Polarized Light Microscopy Study on the Reentrant Phase Transition in a (Ba_{1 – x}K_x)Fe₂As₂ Single Crystal with x = 0.24

Abstract

A sequence of structural/magnetic transitions on cooling is reported in the literature for hole-doped iron-based superconductor (Ba_{1 − x}K_x)Fe₂As₂ with x = 0.24. By using polarized light microscopy, we directly observe the formation of orthorhombic domains in (Ba_{1 − x}K_x)Fe₂As₂ (x = 0.24) single crystal below a temperature of simultaneous structural/magnetic transition T_N ~ 80 K. The structural domains vanish below ~30 K, but reappear below T = 15 K. Our results are consistent with reentrance transformation sequence from high-temperature tetragonal (HTT) to low temperature orthorhombic (LTO1) structure at T_N ~ 80 K, LTO1 to low temperature tetragonal (LTT) structure at T_c ~ 25 K, and LTT to low temperature orthorhombic (LTO2) structure at T ~ 15 K.

1. Introduction

Iron-based superconductors show rich composition and pressure dependences of phase diagrams [1,2,3]. Similar to high T_c cuprates—heavy fermion and organic superconductors [4]—the dome of superconductivity emerges on suppression of magnetic order, with maximum T_c in the vicinity of a putative quantum critical point where magnetism vanishes. Contrary to the cuprates—in which magnetic order is of Neel type [5]—the parent compounds of iron-based compounds LnOFeAs (Ln = rare earth metals) and AeFe₂As₂ (Ae = alkaline earth metals) show a magnetic transition into stripy antiferromagnetic phase [1], preceded or concomitant with a phase transition from high-temperature tetragonal (HTT, referred to C₄ phase) to low-temperature orthorhombic (LTO, referred to C₂ phase) structure. Even more complicated phase diagrams are reported for hole-doped (Ba_{1 − x}K_x)Fe₂As₂, both under pressure [6,7] and at ambient pressure [8]. Similar anomaly in a much broader composition range is observed in (Ba_{1 − x}Na_x)Fe₂As₂ [9,10] and (Sr_{1 − x}Na_x)Fe₂As₂ [11]. The anomaly was linked to a phase reentrant behavior from low-temperature orthorhombic (LTO C₂ phase) to low-temperature tetragonal (LTT C₄ phase) structure [8,9,10,11].

In (Ba_{1 − x}K_x)Fe₂As₂, the anomaly was overlooked in early studies on polycrystalline material [12] and in single crystals [13,14], since it is found only in a very narrow doping range (0.24 < x < 0.27) in the phase diagrams, on the verge of magnetism suppression. Spanning Δx ~ 0.14 in composition, the LTT C₄ phase in (Sr_{1 − x}Na_x)Fe₂As₂ is found to extend over a larger range of compositions, and to exhibit a significantly higher transition temperature, T_re ~ 65 K, than in either of the other systems in which it has been observed [11]. Interestingly, the magnetic moments in the high temperature C₂ phase are aligned in the ab plane, but they reorient on cooling below T_re, and point along the c direction in (Ba_{1 − x}Na_x)Fe₂As₂ with x = 0.35 [15].

In previous studies, the tetragonal-to-orthorhombic reentrant transition was revealed by neutron and X-ray diffraction measurements [9,11] and high-resolution thermal-expansion and specific-heat measurements [8,10]. It should be pointed out that the orthorhombic distortion leads to the formation of structural domains in the LTO state, revealed and quantified by using polarized light microscopy [16,17,18,19,20]. Here, we use polarized light microscopy to study the temperature evolution of orthorhombic domain patterns in a single crystal of (Ba_{1 − x}K_x)Fe₂As₂ (x = 0.24). The observed appearance, disappearance, and reappearance of domain patterns on cooling are consistent with previous reports of the transformation sequence.

