function of eigenmode energy (where this energy is the one obtained for the AFM ground state). Equivalent AFM and FM vibrational frequencies are unequivocally identified with the largest projection (scalar product) between AFM and FM Γ-phonon eigenmodes. Note that modes with a positive (negative) shift will tend to soften (harden) as T increases. Phonon frequency shifts for the Embedded Image phase span over a smaller energy interval than those for the Embedded Image phase, indicating that the former structure is vibrationally softer than the latter. In both phases, phonon eigenmodes presenting largest spin couplings correspond to medium- and high-energy excitations dominated by Co and O atoms; in contrast, low-energy eigenmodes dominated by Bi and O atoms, including those associated to the polar distortion in BCO, present small |Δω| values.

  • Fig. 4 Calculated quasi-harmonic free energies of BCO’s competing polymorphs, as a function of temperature and at fixed pressure Pf = 2.5 GPa.

    (A) Quasi-harmonic Gibbs free energy is calculated as Embedded Image; our estimates are accurate to within 5 meV/fu. (B) Quasi-harmonic Helmholtz free energy, Embedded Image, where Embedded Image represents the vibrational lattice entropy. Magnetic entropy effects stemming exclusively from the spin fluctuations have been safely neglected in our analysis, because their free energy difference among the Embedded Image and Embedded Image phases amounts to less than 5 meV/fu (see the Supplementary Materials). (C) Quasi-harmonic enthalpy, Embedded Image, where Embedded Image. Black arrows indicate the occurrence of structural transitions characterized by the thermodynamic condition Embedded Image. Black and red vertical lines signal magnetic spin order transformations occurring in the Embedded Image and Embedded Image phases, respectively. Black and red dashed lines in (B) and (C) represent results obtained by constraining AFM magnetic spin order in our quasi-harmonic free energy calculations, showing how spin disorder tends to stabilize the Embedded Image phase (B). Note that the temperature dependence of Embedded Image (B) is smooth; in contrast, the slope changes in Embedded Image (C), which are associated to the spin ordering transitions, are the main cause of the successive structural transformations.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/6/e1700288/DC1

    table S1. Calculated zero-temperature total energy differences between the tetragonal P4mm, orthorhombic Pbnm, and monoclinic Pc phases at zero pressure using several DFT exchange-correlation functionals.

    I. Supplementary discussion: The role of the exchange correlation energy functional

    II. Supplementary discussion: Spin-phase transitions under pressure

    III. Supplementary data

    fig. S1. Spin properties and spin-phase transitions under pressure calculated in BiCoO3.

    fig. S2. Enthalpy energy differences between several crystal structures and the tetragonal P4mm phase calculated at T = 0 K with the PBE+U functional and expressed as a function of pressure.

    fig. S3. Quasi-harmonic Helmholtz free energy calculated in the tetragonal P4mm, orthorhombic Pbnm, and monoclinic Pc phases at zero pressure; the corresponding magnetic spin orders are AFM(C), AFM(G), and AFM(G), respectively.

    fig. S4. Analysis of SP coupling in the tetragonal P4mm phase at the special point Γ.

    fig. S5. Analysis of SP coupling in the orthorhombic Pbnm phase at the special point Γ.

    fig. S6. Analysis of SP coupling in the tetragonal P4mm phase over the corresponding Brillouin zone.

    fig. S7. Analysis of SP coupling in the orthogonal Pbnm phase over the corresponding Brillouin zone.

    fig. S8. AFM(C) magnetic spin order parameter calculated in the tetragonal P4mm phase as a function of pressure and temperature.

    fig. S9. AFM(G) magnetic spin order parameter calculated in the orthorhombic Pbnm phase as a function of pressure and temperature.

    fig. S10. Volume per formula unit calculated in BCO’s polymorphs at a fixed pressure of Pf = 2.5 GPa and expressed as a function of temperature.

    fig. S11. Calculated quasi-harmonic free energies of BCO’s polymorphs at a fixed pressure of Pf = 2.5 GPa.

    fig. S12. Contributions to the Gibbs free energy difference, Formula, calculated in bulk BCO as a function of temperature and pressure.

    fig. S13. Spin free energy difference between the P4mm and Pbnm phases calculated at P = 2.5 GPa as a function of temperature.

    fig. S14. Chemical doping strategy proposed to bring the multiferroic phase competition disclosed in bulk BCO down to zero pressure (oxygen atoms, not indicated in the figure, always enter the formulae as “O3”).

    fig. S15. Phonon spectrum calculated in the Bi3/4La1/4CoO3 compound at zero pressure in the tetragonal P4mm phase.

    fig. S16. Phonon spectrum calculated in the Bi3/4La1/4CoO3 compound at zero pressure in the orthorhombic Pbnm phase.

    References (3136)

  • Supplementary Materials

    This PDF file includes:

    • table S1. Calculated zero-temperature total energy differences between the tetragonal P4mm, orthorhombic Pbnm, and monoclinic Pc phases at zero pressure using several DFT exchange-correlation functionals.
    • I. Supplementary discussion: The role of the exchange correlation energy
      functional
    • II. Supplementary discussion: Spin-phase transitions under pressure
    • III. Supplementary data
    • fig. S1. Spin properties and spin-phase transitions under pressure calculated in BiCoO3.
    • fig. S2. Enthalpy energy differences between several crystal structures and the tetragonal P4mm phase calculated at T = 0 K with the PBE+U functional and expressed as a function of pressure.
    • fig. S3. Quasi-harmonic Helmholtz free energy calculated in the tetragonal P4mm, orthorhombic Pbnm, and monoclinic Pc phases at zero pressure; the
      corresponding magnetic spin orders are AFM(C), AFM(G), and AFM(G), respectively.
    • fig. S4. Analysis of SP coupling in the tetragonal P4mm phase at the special pointΓ.
    • fig. S5. Analysis of SP coupling in the orthorhombic Pbnm phase at the special point Γ.
    • fig. S6. Analysis of SP coupling in the tetragonal P4mm phase over the corresponding Brillouin zone.
    • fig. S7. Analysis of SP coupling in the orthogonal Pbnm phase over the corresponding Brillouin zone.
    • fig. S8. AFM(C) magnetic spin order parameter calculated in the tetragonal P4mm phase as a function of pressure and temperature.
    • fig. S9. AFM(G) magnetic spin order parameter calculated in the orthorhombic Pbnm phase as a function of pressure and temperature.
    • fig. S10. Volume per formula unit calculated in BCO’s polymorphs at a fixed pressure of Pf = 2.5 GPa and expressed as a function of temperature.
    • fig. S11. Calculated quasi-harmonic free energies of BCO’s polymorphs at a fixed pressure of Pf = 2.5 GPa.
    • fig. S12. Contributions to the Gibbs free energy difference, ΔGharmGP4mmharmGPbnmharm, calculated in bulk BCO as a function of temperature and pressure.
    • fig. S13. Spin free energy difference between the P4mm and Pbnm phases calculated at P = 2.5 GPa as a function of temperature.
    • fig. S14. Chemical doping strategy proposed to bring the multiferroic phase competition disclosed in bulk BCO down to zero pressure (oxygen atoms, not indicated in the figure, always enter the formulae as “O3”).
    • fig. S15. Phonon spectrum calculated in the Bi3/4La1/4CoO3 compound at zero pressure in the tetragonal P4mm phase.
    • fig. S16. Phonon spectrum calculated in the Bi3/4La1/4CoO3 compound at zero pressure in the orthorhombic Pbnm phase.
    • References (31–36)

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