Anisotropy of the Seebeck and Nernst coefficients in parent compounds of the iron-based superconductors

In-plane longitudinal and transverse thermoelectric phenomena in two parent compounds of iron-based superconductors are studied. Namely, the Seebeck ($S$) and Nernst (ν) coefficients were measured in the temperature range 10–300 K for $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ and $\mathrm{CaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ single crystals that were detwinned in situ. The thermoelectric response shows sizable anisotropy in the spin density wave (SDW) state for both compounds, while some dissimilarities in the vicinity of the SDW transition can be attributed to the different nature of the phase change in $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ and $\mathrm{CaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$. Temperature dependences of $S$ and ν can be described within a two-band model that contains a contribution from highly mobile, probably Dirac, electrons. The Dirac band seems to be rather isotropic, whereas most of the anisotropy in the transport phenomena could be attributed to “regular” holelike charge carriers. We also observe that the off-diagonal element of the Peltier tensor ${\alpha }_{xy}$ is not the same for the $a$ and $b$ orthorhombic axes, which indicates that the widely used Mott formula is not applicable to the SDW state of iron-based superconductors.

Figure 1

The temperature dependences of the normalized resistivity anisotropy when a sample is cooled under pressure which is released at low temperature and afterward another set of data is collected on warming. Inset presents the schematic diagram of the experimental setup for the resistivity measurements. A sample is denoted as the black square with the current/voltage leads attached at the corners. The current flow was alternately introduced in two different configurations ($I_1$ and $I_2$), and then the respective voltages ($U_1$ and $U_2$) were measured. The detwinning force (F) was applied to the opposite sides of the sample.

Figure 2

The temperature dependences of the thermoelectric power in $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ (solid points: sample No. 1; open points: No. 2) and $\mathrm{CaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ along the orthorhombic $a$ and $b$ axes. Red diamonds at $T\approx 300\mathrm{K}$ show values of $S_a$ before they are matched with $S_b$ in the high-temperature limit. Inset presents the schematic diagram of the experimental setup for the thermoelectric measurements that were performed in two runs in which either the ${\mathrm{F}}_1$ or ${\mathrm{F}}_2$ uniaxial pressure was applied. $\nabla T$ denotes the thermal gradient.

Figure 3

The temperature dependences of the normalized thermopower anisotropy in $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ (solid points: sample No. 1; open points: No. 2) and $\mathrm{CaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$.

Figure 4

The temperature dependences of the Nernst coefficient along the orthorhombic $a$ and $b$ axes for $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ (solid points: sample No. 1; open points: No. 2) and $\mathrm{CaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$. Red diamonds at $T\approx 300\mathrm{K}$ show values of ${\nu }_a$ before they are matched with ${\nu }_b$ in the high-temperature limit. Insets show the respective temperature dependences of the off-diagonal Peltier element $-{\alpha }_{yx}$ along the orthorhombic $a$ and $b$ axes. Light-blue and light-red regions around these plots show the 40% error margin.

Figure 5

The temperature dependences of the normalized Nernst effect anisotropy in $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ (solid points: sample No. 1; open points: No. 2) and $\mathrm{CaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$. Inset shows the high-temperature $\mathrm{BaF}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$ data in enlarged scale to highlight an onset of the anisotropy.