Hole doping in BaFe${}_2$As${}_2$: The case of Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ single crystals

Single crystals of Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ with $x=0$, 0.25, 0.35, 0.4 were grown using a self-flux high temperature solution growth technique. The superconducting and normal state properties were studied by temperature dependent magnetic susceptibility, electrical resistivity, and specific heat, revealing that the magnetic and structural transition is rapidly suppressed upon Na substitution at the Ba site in BaFe${}_2$As${}_2$, giving rise to superconductivity. A superconducting transition as high as 34 K is reached for a Na content of $x=0.4$. The positive Hall coefficient confirms that the substitution of Ba by Na results in hole doping similar to the substitution of Ba by K. Angle resolved photoemission spectroscopy was performed on all Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ crystals. The Fermi surface of hole-doped Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ is to a large extent the same as the Fermi surface found for the K-doped sister compounds, suggesting a similar impact of the substitution of Ba by either K or Na on the electronic band dispersion at the Fermi level.

Figure 1

(A) Platelike as-grown single crystals of Ba${}_{0.75}$Na${}_{0.25}$Fe${}_2$As${}_2$ from self-flux, (a)–(c) SEM pictures from the same batch of a Ba${}_{0.75}$Na${}_{0.25}$Fe${}_2$As${}_2$ single crystal. (D) Platelike as-grown single crystals of Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$. (d)–(e) SEM pictures from the same batch of a Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$ single crystal which shows the typical layer by layer growth.

Figure 2

XRD pattern of Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ showing only 00$l$ reflections. The XRD data were collected using the platelike crystals.

Figure 3

(a) Susceptibility $\chi =M/B$ for Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ for different doping levels at $H\parallel ab=1$ T. The inset shows the derivative of the static susceptibility. (b) Temperature dependence of the volume susceptibility ${\chi }_{\text{vol}}$ following the ZFC-FC protocol as described in the text. All data have been collected for $B\parallel ab$ and the applied field was 20 Oe.

Figure 4

In-plane electronic resistivity $\rho$ of Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ single crystals for different Na contents $x$ in dependence of the temperature. Inset: Derivative $d\rho /dT$ around the combined structural and magnetic transition.

Figure 5

Hall coefficient $R_H$ of optimally doped Ba${}_{0.6}$Na${}_{0.4}$Fe${}_2$As${}_2$ and undoped compound in dependence of temperature. Inset: Hall resistivity in dependence of applied magnetic field ${\mu }_{0}H$ for both samples at different temperatures. $R_H$ was determined from the average slope ${\rho }_{x,y}$ between 3 and 15 T.

Figure 6

Temperature dependence of the heat capacity measurement on a single crystal of the pristine BaFe${}_2$As${}_2$. The combined structural and magnetic transition is clearly seen at 137 K. The upper inset shows the vicinity of the phase transition on an enlarged scale, while the lower inset shows a linear fit to the data in the temperature range between 4 and 20 K.

Figure 7

The temperature dependent specific heat of (a) Ba${}_{0.6}$Na${}_{0.4}$Fe${}_2$As${}_2$ (b) Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$ in various applied magnetic fields up to 9 T parallel to the c-axis. The insets show a zoom into the superconducting state for both single crystals.

Figure 8

Magnetic phase diagram for $x=0.35$ and 0.40. The blue dotted line represents a linear fit to the data.

Figure 9

(a) Fermi surface (FS) map, recorded at 80 eV excitation energy from the Ba${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ samples with $x=0.35$ ($T_c=29$ K). The photoemission intensity distribution was integrated within $\pm 7$ meV around the Fermi level. (b) An energy-momentum cut, passing through the $\Gamma$ point and imaging the inner and outer $\Gamma$ barrels, recorded at $T=1$ K for the sample with $x=0.4$ ($T_c=34$ K). A smaller superconducting gap can be observed for the outer $\Gamma$ barrel and a larger one for the inner $\Gamma$ barrel. (c) Temperature dependence of the density of states, related to the inner $\Gamma$ barrel, recorded for the sample with $x=0.4$. Inset: Density of states for outer and inner $\Gamma$ barrels at 7 K, fitted to the Dynes function (Ref. 33). The determined values for the superconducting gap are $3\pm 0.5$ and $10.5\pm 1$ meV. (d) Density of states for the inner $\Gamma$ barrel, recorded at 1 and 11 K for the underdoped sample with $x=0.25$ ($T_c=10$ K). The value of the superconducting gap, estimated from the fit, is $1.9\pm 0.5$ meV.