Hole and electron contributions to the transport properties of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ru}}_x\right)}_2{\text{As}}_2$ single crystals

We report a systematic study of structural and transport properties in single crystals of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ru}}_x\right)}_2{\text{As}}_2$ for $x$ ranging from 0 to 0.5. The isovalent substitution of Fe by Ru leads to an increase in the $a$ parameter and a decrease in the $c$ parameter, resulting in a strong increase in the As-Fe-As angle and a decrease in the As height above the Fe planes. On Ru substitution, the magnetic order is progressively suppressed and superconductivity emerges for $x\ge 0.15$ with an optimal $T_c\simeq 20\text{K}$ at $x=0.35$ and coexistence of magnetism and superconductivity between these two Ru contents. Moreover, the Hall coefficient $R_H$, which is always negative and decreases with temperature in ${\text{BaFe}}_2{\text{As}}_2$, is found to increase here with decreasing $T$ and even changes sign for $x\ge 0.20$. For $x_{\text{Ru}}=0.35$, photoemission studies have shown that the number of holes and electrons are similar with $n_e=n_h\simeq 0.11$ carriers/Fe, that is twice larger than found in ${\text{BaFe}}_2{\text{As}}_2$ [V. Brouet, F. Rullier-Albenque, M. Marsi, B. Mansart, J. Faure, L. Perfetti, A. Taleb-Ibrahimi, P. Le Fèvre, F. Bertran, A. Forget, and D. Colson, arXiv:1002.4952 (unpublished)]. Using this estimate, we find that the transport properties of $\text{Ba}{\left({\text{Fe}}_{0.65}{\text{Ru}}_{0.35}\right)}_2{\text{As}}_2$ can be accounted for by the conventional multiband description for a compensated semimetal. In particular, our results show that the mobility of holes is strongly enhanced on Ru addition and overcomes that of electrons at low temperature when $x_{\text{Ru}}\ge 0.15$.

Figure 1

(Color online) (a) Variation in the lattice parameters $a$ and $c$, their ratio $a/c$ and the unit-cell volume $V$, normalized to their values for the undoped compound, as a function of the Ru content $x$ (determined by x-ray diffraction). (b) The same for different crystallographic parameters: the two As-Fe-As tetrahedral angles, ${\alpha }_1$ and ${\alpha }_2$, the $c$-axis coordinate of As, $z_{\text{As}}$, the Fe-As interatomic distance $r\left(\text{Fe-As}\right)$ and the height of As above Fe layers, $d_{\text{Fe-As}}$.

Figure 2

(Color online) (a) Temperature dependence of the in-plane resistivity $\rho \left(T\right)$ of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ru}}_x\right)}_2{\text{As}}_2$ single crystals. The arrows point the strong anomalies in the $\rho \left(T\right)$ curves that signal the occurrence of the magnetostructural transition. They are determined more precisely in (b) which shows $d\rho /dT$ versus $T$. For the $x=0.26$ sample, the arrow corresponds to the maximum of the Hall coefficient as explained in the text. (c) Picture of a typical sample mounted in the van der Pauw configuration.

Figure 3

(Color online) Phase diagram of the $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ru}}_x\right)}_2{\text{As}}_2$ system showing the evolution of the structural-magnetic transition $T_{\text{S-M}}$ and critical temperatures $T_c$ versus Ru content $x_{\text{Ru}}$. Values of $T_c$ are taken at the midpoint of superconducting transitions. The sample with $x=0.5$ is no longer superconducting as shown by superconducting quantum interference device magnetometer measurements.

Figure 4

(Color online) $T$ dependence of the Hall coefficient $R_H\left(T\right)$ for various compositions. The temperatures at which $R_H$ starts decreasing due to the apparition of the $M\text{−}S$ transition correspond exactly to those where anomalies are seen in the resistivity curves (arrows). The inset shows that the Hall resistivity ${\rho }_{xy}$ of the $x=0.35$ sample is linear in magnetic field up to 14 T whatever $T$. A sign change in the slope occurs between 93 and 120 K.

Figure 5

(Color online) $T$ dependence of the Hall coefficient $R_H\left(T\right)$ in the vicinity of $R_H=0$ for (a) $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Ru}}_x\right)}_2{\text{As}}_2$ and (b) $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$, from Ref. 10.

Figure 6

(Color online) (a) Respective resistivities of electrons and holes for $\text{Ba}{\left({\text{Fe}}_{0.65}{\text{Ru}}_{0.35}\right)}_2{\text{As}}_2$ obtained from the data of resistivity and Hall coefficient using Eqs. (2, 3) with $n_e=n_h=0.11$, as given by ARPES measurements on similar samples (Ref. 19). The raw data for resistivity and Hall coefficient are recalled in the inset. (b) The resistivity curves for $\text{Ba}{\left({\text{Fe}}_{0.93}{\text{Co}}_{0.07}\right)}_2{\text{As}}_2$ (Ref. 10) and ${\text{Ba}}_{0.65}{\text{K}}_{0.35}{\text{Fe}}_2{\text{As}}_2$ (Ref. 14) are given for comparison.

Figure 7

(Color online) Respective resistivities of electrons and holes for ${\text{BaFe}}_2{\text{As}}_2$ in the paramagnetic phase $\left(T>T_{\text{S-M}}\right)$ obtained from resistivity and Hall coefficient data using Eqs. (2, 3) using different estimates for the carrier number. The full symbols are for $n=n_e=n_h=0.06$ carriers/Fe as determined by ARPES measurements (Ref. 36) while the full and dotted lines correspond to the extremal values of $n$ due to the $\pm 0.02$ error bar. The empty symbols are for the LDA estimate $n=n_e=n_h=0.15$ carriers/Fe.

Figure 8

(Color online) Same decompositions as that performed in Fig. 6a for different Ru contents, assuming a linear variation in the number of carriers with $x$: $n=0.06+0.14x$ carriers/Fe. Full and dotted lines are for ${\rho }_e$ and ${\rho }_h$, respectively. For the sake of clarity, the data corresponding to $x=0.35$ [Fig. 6a] are not reported in this plot.