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Trends in pressure-induced layer-selective half-collapsed tetragonal phases in the iron-based superconductor family AeAFe4As4

Vladislav Borisov, Paul C. Canfield, and Roser Valentí
Phys. Rev. B 98, 064104 – Published 24 August 2018
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  • INTRODUCTION
  • METHODS
  • RESULTS (ZERO PRESSURE)
  • FIRST HALF-COLLAPSED TETRAGONAL…
  • SECOND HALF-COLLAPSED TETRAGONAL…
  • As HEIGHT ASYMMETRY
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    By performing pressure simulations within density functional theory for the family of iron-based superconductors AeAFe4As4 with Ae=Ca, Sr, Ba and A=K, Rb, Cs we predict in these systems the appearance of two consecutive half-collapsed tetragonal transitions at pressures Pc1 and Pc2, which have a different character in terms of their effect on the electronic structure. We find that, similar to previous studies for CaKFe4As4, spin-vortex magnetic fluctuations on the Fe sublattice play a key role for an accurate structure prediction in these materials at zero pressure. We identify clear trends of critical pressures and discuss the relevance of the collapsed phases in connection to magnetism and superconductivity. Finally, the intriguing cases of EuRbFe4As4 and EuCsFe4As4, where Eu magnetism coexists with superconductivity, are discussed as well in the context of half-collapsed phases.

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    • Received 6 June 2018

    DOI:https://doi.org/10.1103/PhysRevB.98.064104

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    First-principles calculationsStructural phase transition
    1. Physical Systems
    Ferromagnetic superconductorsHigh-temperature superconductorsIron-based superconductors
    1. Techniques
    Density functional theory
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Vladislav Borisov1,*, Paul C. Canfield2,3, and Roser Valentí1

    • 1Institute of Theoretical Physics, Goethe University Frankfurt am Main, D-60438 Frankfurt am Main, Germany
    • 2Ames Laboratory US DOE, Iowa State University, Ames, Iowa 50011, USA
    • 3Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

    • *Corresponding author: borisov@itp.uni-frankfurt.de

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    Vol. 98, Iss. 6 — 1 August 2018

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    Images

    • Figure 1
      Figure 1

      (a) Cations of alkali (1+) and alkaline-earth (2+) elements, as well as divalent Eu, together with their ionic radii from Refs. [5, 9]. (b) The 122 and (c) 1144 structures of iron pnictides. In general, the 1144 phase of AeAFe4As4 is stable when the difference in the ionic radii Δr=|r(Ae)−r(A)| is larger than 0.3 Å. Possible Fe magnetic orders are shown in (d) stripe order and (e) “hedgehog” or spin-vortex order.

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    • Figure 2
      Figure 2

      (a), (b) Characteristic evolution of the non-spin-polarized band structure [31] and (c), (d) the energy position E of the antibonding As-As pz orbital relative to the Fermi energy EF across a hcT transition in AeAFe4As4 (BaCsFe4As4 data are taken here as an example). Upon the first hcT, only the As-As pz antibonding band from the As facing the smaller cation layer, in this case Ae (blue lines), shifts abruptly above the Fermi level (plot c), while the band from As facing the larger cation layer (orange lines) remains occupied. This suggests that As-As bonds are strongly formed across the Ae layer. The second hcT at higher pressures is identified in the same fashion and, in contrast to the first hcT, reveals a smooth shift of the corresponding As bands across the Fermi level (plot d).

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    • Figure 3
      Figure 3

      Correlation between the zero-pressure a- and c-lattice parameters and the sum of the ionic radii r1+r2 of the spacer cations (r1 for Ae and Eu and r2 for A cations) for different 1144 iron pnictides. The measured (circles) and theoretical values (triangles) are shown for each system. Filled symbols indicate the parameters of the Eu-based systems and the star shows the low-temperature data for CaKFe4As4 [6]. The theory prediction is obtained using GGA and the spin-vortex configuration of Fe moments, following previous work [4], from which the data for CaKFe4As4 is taken for this plot. Dashed lines show results of purely nonmagnetic calculations.

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    • Figure 4
      Figure 4

      Pressure evolution of (a) lattice parameters a=b and c, (b) volume and c/a ratio and (c) As-As distances across both hcT transitions for EuRbFe4As4. The critical pressures of the two half-collapsed transitions are marked by vertical dashed lines. Here, the first hcT and the collapse of Fe moments occur simultaneously.

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    • Figure 5
      Figure 5

      Pressure evolution of (a) lattice parameters a=b and c, (b) volume and c/a ratio, and (c) As-As distances across both hcT transitions for EuCsFe4As4. The critical pressures of the two half-collapsed transitions are marked by vertical dashed lines. Here, the first hcT and the collapse of Fe moments occur simultaneously.

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    • Figure 6
      Figure 6

      (a) Definition of two different As heights in 1144 compounds. (b) As height asymmetry Eq. (1) vs pressure for EuRbFe4As4 and EuCsFe4As4. The critical pressures Pc1 and Pc2 for both hcT are indicated by the vertical dashed (EuRb) and dotted (EuCs) lines. Similar qualitative behavior is observed for other 1144 systems.

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    • Figure 7
      Figure 7

      Comparison of the As-4pz orbitals for CaRbFe4As4 structures relaxed at zero pressure (a) using the spin-vortex Fe order or (b) nonmagnetically. In the latter case, the As-As bonds across Ca are already formed, as opposed to the former structure, which emphasizes the importance of spin-vortex fluctuations in 1144 systems. For both relaxed geometries, the band structure is non-spin-polarized [31]. The color code is the same as in Fig. 2.

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    • Figure 8
      Figure 8

      Comparison of the calculated pressure-dependent c-lattice parameter of CaCsFe4As4 for two different energy cutoff values 600 eV and 800 eV.

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    • Figure 9
      Figure 9

      Pressure evolution of (a) lattice parameters a=b and c, (b) volume and c/a ratio, and (c) As-As distances across both hcT transitions for CaRbFe4As4. The critical pressures of the two half-collapsed transitions are marked by vertical dashed lines and the pressure range between the first hcT and the subsequent collapse of Fe moments is indicated by shading.

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    • Figure 10
      Figure 10

      Pressure evolution of (a) lattice parameters a=b and c, (b) volume and c/a ratio, and (c) As-As distances across both hcT transitions for CaCsFe4As4. The critical pressures of the two half-collapsed transitions are marked by vertical dashed lines and the pressure range between the first hcT and the subsequent collapse of Fe moments is indicated by shading.

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    • Figure 11
      Figure 11

      Pressure evolution of (a) lattice parameters a=b and c, (b) volume and c/a ratio, and (c) As-As distances across both hcT transitions for SrRbFe4As4. The critical pressures of the two half-collapsed transitions are marked by vertical dashed lines. Here, the first hcT and the collapse of Fe moments occur simultaneously.

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    • Figure 12
      Figure 12

      Pressure evolution of (a) lattice parameters a=b and c, (b) volume and c/a ratio, and (c) As-As distances across both hcT transitions for SrCsFe4As4. The critical pressures of the two half-collapsed transitions are marked by vertical dashed lines. Here, the first hcT and the collapse of Fe moments occur simultaneously.

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    • Figure 13
      Figure 13

      Pressure evolution of (a) lattice parameters a=b and c, (b) volume and c/a ratio, and (c) As-As distances across both hcT transitions for BaCsFe4As4. The critical pressures of the two half-collapsed transitions are marked by vertical dashed lines and the pressure range between the collapse of Fe moments and the subsequent first hcT is indicated by shading.

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