Observation of the magnetic $C_4$ phase in ${\mathrm{Ca}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ and its universality in the hole-doped 122 superconductors

Since its discovery in 2014, the magnetic tetragonal $C_4$ phase has been identified in a growing number of hole-doped 122 Fe-based superconducting compounds. Exhibiting a unique double-Q magnetic structure and a strong competition with both superconducting and magnetic order parameters, the $C_4$ phase and the conditions of its formation are of significant interest to understanding the fundamental mechanisms in these materials. Particularly, separating the importance of direct changes to the relative size of hole and electron pockets at the Fermi surface (achieved via charge doping) from the role of structural changes due to differences of ionic radii of dopants is useful to determine the underlying parameter which causes the $C_4$ instability. Here, we report the discovery of the $C_4$ phase in a fourth member of the hole-doped 122 materials ${\mathrm{Ca}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}(0.20\le x\le 0.50)$ as determined from neutron and x-ray powder diffraction studies. The maximum of the $C_4$ dome is observed at $x=0.44$ with a reentrant temperature $T_r=52$ K and an extent of $\mathrm{\Delta }x\sim 0.07$ in composition. It is observed that for a range of compositions within the $C_4$ dome $(0.40\le x\le 0.42$), there is a second reentrance $(T_{r_2}<T_r)$ where the antiferromagnetic $C_2$ phase is recovered—a feature previously only seen in ${\mathrm{Ba}}_{\text{1-x}}{\mathrm{K}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$. A phase diagram is presented for ${\mathrm{Ca}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ and compared to the other $\mathrm{Na}$-doped 122's—$A_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ with $A$ = Ba, Sr, and Ca. The structural parameters for these three systems are compared and the importance of the “chemical pressure” due to changing the $A$-site ion ($A$ = Ba, Sr, Ca) is discussed.

Figure 1

The superconducting transitions for all measured powders. Magnetization normalized to the mass of the samples used for neutron diffraction (left) and x-ray diffraction (right). All samples show either bulk superconductivity or are nonsuperconducting. The slight variation in diamagnetic response is consistent with small FeAs impurities seen in diffraction patterns.

Figure 2

(a) Diffractograms of the 112 nuclear peak and the magnetic $\frac{1}{2}\frac{1}{2}1$ and $\frac{1}{2}\frac{1}{2}3$ peaks for the ${\mathrm{Ca}}_{\text{0.58}}{\mathrm{Na}}_{\text{0.42}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ sample. Diffractograms of the 112 peak for the (b) $x=0.40$ and (c) 0.45 samples. The diffractograms of the nuclear peak and magnetic peaks were compiled from x-ray (11BM-B) and neutron (POWGEN) diffraction patterns, respectively.

Figure 3

Neutron diffraction patterns collected on POWGEN at 10 K for a series of compositions near the $C_4$ dome. Indicated with arrows are the $\frac{1}{2}\frac{1}{2}3$ and $\frac{1}{2}\frac{1}{2}1$ magnetic reflections. Patterns are arbitrarily offset to aid in visual comparison.

Figure 4

(a), (b) Lattice parameters of the $x=0.35,0.40,0.45,0.50$ samples extracted from Rietveld refinements. (a) The $a$ lattice parameter for the tetragonal phases is indicated by filled symbols and has been scaled by a factor of $\sqrt{2}$ to aid in visual comparison. (b) The refined phase fraction of the tetragonal (red) and orthorhombic (blue) phases in a mixed phase refinement for the $40\%$ sample. Waterfall plots showing the temperature dependence of the (c), (e) 112 and (d), (f) 220 nuclear peaks of the $40\%$ and $42\%$ samples, respectively.

Figure 5

Phase diagram of ${\mathrm{Ca}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$. Filled and open symbols are transitions determined from x-ray and neutron data, respectively. The parent compound's transition temperature was taken from Ref. [38]. The red, blue, and green shaded areas represent the AFM orthorhombic, superconducting, and AFM tetragonal phases, respectively. The shaded region indicates phase coexistence between the $C_4$ phase and a reentrant $C_2$ phase. Coincident structural and magnetic transitions are represented for each phase by a solid line. Inset: an enlarged view showing details of the $C_4$ dome.

Figure 6

(a) Phase diagrams of the three ${\mathrm{Na}}^{+}$-doped 122 systems overlaid. The solid, dashed, and short-dashed lines correspond to the ${\mathrm{Ba}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}, {\mathrm{Sr}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$, and ${\mathrm{Ca}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ phase boundaries, respectively. The blue, red, and green shaded regions correspond to the AFM $C_2$, AFM $C_4$, and SC phases, respectively. The composition dependence of the FeAs layer tetrahedral angles at 10 K for (b) ${\mathrm{Ba}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$, (c) ${\mathrm{Sr}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$, and (d) ${\mathrm{Ca}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$. Values for the angles of ${\mathrm{Ba}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ and ${\mathrm{Sr}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ were taken from Refs. [30] and [20], respectively.

Figure 7

Compositional dependence of the unit cell: (a) volume, (b) $c$ axis, (c) $a_{\mathrm{tet}}$ direction, and (d) $c/a$ ratio for the three ${\mathrm{Na}}^{+}$-doped 122 systems at 300 K. (e) The refined magnetic moment plotted as a function of the orthorhombic order parameter $\delta$ (where $\delta$ has been scaled by a factor of ${10}^3)$ for data collected at 10 K. (f) The ${\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ layer with the ${\alpha }_1$ and two ${\alpha }_2$ angles indicated. Data for ${\mathrm{Ba}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ and ${\mathrm{Sr}}_{\text{1-x}}{\mathrm{Na}}_{\text{x}}{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ were taken from Refs. [30] and [20], respectively.

Figure 8

Fe-As (left) and $A$-Fe (right) bond lengths of the three Na-doped 122 materials at 10 K.