Sequential structural and antiferromagnetic transitions in ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ under pressure

The discovery of superconductivity in the two-leg ladder compound ${\mathrm{BaFe}}_2{\mathrm{S}}_3$ has established the 123-type iron chalcogenides as a novel and interesting subgroup of the iron-based superconductor family. However, in this 123 series, ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ is an exceptional member, with a magnetic order and crystalline structure different from all others. Recently, an exciting experiment reported the emergence of superconductivity in ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ at high pressure [J. Ying et al., Phys. Rev. B 95, 241109(R) (2017)]. In this paper, we report a first-principles study of ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$. Our analysis unveils a variety of qualitative differences between ${\mathrm{BaFe}}_2{\mathrm{S}}_3$ and ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$, including in the latter an unexpected chain of transitions with increasing pressure. First, by gradually reducing the tilting angle of iron ladders, the crystalline structure smoothly transforms from $Pnma$ to $Cmcm$ at $\sim 6$ GPa. Second, the system becomes metallic at 10.4 GPa. Third, its unique ambient-pressure Block antiferromagnetic ground state is replaced by the more common stripe (so-called CX-type) antiferromagnetic order at $\sim 12$ GPa, the same magnetic state as the 123-S ladder. This transition is found at a pressure very similar to the experimental superconducting transition. Finally, all magnetic moments vanish at 30 GPa. This reported theoretical diagram of the complete phase evolution is important because of the technical challenges to capture many physical properties in high-pressure experiments. The information obtained in our calculations suggests different characteristics for superconductivity in ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ and ${\mathrm{BaFe}}_2{\mathrm{S}}_3$: in 123-S pairing occurs when magnetic moments vanish, while in 123-Se the transition region from Block- to CX-type magnetism appears to catalyze superconductivity. Finally, an additional superconducting dome above $\sim 30$ GPa is expected to occur.

Figure 1

(a) and (b) Schematic crystal structures of $A{\mathrm{Fe}}_2{X}_3$ with the following convention: green = $A$, yellow = $X$, brown = Fe. (a) corresponds to space group No. $62Pnma$. (b) corresponds to space group No. $63Cmcm$. The key difference between these structures is the tilting/nontilting of the iron ladders. (c) Sketch of some possible spin patterns studied here. Spin up and down are distinguished by brown and gray, respectively. A and B are the ladder indexes in one unit cell, as indicated in (a) and (b). Note A and B are ladders located in different layers.

Figure 2

Evolution of the magnetic and electronic structures of ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ as a function of pressure. (a) Energies (per Fe) of the various magnetic orders indicated. (b) Local magnetic moments of Fe, integrated within the default Wigner-Seitz sphere as specified by vasp. The inset shows an amplified view near the transition. (c) Band gaps for the many states analyzed.

Figure 3

Evolution of the crystalline structure of ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ varying pressure. (a) The tilting angle of the iron ladders in the Block-B magnetic state [see sketch in Fig. 1]. (b) Lattice constants, normalized to the original ones at zero pressure. (c) The Fe-Fe distance along the leg ladder direction. In both (b) and (c), the results for the dominant CX and Block-B phases are shown for comparison. In (c), there are two distances for the Block-B phase because there are two types of bonds along the legs: AFM and FM.

Figure 4

Phase diagram of ${\mathrm{BaFe}}_2{X}_3(X$= S, Se) varying pressure, according to experimental data [27, 30, 36] and to our present and previous [24] DFT calculations. The curves of AFM Néel temperatures (red solid lines), including the superconducting (SC) domes, are all from experiments. For example, see Fig. 4 of Ref. [36]. (a) Results for ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$. The superconducting dome beyond 30 GPa is a theoretical prediction to be verified in future experiments. (b) Results for ${\mathrm{BaFe}}_2{\mathrm{S}}_3$. The dashed portion of the curve for $T_{\mathrm{N}}$ is an assumed smooth drop with increasing pressure (experimental data are lacking). Right axis: local magnetic moments. Open symbols: experimental data at low temperature. Solid symbols: DFT data (at zero temperature).

Figure 5

Electronic structure of ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ from DFT. (a) and (b) Band structures at 0 and 12 GPa for the hypothetical NM state for comparison. The Fermi level is shown with dashed lines. The bandwidths of the iron bands increase with increasing pressure (e.g., see the branch highlighted in red). (c) and (d) Band structures at 0 GPa (Block-B) and 12 GPa (CX) for the magnetic states for comparison. (e) and (f) Electron density profiles of the iron ladders at 0 and 12 GPa for the hypothetical NM state for comparison. The increase in the red intensity of the iron atoms at 12 GPa, compared to 0 GPa, is indicative of electronic doping by pressure. Top panel: cut in an iron ladder plane; bottom panel: cut in a Se plane.