Electronic structure and coexistence of superconductivity with magnetism in $\mathrm{Rb}\mathrm{Eu}{\mathrm{Fe}}_4{\mathrm{As}}_4$

In the novel stoichiometric iron-based material ${\mathrm{RbEuFe}}_4{\mathrm{As}}_4$, superconductivity coexists with a peculiar long-range magnetic order of Eu 4f states. Using angle-resolved photoemission spectroscopy, we reveal a complex three-dimensional electronic structure and compare it with density functional theory calculations. Multiple superconducting gaps were measured on various sheets of the Fermi surface. High-resolution resonant photoemission spectroscopy reveals magnetic order of the Eu 4f states deep into the superconducting phase. Both the absolute values and the anisotropy of the superconducting gaps are remarkably similar to the sibling compound without Eu, indicating that Eu magnetism does not affect the pairing of electrons. A complete decoupling between Fe- and Eu-derived states was established from their evolution with temperature, thus unambiguously demonstrating that superconducting and a long-range magnetic orders exist independently from each other. The established electronic structure of ${\mathrm{RbEuFe}}_4{\mathrm{As}}_4$ opens opportunities for the future studies of the highly unorthodox electron pairing and phase competition in this family of iron-based superconductors with doping.

Figure 1

Structure and FS topology. (a) Layered crystal structure and (b) bulk Brillouin zone of ${\mathrm{RbEuFe}}_4{\mathrm{As}}_4$. (c) The $k_x-k_y$ FS map, measured using 70 eV photons in linear vertical (LV) polarization. (d) Band dispersions in $\mathrm{M}-\mathrm{\Gamma }-\mathrm{M}$ direction measured using 113 eV photons for LV polarization. All data measured at 40 K. (e) Calculated FS for $k_z$ = 0 for FM configuration of Eu moments. (f) Calculated band dispersions in $\mathrm{M}-\mathrm{\Gamma }-\mathrm{M}$ direction showing Fe 3d (green) and Eu 4f (blue) bands.

Figure 2

Superconducting properties from ARPES. (a) Hole pocket FS at Z-point (40 K); (b, c) band dispersions at Z-point below and above ${\mathrm{T}}_{\mathrm{c}}$ measured along high symmetry direction are shown as a red double arrow in (a); white arrows indicate corresponding $k_{\mathrm{F}}$ positions; (d) Electron pocket FS at M-point (40 K); (e, f) band dispersions at M-point below and above ${\mathrm{T}}_{\mathrm{c}}$ measured along high symmetry direction shown as a red double arrow in (d); white arrows indicate corresponding $k_{\mathrm{F}}$ positions; (g, h) photoemission spectra at equivalent $k_{\mathrm{F}}$ positions above and below ${\mathrm{T}}_{\mathrm{c}}$ together with the superconducting gap fit for hole and electron pockets; (i) temperature dependence of the superconducting gap obtained for three different FS sheets of the hole pocket at Z-point.

Figure 3

Superconducting properties from Andreev reflection spectroscopy. (a) Typical $I-V$ (red) and dynamic conductance $dI/dV$ (blue) curves for double-stack junction (m = 2). Gray strips highlight the dip positions for two gaps. (b) Temperature dependence of the two gaps derived from the voltage dips in dynamic conductance data of m = 2 stack in the entire temperature range up to ${\mathrm{T}}_{\mathrm{c}}$. Green circles represent a larger gap and blue diamonds represent a smaller gap correspondingly. Gray lines show the BCS-like fit.

Figure 4

DFT electronic structure. Band dispersions with the Fe 3d orbital character for FM (left column), A-type AFM (middle column), and helical AFM (right column) Eu magnetic structures. Calculations are done for 1, 2, and 4 formula units per cell correspondingly.

Figure 5

Magnetic properties. (a) The resonant Eu $4\mathrm{d}\to 4\mathrm{f}$ photoemission spectra taken at 7, 30, and 40 K with 142 eV of photons and LV polarization; the off-resonant 120 eV survey scan shown as an insert explicitly indicates no admixture of the trivalent Eu state. (b) Two-dimensional color plot presentation of the temperature evolution of the divalent Eu 4f resonant photoemission signal [64]. (c, d) XMCD spectra measured for Eu ${\mathrm{M}}_{5,4}$ and Fe ${\mathrm{L}}_{3,2}$ absorption edges.

Figure 6

(a) $k_y-k_z$ FS map for holelike bands measured with LH photons. (b) Band dispersions in $\mathrm{M}-\mathrm{\Gamma }-\mathrm{M}$ direction measured using 113 eV photons and LH polarization. (c) Band dispersions in $\mathrm{A}-\mathrm{Z}-\mathrm{A}$ direction measured using 89 eV photons and LH polarization. All data measured at 40 K.

Figure 7

Band dispersions at Z-point as a function of temperature measured along high symmetry R-Z-R direction.

Figure 8

Temperature dependence of the symmetrised EDCs at equivalent $k_{\mathrm{F}}$ positions for three different FS sheets of the hole pocket at Z-point.

Figure 9

Typical $I-V$ curve (right Y-axis), and comparison of the dynamic conductance (left Y-axis) for the two different, single- and double- stack junctions. Gray strips highlight the dip positions.

Figure 10

The 3D-plot of the entire set of $dI/dV$ vs $V$ and $T$ curves for the double-stack junction $m=2$ (the $V_i$ values are doubled relative to Fig. 9.