Combined effects of pressure and Ru substitution on BaFe${}_2$As${}_2$

The $ab$ plane resistivity of Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ ($x=0.00$, 0.09, 0.16, 0.21, and 0.28) was studied under nearly hydrostatic pressures, up to 7.4 GPa, in order to explore the $T-P$ phase diagram and to compare the combined effects of isoelectronic Ru substitution and pressure. The parent compound BaFe${}_2$As${}_2$ exhibits a structural/magnetic phase transition near 134 K. At ambient pressure, progressively increasing Ru concentration suppresses this phase transition to lower temperatures at an approximate rate of $\sim$5 K/% Ru correlated with the emergence of superconductivity. By applying pressure to this system, a similar behavior is seen for each concentration: the structural/magnetic phase transition is further suppressed and superconductivity induced and ultimately, for larger $x$ Ru and $P$, suppressed. A detailed comparison of the $T-P$ phase diagrams for all Ru concentrations shows that 3 GPa of pressure is roughly equivalent to $10\%$ Ru substitution. Furthermore, due to the sensitivity of Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ to pressure conditions, the melting of the liquid media, $4:6$ light mineral oil : $n$-pentane and $1:1$ isopentane : $n$-pentane, used in this study could be readily seen in the resistivity measurements. This feature was used to determine the freezing curves for these media and to infer their room temperature, hydrostatic limits: 3.5 and 6.5 GPa, respectively.

Figure 1

$T-x$ phase diagram for Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$.[11] Open symbols indicate the Ru concentrations that were studied under pressure.

Figure 2

Temperature dependence of the resistivity of BaFe${}_2$As${}_2$ for pressures up to 5.32 GPa measured using the modified Bridgman cell. (a) Measurements are shown for temperatures up to 300 K. Inset shows criteria used for the determination of $T_{\mathrm{sm}}$. (b) Same measurements shown for temperatures up to 70 K with criterion used for $T_{c,\rho =0}$. Inset shows the criterion used for $T_{c,\mathrm{onset}}$.

Figure 3

Resistivity measurements of BaFe${}_2$As${}_2$ with applied currents of 0.01, 0.1, and 1 mA at (a) 3.64 GPa and (b) 6.21 GPa.

Figure 4

$T-P$ phase diagram for two sets of measurements of BaFe${}_2$As${}_2$ using the Bridgman cell. The isopentane : $n$-pentane mixture was used as the liquid pressure-transmitting medium for both measurements.

Figure 5

Temperature dependence of the resistivity of Ba(Fe${}_{0.91}$Ru${}_{0.09}$)${}_2$As${}_2$ up to 1.83 and 4.94 GPa using a piston cylinder cell and a Bridgman cell, respectively. (a) Shown for temperatures up to 300 K. The 0.66, 1.50, and 1.83 GPa measurements have been shifted down by 0.035, 0.045, and 0.06 m$\Omega$cm, respectively, for clarity. (b) Shown for temperatures up to 35 K. (c) and (d) Criteria used to determine $T_{\mathrm{sm}}$ and their corresponding error bars.

Figure 6

$T-P$ phase diagram for measurements of Ba(Fe${}_{0.91}$Ru${}_{0.09}$)${}_2$As${}_2$. Open and solid symbols indicate measurements using the piston cylinder cell and the modified Bridgman cell, respectively.

Figure 7

Temperature dependence of the resistivity of Ba(Fe${}_{0.84}$Ru${}_{0.16}$)${}_2$As${}_2$ up to 2.30 and 4.97 GPa measured using the piston cylinder cell and the modified Bridgman cell, respectively. (a) Shown for temperatures up to 300 K. (b) Shown for temperatures up to 30 K.

Figure 8

$T-P$ phase diagram for measurements of Ba(Fe${}_{0.84}$Ru${}_{0.16}$)${}_2$As${}_2$. Open and solid symbols indicate measurements using the piston cylinder cell and the modified Bridgman cell, respectivdely.

Figure 9

Temperature dependence of the resistivity of Ba(Fe${}_{0.79}$Ru${}_{0.21}$)${}_2$As${}_2$ up to 1.12 and 7.39 GPa measured using the piston cylinder cell and the modified Bridgman cell, respectively. (a) Shown for temperatures up to 300 K. (b) Shown for temperatures up to 30 K.

Figure 10

$T-P$ phase diagram for measurements of Ba(Fe${}_{0.79}$Ru${}_{0.21}$)${}_2$As${}_2$. Open and solid symbols indicate measurements using the piston cylinder cell and the modified Bridgman cell, respectively.

Figure 11

Temperature dependence of the resistivity of Ba(Fe${}_{0.72}$Ru${}_{0.28}$)${}_2$As${}_2$ up to 2.22 GPa measured using the piston cylinder cell. (a) Shown for temperatures up to 300 K. (b) Shown for temperatures up to 20 K.

Figure 12

$T-P$ phase diagram for measurements of Ba(Fe${}_{0.72}$Ru${}_{0.28}$)${}_2$As${}_2$ using the piston cylinder cell.

Figure 13

Combined phase diagram for all Ru concentrations. Open and closed symbols are transition temperatures from measurements using the piston cylinder cell and Bridgman cell, respectively. Lines are guides for the eyes.

Figure 14

Comparison of the $T-x$ phase diagram for Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ and $T-P$ phase diagram of BaFe${}_2$As${}_2$ with a ratio of 3 GPa to $x=0.10$ Ru relating the two horizontal axes.

Figure 15

Phase diagram of all Ru concentrations each shifted by 3 GPa for every $x=0.10$ Ru substitution. Open and closed symbols are transition temperatures from measurements using the piston cylinder cell and Bridgman cell, respectively.

Figure 16

Comparison of $T-x$ phase diagram and the maximum $T_{c,\rho =0}$ achieved with pressure at various Ru concentrations. Solid stars are $T_{c,\max }$ values from this study. The open star is the $T_{c,\max }$ reported by Colombier et al.[13]

Figure 17

(a) Feature in resistivity data for Ba(Fe${}_{0.79}$Ru${}_{0.21}$)${}_2$As${}_2$ at 2.27, 3.28, and 3.99 GPa. Dashed are extrapolations of the lower temperature, linear $\rho \left(T\right)$ data. (b) Feature in $d\rho /dT$ indicative of the melting of the liquid medium.

Figure 18

Combined phase diagram of the melting of the liquid medium ($1:1$ isopentane : $n$-pentane).

Figure 19

Combined phase diagram of the melting of the liquid medium $4:6$ light mineral oil : $n$-pentane.