2. Results and Discussion

Although large single crystals are easily obtained by self-flux method, we find that the composition of the crystals varies significantly over the boule, as reflected in the measured characteristic transition temperatures. Superconducting transition temperatures T_cs of cleaved small plates span nearly 8 K from the top to the bottom of a large bulk crystal. Furthermore, some of cleaved crystals show a broad transition, due to the distribution of x. For our further study, we selected only samples showing sharp superconducting transitions in magnetization measurements, as illustrated in Figure 1a. Figure 1b shows the temperature dependence of resistivity of (Ba_{1 − x}K_x)Fe₂As₂ (x = 0.24). The superconducting transition temperatures as determined by two measurements match quite well. The temperature-dependent resistivity derivative—$\mathrm{d}\mathsf{\rho }/\mathrm{d}T$ vs. T (inset in Figure 1b)—shows a clear dip at T_N = 80.8 K, which signals the simultaneous orthorhombic/antiferromagnetic transition. These values of T_c(x = 0.24) = 26 K and T_N(x = 0.24) = 80.8 K match very well with literature values T_c(x = 0.24) = 26 K and T_N(x = 0.24) = 79 K [21], showing correct x determination.

Figure 2 shows the temperature dependence of polarized light images of the cleaved surface of (Ba_{1 − x}K_x)Fe₂As₂ (x = 0.24) single crystal, used in magnetization measurements (Figure 1a). The cleavage plane is a tetragonal (001) plane. The image of the sample at 80 K reveals a regular pattern of domain boundaries running in two orthogonal directions (close to horizontal and vertical directions) as shown by the dashed lines. These lines show temperature evolution, and should be distinguished from temperature-independent features observed in the bottom left corners of the image patterns, representing terraces on the sample surface. The domain wall pattern represents boundaries of 45° domains [16] and runs parallel to tetragonal (100) and (010) directions. The temperature of the domain pattern formation is consistent with the temperature of the simultaneous structural/magnetic transition, as determined from a position of a dip in the temperature-dependent resistivity derivative (inset in Figure 1b), positioned at T_N = 80.8 K. The domain formation below T_N is observed in parent [16] and both electron [17] and hole [18] doped AeFe₂As₂. This is due to random orientation of the directions of orthorhombic $a_O$ and $b_O$ axes of the orthorhombic phase, rotated by 45° from the $a_{\mathrm{T}}$ axis in the tetragonal lattice symmetry. There is a slight volume change in the unit cell before and after the structural phase transition at T_N [22]. The orthorhombic distortion defined as $\mathsf{\delta }=\left(a_{\mathrm{O}}-b_{\mathrm{O}}\right)/\left(a_{\mathrm{O}}+b_{\mathrm{O}}\right)$ increases from zero to $2\times {10}^{-3}$ on cooling [22]. The tensile stresses accompanying the transformation are partially released by the formation of domain twin boundaries (lines in Figure 2), leading to the formation of 45°-type structural domains, with walls running parallel to the [001] direction of the lattice [16].

The domain pattern in (Ba_{1 − x}K_x)Fe₂As₂ (x = 0.24) remains stable down to 30 K. With further cooling down to T = 25 K, the domains vanish, which is contrary to observations in parent and lower-doped (Ba_{1 − x}K_x)Fe₂As₂ samples [16,18]. Interestingly, the domain pattern emerges again at T = 15 K. This sequence of transformations is consistent with reentrant transformation into tetragonal phase [8].

In Figure 3, we compare the observations of our study with the doping dependence of the phase diagram of (Ba_{1 − x}K_x)Fe₂As₂ as determined from thermal expansion and heat capacity measurements [8]. Due to possible error in composition determination with different techniques, it is more appropriate to compare sample transition temperatures, rather than composition x. The T_N of our sample (80.8 K) is somewhat higher than that in samples at the center of the anomaly [8], suggesting that our sample is located to the left (lower x) in the doping phase diagram. The domain disappearance/reappearance features in the polarized optical images (Figure 2) are found at temperatures which are in reasonable agreement with T_re1 and T_re2 features.

