Uniaxial-strain mechanical detwinning of ${\text{CaFe}}_2{\text{As}}_2$ and ${\text{BaFe}}_2{\text{As}}_2$ crystals: Optical and transport study

The parent compounds of iron-arsenide superconductors, $A{\text{Fe}}_2{\text{As}}_2$ $\left(A=\text{Ca},\text{Sr},\text{Ba}\right)$, undergo a tetragonal to orthorhombic structural transition at a temperature $T_{\text{TO}}$ in the range 135–205 K depending on the alkaline-earth element. Below $T_{\text{TO}}$ the free standing crystals split into equally populated structural domains, which mask intrinsic, in-plane, anisotropic properties of the materials. Here we demonstrate a way of mechanically detwinning ${\text{CaFe}}_2{\text{As}}_2$ and ${\text{BaFe}}_2{\text{As}}_2$. The detwinning is nearly complete, as demonstrated by polarized light imaging and synchrotron x-ray measurements, and reversible, with twin pattern restored after strain release. Electrical resistivity measurements in the twinned and detwinned states show that resistivity, $\rho$, decreases along the orthorhombic $a_o$ axis but increases along the orthorhombic $b_o$ axis in both compounds. Immediately below $T_{\text{TO}}$ the ratio ${\rho }_{bo}/{\rho }_{ao}=1.2$ and 1.5 for Ca and Ba compounds, respectively. Contrary to ${\text{CaFe}}_2{\text{As}}_2$, ${\text{BaFe}}_2{\text{As}}_2$ reveals an anisotropy in the nominally tetragonal phase, suggesting that either fluctuations play a larger role above $T_{\text{TO}}$ in ${\text{BaFe}}_2{\text{As}}_2$ than in ${\text{CaFe}}_2{\text{As}}_2$ or that there is a higher temperature crossover or phase transition.

Figure 1

(Color online) [(a) and (b)] Schematics of domain formation during tetra-ortho transition. Orthorhombic phase is realized through displacement of atoms along the diagonal of the tetragonal lattice with doubling the unit-cell volume and $45°$ rotation of the crystallographic axes (Ref. 25). The domains are distinguished by the direction of the distortion, $a_o$, shown for four domains with the arrows. (c) A single-crystal sample of ${\text{CaFe}}_2{\text{As}}_2$, mounted on a horseshoe. [(d)–(h)] Polarized light image of the crystal without external strain (d), strained to a progressively higher values [(e)–(g)], and after strain release (h).

Figure 2

(Color online) A polarized light image (5 K, $T⪡T_{\text{TO}}$) of a single-crystal strip of ${\text{CaFe}}_2{\text{As}}_2$ cut along the tetragonal [110] direction before contacts were made (top). The sample was mounted in a usual four-probe contact configuration with potential contacts located on the sample surface opposite to the surface in the image. Strain was applied to the sample at room temperature through current contacts and the image was taken at 5 K on a clear surface under the potential contacts. A big single-domain area can be seen between potential contacts, however, large heavily twinned areas are found above the contacts (circles in the image), revealing notable local reduction in strain by surface tension at the contact points.

Figure 3

(Color online) (a) A polarized light image (5 K, $T⪡T_{\text{TO}}$) of a single crystalline strip sample of ${\text{CaFe}}_2{\text{As}}_2$ with soldered contacts before being mounted on a horseshoe. On application of strain in a horizontal direction through the potential contacts, a strain-free area at the left end of the sample remains heavily twinned (b) while the central area turns into a nearly single-domain state, with small twinned areas at the bottom of the image (c). After three thermal cycles from the 300 to 5 K range, strain in the sample is partially released (d), however, large single-domain areas remain, demonstrating the reproducibility of the strain-induced detwinning.

Figure 4

(Color online) Left panel. Temperature-dependent electrical resistance measured on a sample A of ${\text{CaFe}}_2{\text{As}}_2$ in twinned ($R_t$, blue curve) and detwinned ($R_{ao}$, red curve) states. The third curve is obtained as hypothetical $R_{bo}=2R_t-R_{ao}$, impossible to measure in the same contact arrangement, see text for details. Inset shows zoom of the transition region for samples A and B, revealing diminishing amplitude of the resistance jump in ${\rho }_{ao}\left(T\right)$ with identical transition sharpness and position. Right panel shows resistance of sample C in which resistivity was measured along $b$ axis in transverse to strain contact configuration (see Fig. 5) in stress-free and stressed (partially detwinned) states. Inset shows zoom of the transition area. This data directly show an increase in the resistance jump in ${\rho }_{bo}$.

Figure 5

(Color online) Top panel. Image of the sample for resistivity measurements in transverse to the strain (horizontal) direction. The current contacts are made along the whole length of the top and bottom edges of the sample, right and left sample edges are covered with epoxy glue to provide homogeneous deformation of the sample and wires. Straining force is applied on horseshoe, similar to Fig. 1c. Potential contacts are made small to minimize the effect on the strain distribution. Middle and bottom panels show area close to potential contacts in stress-free and stressed states.

Figure 6

(Color online) Left panel. Temperature-dependent electrical resistance measured on a sample D of ${\text{BaFe}}_2{\text{As}}_2$ in twinned ($R_t$, black curve) and detwinned $R_{ao}$, red curve) states. The third curve is obtained as hypothetical $R_{bo}=2R_t-R_{ao}$, impossible to measure in the same contact arrangement. Inset shows zoom of the transition region for samples D and E. Right panel shows resistance for sample F in which resistivity was measured along $b$ axis in transverse to strain contact configuration in stress-free (blue line) and stressed (partially detwinned, yellow line) states. Inset shows zoom of the transition area in normalized resistance plot in comparison with resistance of sample D in the detwinned state.

Figure 7

(Color online) Sections of reciprocal $\left(HK0\right)$ planes around the position of the tetragonal ${\left(220\right)}_T$ reflection recorded from the ${\text{BaFe}}_2{\text{As}}_2$ sample by high-energy x-ray diffraction as described in the text. In the orthorhombic state at $T=25\text{K}$, the ${\left(400\right)}_{O1}$ and ${\left(040\right)}_{O2}$ reflections are related to different domains $O1$ and $O2$, respectively. Analysis of the intensities in pattern recorded at different positions on the sample, below a contact in the upper panels and between the contacts in the lower panels, yield the indicated percent values for the domain $O1$ population bolstered by the applied strain.

Figure 8

(Color online) Spatial distribution of the population of $O1$ domains in strained ${\text{BaFe}}_2{\text{As}}_2$. The population was determined from the relative intensities of the ${\left(400\right)}_{O1}$ and ${\left(040\right)}_{O2}$ peaks, as shown in Fig. 7. The area between the contacts, through which the strain was applied, was probed in 0.2 mm vertical and horizontal steps, determined by the x-ray beam size. The number and color in each pixel correspond to the percent value for the domain $O1$ population. The pixel in the upper right corner corresponds to an area under the contact.

Figure 9

(Color online) Fermi surfaces for Ca122 (left panels) and Ba122 (right panels), obtained in the LDA band-structure calculation (low magnetic moment). One reciprocal-lattice unit cell is shown, with the $\Gamma$ points located in the eight corners. The top panels represent a general view (directions of the axes as shown), the next row represents the view from the top, along the $k_z$ direction ($k_x\text{−}{k}_y$ plane), the third row represents the front view, along the $k_y$ direction ($k_x\text{−}{k}_z$ plane), the last row presents the side view, along the $x$ direction ($k_y\text{−}{k}_z$ plane). The light shaded (cyan) surfaces are electron pockets, the dark (blue) one are the hole pockets.