Structure and composition of the superconducting phase in alkali iron selenide $K_y{\mathrm{Fe}}_{1.6+x}{\mathrm{Se}}_2$

We use neutron diffraction to study the temperature evolution of the average structure and local lattice distortions in insulating and superconducting potassium iron selenide $K_y{\mathrm{Fe}}_{1.6+x}{\mathrm{Se}}_2$. In the high temperature paramagnetic state, both materials have a single phase with a crystal structure similar to that of the BaFe${}_2$As${}_2$ family of iron pnictides. While the insulating $K_y{\mathrm{Fe}}_{1.6+x}{\mathrm{Se}}_2$ forms a $\sqrt{5}\times \sqrt{5}$ iron vacancy ordered block antiferromagnetic (AF) structure at low temperature, the superconducting compounds spontaneously phase separate into an insulating part with $\sqrt{5}\times \sqrt{5}$ iron vacancy order and a superconducting phase with chemical composition of K${}_z$Fe${}_2$Se${}_2$ and BaFe${}_2$As${}_2$ structure. Therefore, superconductivity in alkaline iron selenides arises from alkali deficient K${}_z$Fe${}_2$Se${}_2$ in the matrix of the insulating block AF phase.

Figure 1

In plane structures proposed for various $A_y$Fe${}_{1.6+x}{\mathrm{Se}}_2$ phases: (a) Main vacancy ordered phase with $\sqrt{5}\times \sqrt{5}$ block AF order [10, 11, 12, 13]. The $+$ and $-$ signs indicate Fe spin directions relative to the FeSe plane. (b) Proposed phase for semiconductor, where spin directions are marked as arrows (Ref. [23]). (c) Suggested superconducting phase with $\sqrt{8}\times \sqrt{10}$ iron vacancy order (Ref. [20]). (d) Iron-disordered, partially occupied orthorhombic phase with BaFe${}_2$As${}_2$ iron pnictide structure. (e)–(g) Schematic for phase separation through spontaneous nucleation in the temperature region of iron mobility. A disordered $I4/mmm$ phase above $T_s$. Below $T_N$, the $I4/m^{\prime }$ symmetry insulating phase forms at random sites and spreads, enriching the iron in the remaining disordered phase until either full iron occupation of second phase (slow cooling) or temperature drops below the zone of iron mobility (quenching).

Figure 2

Region of powder diffraction spectra with corresponding single phase fits for the (a) insulating and (b) superconducting sample, each fit with an $I4/mmm$ symmetry phase at 590 K and $I4/m^{\prime }$ symmetry phase at 15 K. FIG. 2. (Continuted) (b inset) The unfit peaks in the superconducting sample with only the $I4/m^{\prime }$ symmetry are marked with arrows. There is an unidentified impurity peak near 3.2 Å${}^{-1}$ marked as $*$ in the superconducting sample. The peak has no temperature dependence. Side cut of pure (c) FeSe and (d) KFe${}_2$Se${}_2$ crystal structures. Darker atoms are placed in front of iron while lighter ones are behind. Note inversion of middle layer necessary to form the BaFe${}_2$As${}_2$ symmetry phase from FeSe. (e) Best fits using different proposed second phases. FeSe can be interpreted as a K-intercalated sample with no K ordering. (f) Best fit using orthorhombic $Fmmm$ symmetry structure akin to that of BaFe${}_2$As${}_2$. The inset shows clear broadening of the $\left(112\right)$ peak at base temperature (blue dots) compared to above $T_s$ (line). Such broadening can be induced by a small orthorhombic lattice distortion. (g) Comparison of the fits using pure $\sqrt{5}\times \sqrt{5}$ iron vacancy order without AF order (green), the effect of AF order (orange), the superconducting phase (blue), and the combination of all phases (red). At 15 K, the lattice parameters of the block AF phase for the superconducting and insulating samples are $a=8.68535\left(6\right)$ Å, $c=14.0054\left(2\right)$ Å and $a=8.68403\left(5\right)$ Å, $c=14.0084\left(2\right)$ Å, respectively. The lattice parameters for the K${}_z$Fe${}_2$Se${}_2$ phase are $a=5.3966\left(3\right)$, $b=5.3653\left(3\right)$, and $c=14.043\left(1\right)$ Å.

Figure 3

Pair distribution function at base temperature of the insulating and superconducting samples. (a) The insulator at base temperature is fit using only the $I4/m^{\prime }$ symmetry phase (inset, blue line). The split in the Fe-Fe peak results from a contraction of [Fe-Fe]${}_1$ and rotation of inner iron square. (b) The superconductor requires an addition phase, here fit with $Fmmm$ symmetry (inset, green line) and disordered Fe vacancies. The Fe-Fe bond distance in the additional phase matches the [Fe-Fe]${}_1$ distance, resulting in an increase of intensity relative to [Fe-Fe]${}_2$.

Figure 4

(a) Refined lattice parameters for the insulating sample. All results are reported using the $I4/m^{\prime }$ symmetry unit cell. (b) Refined magnetic moment shows hysteresis and strengthens upon annealing. (c) Refined iron concentration for iron occupation by site also shows enhanced vacancy ordering below 450 K upon warming from a quenched state. (d) Iron site labels in the $I4/m^{\prime }$ symmetry phase. All arrows indicate direction in thermal cycle.

Figure 5

(a) Refined lattice parameters for both insulating (blue) and superconducting (green) phases. Second phase features notable compression (2% at 15 K), orthorhombicity (0.29%), and hysteresis along the $c$ axis. (b) Refined magnetic moment in insulating phase showing same behavior as pure insulator. (c) Refined iron occupation in insulating phase by site. Notable refinement of vacancy order upon temperature cycling. (d) Refined main phase fraction upon temperature cycling. A clear increase in main phase fraction upon warming to 450 K in a quenched sample. Solid lines are guides to the eye.