Sustained phase separation and spin glass in Co-doped ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$ single crystals

We present Co substitution effects in ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ ($0.06\le z\le 1.73$) single-crystal alloys. By 3.5% of Co doping superconductivity is suppressed, whereas phase separation of semiconducting ${\mathrm{K}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ and superconducting/metallic ${\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{Se}}_2$ is still present. We show that the arrangement and distribution of the superconducting phase (stripe phase) are connected with the arrangement of K, Fe, and Co atoms. Semiconducting spin glass is found in proximity to the superconducting state, persisting for large Co concentrations. At high Co concentrations a ferromagnetic metallic state emerges above the spin glass. This is coincident with changes of the unit cell and arrangement and connectivity of the stripe conducting phase.

Figure 1

(a) High-energy synchrotron x-ray diffraction data of the ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ series, normalized by the intensity of (002) reflection for comparison. Data are offset for clarity and labeled by respective Co content as measured by EDX. Vertical dashed lines are provided as a visual reference. Vertical arrow indicates (110) reflection, which is a hallmark of the $I4/m$ phase. Coexistence of the $I4/m$ and $I4/mmm$ phases can be visually tracked up to $z=0.92\left(4\right)$ cobalt content in the samples studied. (b) Modeling of powder diffraction data for a sample with $z=0.92\left(4\right)$. Crosses represent data, red solid line is the model, and green solid line is the difference, which is offset for clarity. Vertical ticks mark the reflections in the $I4/mmm$ (top row) and $I4/m$ (bottom row) phases. (c) and (d) Evolution with EDX-established Co content of refined lattice parameters for $I4/mmm$ (solid blue circles) and $I4/m$ (open red circles). All parameters are expressed in the $I4/m$ metrics (see text). The shaded region is where the signatures of the phase coexistence could be reliably established from the diffraction data.

Figure 2

Backscattered electron images of SEM measurement and EDX mappings of ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ when (a) $z=0.61\left(6\right)$, (b) $z=0.92\left(4\right)$, and (c) $z=1.50\left(3\right)$.

Figure 3

(a) Temperature dependence of the in-plane resistivity $\rho \left(T\right)$ of ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ series at zero (solid symbols) and 9 T field (open symbols). The black solid lines are the fitted result using the thermal activation model. (b) The relation between $C/T$ and $T^2$ for ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ series at low temperature. The solid lines represent fits by the equation $C/T=\gamma +{\beta }_3{T}^2+{\beta }_5{T}^4$. (c) Temperature dependence of thermoelectric power $S\left(T\right)$ for ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ series. The inset shows the thermoelectric power at $T=180$ K for different Co concentrations.

Figure 4

Temperature dependence of dc magnetic susceptibilities of ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ series for (a) $H\perp c$ and (b) $H\parallel c$ at $H=1$ kOe in ZFC and FC below 350 K. Insets in (a) and (b) are $M-H$ curves of ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ with $z=0.61\left(6\right)$ for $H\perp c$ and $H\parallel c$, respectively, at 1.8 K (black solid inverse triangle) and 300 K (red open inverse triangle). (c) Temperature dependence of ac susceptibility ${\chi }^{\prime }\left(T\right)$ measured at five different frequencies for $z=0.27\left(0\right)$ of ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$. The inset shows the frequency dependence of $T_f$ with the linear fitting (solid line). (d) TRM vs time for $z=0.27\left(0\right)$ of ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2$ at 10 K and $t_w=100$ s with different dc fields with fittings using stretched exponential function (solid lines). (e) $M_{TRM}$ vs $t$ at 10 and 150 K with $H=1$ kOe and $t_w=100$ s. (f) $H$-field dependence $\tau \left(s\right)$ (black solid square) and $1-n$ (red solid circle).

Figure 5

(a) Raman scattering spectra of ${\mathrm{K}}_{0.6}{\mathrm{Co}}_{1.73}{\mathrm{Se}}_2$ single crystals in various scattering configurations ($\mathbf{x}=\left[100\right],\mathbf{y}=\left[010\right],{\mathbf{x}}^{\prime }=1/\sqrt{2}\left[110\right],{\mathbf{y}}^{\prime }=1/\sqrt{2}\left[1\overline{1}0\right]$). (b) Raman scattering spectra of ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y-z}{\mathrm{Co}}_z{\mathrm{Se}}_2, [0\le z\le 1.73(4\left)\right]$ single crystals measured at room temperature from the (001) plane of the samples.

Figure 6

Magnetic and transport phase diagram. Open squares and open circles are spin-glass characteristic temperature $T_f$ for the $H\perp c$ and $H\parallel c$ directions, respectively. Open triangles are the ferromagnetic transition temperature, and open diamonds are the thermoelectric power ${\mathrm{S}}_T$ at 180 K. Open hexagons are resistivity maximums ${\rho }_{\max }$, which show the semiconductor (brighter yellow region) to metal (darker orange region) crossover. The lines at the top denote the regions of the ordered $I4/m$ and $I4/mmm$ space groups.