In the iron-based superconductors, the iron spins order antiferromagnetically in a stripe pattern below T_N with a wavevector of either Q1 = (π,0) or Q2 = (0,π). The formation of magnetic stripe structure is accompanied by the C₄ (HTT phase)-C₂ (LTO phase) phase via magnetoelastic coupling at T_N [1,2]. In the hole-doped (Sr_{1 − x}Na_x)Fe₂As₂, Mössbauer data revealed that the reentrant C₄ phase is characteristic of a double-Q magnetic structure below T_re, where magnetic structure comprises the superposition of two orthogonal stripes (i.e., Q1 and Q2) [23]. It should be pointed out that the C₂ phase could be restored in (Ba_{1 − x}Ka_x)Fe₂As₂ below T_re2 (see Figure 3). However, the reentrant C₄ phase is robust in (Ba_{1 − x}Na_x)Fe₂As₂ [9,10] and (Sr_{1 − x}Na_x)Fe₂As₂ [11] when cooled down to low temperatures. Here, the disorder and strain caused by the large mismatch of ionic radius of dopants may stabilize double-Q order (i.e., C₄ phase) [24]. The fact that the interplay between magnetic and lattice structures leads to reentrant phase transition is manifested in other compounds. For example, BaFe₂(PO4)₂ undergoes a rare reentrant structural transition owing to the competition between uniaxial magnetism and the Jahn–Teller distortion [25,26].

3. Materials and Methods

Single crystals of (Ba_{1 − x}K_x)Fe₂As₂ were grown by using the self-flux method. Details of the synthesis and characterization can be found elsewhere [27,28]. Briefly, the starting materials of Ba and K lump, and Fe and As powder were weighed and loaded into an alumina crucible in a glovebox. The alumina crucible was sealed in a tantalum tube by arc welding. The tantalum tube was sealed in a quartz ampoule to prevent the tantalum tube from oxidizing in the furnace. We developed an inverted-temperature-gradient method [28] to grow large and high-quality single crystals of (Ba_{1 − x}K_x)Fe₂As₂. The crystallization processes from the top of a liquid melt helps to expel impurity phases during crystal growth, as shown in Figure 4.

The composition of the crystals was determined using wavelength dispersion X-ray spectroscopy (WDS) (JEOL 8200 Electron Microprobe, JEOL, Peabody, MA, USA) of electron microprobe analysis. The polarized optical images were taken in a Leica DMLM microscope (Leica Microsystems Wetzlar GmbH, Wetzlar, Germany) with polarizer and analyzer. A helium flow cryostat was positioned on the x–y–z stage of the microscope and allowed direct imaging from room temperature down to 5 K.

Magnetization was measured by using Physical Property Measurement System (PPMS) equipped with Vibrating Sample Magnetometer (VSM) (Quantum Design, San Diego, CA, USA), and in-plane resistivity ${\varrho }_{ab}$ was measured using the AC transport option of PPMS.

White-light optical images were taken in a Leica Digital & Light Microscope (DMLM) polarization microscope with polarizer and analyzer in almost crossed position. They were taken in reflection mode on cleaved sample (001) plane. A helium flow cryostat was positioned on the x–y stage of the microscope and allowed direct imaging from room temperature down to 5 K. High resolution static images video were recorded. The contrast of the domain images is higher for larger difference in the rotation of the polarization plane between neighboring domains, proportional to the degree of orthorhombic distortion, $\mathsf{\delta }=\left(a_{\mathrm{O}}-b_{\mathrm{O}}\right)/\left(a_{\mathrm{O}}+b_{\mathrm{O}}\right)$. Quantitative analysis of the images enables in determination of the orthorhombic order parameter [19,20]. This was not possible due to low contrast of the images.

4. Conclusions

Large single crystals of (Ba_{1 − x}K_x)Fe₂As₂ were grown by self-flux method. Magnetization measurements were used to screen large pieces of (Ba_{1 − x}K_x)Fe₂As₂ single crystals, with homogeneous samples selected using superconducting transition width as a criterion. Samples with T_c of 25 K were used to study tetragonal-orthorhombic-tetragonal-orthorhombic transformation sequence using resistivity and polarized optical imaging. We found domain formation at T_N = 80 K, as common for underdoped iron-based superconductors. Contrary to all previous cases, though, the pattern shows transformation with cooling. Our observations are in agreement with reentrant orthorhombic transformation in the material.