Structural, magnetic, and superconducting properties of Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$

We report the results of a systematic investigation of the phase diagram of the iron-based superconductor system, Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$, from $x=0.1$ to $x=1.0$ using high-resolution neutron and x-ray diffraction and magnetization measurements. We find that the coincident structural and magnetic phase transition to an orthorhombic structure with space group $Fmmm$ and a striped antiferromagnet with space group $F_{C}m{m}^{\prime }{m}^{\prime }$ in Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ is of first order. A complete suppression of the magnetic phase is observed by $x$ $=$ 30$\%$, and bulk superconductivity occurs at a critical concentration near 15$\%$. We compare our findings to the previously reported results of the hole-doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ solid solution in order to resolve the differing effects of band filling and $A$-site cation size on the properties of the magnetic and superconducting ground states. The substantial size difference between Na and K causes various changes in the lattice trends, yet the overarching property phase diagram from the Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ phase diagram carries over to the Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ solid solution. We note that the composition dependence of the $c$ axis turns over from positive to negative around $x$ $=$ 0.35, unlike the K-substituted materials. We show that this can be understood by invoking steric effects; primarily the Fe${}_2$As${}_2$ layer shape is dictated mostly by the electronic filling, which secondarily induces an interlayer spacing adjusted to compensate for the given cation volume. This exemplifies the primacy of even subtle features in the Fe${}_2$As${}_2$ layer in controlling both the structure and properties in the uncollapsed 122 phases.

Figure 1

Magnetization measurements of Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ system. All the samples were measured in a 0.1-G applied magnetic field. Magnetization values are normalized to the mass of the samples.

Figure 2

Variation of lattice constants $a$ and $b$ as a function of temperature for $x$ $=$ 0.1, 0.15, 0.2, and 0.3 samples determined by neutron diffraction. The lattice constants in the tetragonal phase are multiplied by $\sqrt{2}$.

Figure 3

Temperature dependence of the (110) peak measured by neutron diffraction in the vicinity of structural transition temperature $T_{\mathrm{s}}$ for $x$ $=$ 0.1, 0.15, 0.2. The bold curve shows the peak at the estimated $T_{\mathrm{s}}$. The $x$ $=$ 0.3 sample remains tetragonal down to 4 K.

Figure 4

Temperature dependence of the unit-cell volume for $x$ $=$ 0, 0.1, 0.15, and 0.2 determined by Rietveld refinements using synchrotron x-ray data.

Figure 5

(a) Na content dependence $a$ extracted from neutron (4 K) and x-ray (8 K) data. For orthorhombic samples, $a_{\mathrm{tet}}=\sqrt{a^2+b^2}/2$. (b) the $c$-axis and (c) unit-cell volume as a function of increasing Na content extracted from neutron (4 K, open blue circles) and x-ray (300 K, red squares and 8 K, solid blue circles) data. (d) and (e) 11BM-B data collected at room temperature showing the tetragonal (110) and (002) peaks for various Na concentrations.

Figure 6

(a) Layer widths (left panels) and volumes (right panels) for the Fe${}_2$As${}_2$ layer (top panels) and As-As spacing across the $A$ site (bottom panels). (b) Depiction of how the $c$ axis can be broken into As-As and Fe${}_2$As${}_2$ spacings. (c) Schematic for how Fe-Fe bond length affects the Fe${}_2$As${}_2$ width viewed along the (110) direction. The K-doped data are taken from Ref. 5.

Figure 7

Variation of Fe-Fe and Fe-As bond lengths in Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ with $x$ at 4 K (neutron data) and 300 K (x-ray data), and with temperature (neutron data) for $x$ $=$ 0.1, 0.15, 0.2, and 0.3. Blue circles represent the Fe-As bonds. Black and red squares represent the Fe-Fe bond lengths merging at $T_{\mathrm{s}}$. Solid lines are guides for the eye.

Figure 8

Variation of As-Fe-As bond angles in Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ with $x$ at 1.7 K and with temperature. The top-right panel shows α${}_1$, ${\alpha }_2^{\prime }$, and ${\alpha }_2^{\prime \prime }$ in orthorhombic setting. Blue triangles represent α${}_1$, red circles and black squares represent ${\alpha }_2^{\prime }$ and ${\alpha }_2^{\prime \prime }$ merging into one α${}_2$ at $T_{\mathrm{s}}$. Solid lines are guides to the eye. Comparison of angles and $T_{\mathrm{c}}$ (pink shaded region) as a function of composition is shown in the top-left panel. Optimal $T_{\mathrm{c}}$ occurs near perfect tetrahedral shape.

Figure 9

Superconducting quantum interference device (SQUID) magnetization measurements for $x$ $=$ 0, 0.1, 0.15, and 0.2 in a 2-kG applied magnetic field. Insets are the first derivatives of the magnetization curves $dM$/$dT$ (10${}^{-5}$) used to determine the Néel temperatures.

Figure 10

Neutron diffraction from Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ at 1.7 K with the magnetic Bragg peaks at a $d$ spacing of 2.45 and 3.43 Å indicated by the arrows. They are absent above $T_{\mathrm{N}}$ for $x$ $=$ 0.1, 0.15, and 0.2. At $x$ $=$ 0.3, a nearly negligible amount of intensity is detected above background.

Figure 11

Temperature dependences of the orthorhombic (solid red squares) and magnetic (open blue circles) order parameters for $x$ $=$ 0, 0.1, 0.15, and 0.2 samples.

Figure 12

Phase diagram of Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$. P/T is the normal state paramagnetic tetragonal phase and AF/T refers to the antiferromagnetic tetragonal phase ($C$4 in the text) (Ref. 25). The $x$ $=$ 1.0 point is taken from Ref. 22.