Possible origin of the nonmonotonic doping dependence of the in-plane resistivity anisotropy of Ba(Fe${}_{1-x}{T}_x$)${}_2$As${}_2$ ($T=\text{Co}$, Ni and Cu)

The in-plane resistivity anisotropy has been measured for detwinned single crystals of Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$ and Ba(Fe${}_{1-x}$Cu${}_x$)${}_2$As${}_2$. The data reveal a nonmonotonic doping dependence, similar to previous observations for Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$. Magnetotransport measurements of the parent compound reveal a nonlinear Hall coefficient and a large linear term in the transverse magnetoresistance. Both effects are rapidly suppressed with chemical substitution over a similar compositional range as the onset of the large in-plane resistivity anisotropy. This suggests that the relatively small in-plane anisotropy of the parent compound in the spin-density wave state is due to the presence of an isotropic, high mobility pocket of the reconstructed Fermi surface. Progressive suppression of the contribution to the conductivity arising from this isotropic pocket with chemical substitution eventually reveals the underlying in-plane anisotropy associated with the remaining Fermi surface pockets.

Figure 1

(a) Image of the surface of an unstressed single crystal of BaFe${}_2$As${}_2$ at a temperature below 10 K, obtained using polarized-light microscopy, as described in the main text. Stripes of light and dark contrast are associated with different twin orientations. Arrows indicate the orientation of crystal $a$ and $b$ axes. (b) Image of an unstressed crystal of Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$ with $x=0.014$, also revealing horizontal stripes corresponding to the two twin orientations, but with a significantly reduced contrast. The jagged feature running from top to bottom of the image is due to surface morphology. To better reveal the stripes, the intensity was integrated in the horizontal direction and plotted as a function of vertical position, $y$ (right-hand axis). (c) Same region of the same crystal as shown in panel (b), but with uniaxial stress applied in the direction indicated, revealing the detwinning effect of the uniaxial stress. Note the absence of horizontal stripes in both the photograph and also the integrated intensity plot. (d) In-plane resistivity anisotropy expressed as ${\rho }_b/{\rho }_a$ for three different crystals of Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$ with $x\sim 0.017$, illustrating that the measurements are reproducible.

Figure 2

Temperature dependence of the in-plane resistivity ${\rho }_a$ (green curves) and ${\rho }_b$ (red curves) of stressed crystals of (a) Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$ and (b) Ba(Fe${}_{1-x}$Cu${}_x$)${}_2$As${}_2$. Data have been normalized by the value at 300 K. Values of $x$ are labeled in each panel. Vertical lines mark $T_s$(dot-dashed line) and $T_N$(dashed line) determined from $d\rho \left(T\right)/dT$ for unstressed conditions.

Figure 3

In-plane resistivity anisotropy ${\rho }_b/{\rho }_a$ as a function of temperature and doping for (a) Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, (b) Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$, and (c) Ba(Fe${}_{1-x}$Cu${}_x$)${}_2$As${}_2$. The color scale has been obtained by a linear interpolation between adjacent data points. The same scale has been used for all three panels. Black circles, squares, and triangles indicate $T_s$, $T_N$, and $T_c$, respectively, determined for unstressed conditions. $T_c$ for Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$ was defined by the midpoint of the superconducting transitions, while it represents the onset temperature of the transition for Ba(Fe${}_{1-x}$Cu${}_x$)${}_2$As${}_2$.

Figure 4

Field dependence of the transverse resistivity ${\rho }_{xy}$ at a temperature $T=25$ $\text{K}$ with $B\parallel c$ for (a) Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, (b) Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$, and (c) Ba(Fe${}_{1-x}$Cu${}_x$)${}_2$As${}_2$. Compositions are labeled in the legends.

Figure 5

Left axes: composition dependence of ${\rho }_{xy}/B$ at 25 K for (a) Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, (b) Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$, and (C) Ba(Fe${}_{1-x}$Cu${}_x$)${}_2$As${}_2$. Values of ${\rho }_{xy}/B$ were evaluated at 0, 2, 5, 9, and 14 T, as described in the main text. Right axes (black data points): composition dependence of ${\rho }_b/{\rho }_a$ at 25 K.

Figure 6

Transverse magnetoresistance (MR) ($\Delta \rho /\rho$) of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ for (a) $x$ $=$ 0 and (b) 3.5% at $T=25\text{K}$. The $\text{MR}$ has been measured on detwinned samples with current along $a$/$b$ axis (green/red curves), and also on twinned sample (black curve). (c),(d) The $\text{MR}$ of twinned samples of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$, respectively, at 25 K. *Data for $x$ $=$ 0 have been scaled down by a factor of 2 for clarity.

Figure 7

(a) Field derivative of $\text{MR}$ of twinned samples of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and (b) Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$. *Data for $x$ $=$ 0 have been scaled down by a factor of 2 for clarity. (c) Field derivative of $\text{MR}$ ($d\mathrm{MR}/dB$) measured on a twinned sample of the parent compound at $T=25\text{K}$. A critical field scale $B^{*}$ clearly divides the $\text{MR}$ behavior into two regimes: below $B^{*}$ the $\text{MR}$ shows a weak-field quadratic behavior and above $B^{*}$ $\text{MR}$ shows a high-field linear behavior. (d) Doping evolution of the field scale $B^{*}$ (blue circles) and the high-field $\mathrm{MR}$ linear coefficient $A_1$ (red squares), for Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$ (solid and open symbols, respectively).

Figure 8

The doping evolution of the effective $\text{MR}$ mobility ${\mu }_{\mathrm{MR}}$ and effective $\text{MR}$ carrier density $n_{\mathrm{MR}}$ of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ and Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$ extracted from weak-field $\text{MR}$, as described in the main text.

Figure 9

Doping evolution of the in-plane resistivity of the twinned crystals at $T=25\text{K}$ normalized by its room-temperature value and the in-plane resistivity anisotropy ratio ${\rho }_b/{\rho }_a$ of detwinned crystal at $T=25\text{K}$. Data are plotted for (a) Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, (b) Ba(Fe${}_{1-x}$Ni${}_x$)${}_2$As${}_2$, and (c) Ba(Fe${}_{1-x}$Cu${}_x$)${}_2$As${}_2$.