Polarized Light Microscopy Study on the Reentrant Phase Transition in a ( Ba 1 − x K x ) Fe 2 As 2 Single Crystal with x = 0 . 24

A sequence of structural/magnetic transitions on cooling is reported in the literature for hole-doped iron-based superconductor (Ba1 − xKx)Fe2As2 with x = 0.24. By using polarized light microscopy, we directly observe the formation of orthorhombic domains in (Ba1 − xKx)Fe2As2 (x = 0.24) single crystal below a temperature of simultaneous structural/magnetic transition TN ~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 TN ~80 K, LTO1 to low temperature tetragonal (LTT) structure at Tc ~25 K, and LTT to low temperature orthorhombic (LTO2) structure at T ~15 K.


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 AeFe 2 As 2 (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 C 4 phase) to low-temperature orthorhombic (LTO, referred to C 2 phase) structure.Even more complicated phase diagrams are reported for hole-doped (Ba 1 − x K x )Fe 2 As 2 , 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 )Fe 2 As 2 [9,10] and (Sr 1 − x Na x )Fe 2 As 2 [11].The anomaly was linked to a phase reentrant behavior from low-temperature orthorhombic (LTO C 2 phase) to low-temperature tetragonal (LTT C 4 phase) structure [8][9][10][11].
In (Ba 1 − x K x )Fe 2 As 2 , 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 ∆x ~0.14 in composition, the LTT C 4 phase in (Sr 1 − x Na x )Fe 2 As 2 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 C 2 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 )Fe 2 As 2 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 )Fe 2 As 2 (x = 0.24).The observed appearance, disappearance, and reappearance of domain patterns on cooling are consistent with previous reports of the transformation sequence.

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 c s 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 )Fe 2 As 2 (x = 0.24).The superconducting transition temperatures as determined by two measurements match quite well.The temperature-dependent resistivity derivative-dρ/dT vs. T (inset in Figure 1b  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 (Ba1 − xKx)Fe2As2 (x = 0.24).The observed appearance, disappearance, and reappearance of domain patterns on cooling are consistent with previous reports of the transformation sequence.

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 Tcs 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 (Ba1 − xKx)Fe2As2 (x = 0.24).The superconducting transition temperatures as determined by two measurements match quite well.The temperature-dependent resistivity derivative-dρ/d vs. T (inset in Figure 1b   Figure 2 shows the temperature dependence of polarized light images of the cleaved surface of (Ba 1 − x K x )Fe 2 As 2 (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 AeFe 2 As 2 .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 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 δ = (a O − b O ) / (a O + b O ) increases from zero to 2 × 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 Figure 2 shows the temperature dependence of polarized light images of the cleaved surface of (Ba1 − xKx)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 TN = 80.8 K.The domain formation below TN 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 and axes of the orthorhombic phase, rotated by 45° from the axis in the tetragonal lattice symmetry.There is a slight volume change in the unit cell before and after the structural phase transition at TN [22].The orthorhombic distortion defined as δ = ( − )/( + ) increases from zero to 2 10 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 )Fe 2 As 2 (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 )Fe 2 As 2 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 )Fe 2 As 2 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 T re1 and T re2 features.The domain pattern in (Ba1 − xKx)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 (Ba1 − xKx)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 (Ba1 − xKx)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 TN 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 Tre1 and Tre2 features.In the iron-based superconductors, the iron spins order antiferromagnetically in a stripe pattern below TN 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 TN [1,2].In the hole-doped (Sr1 − xNax)Fe2As2, Mössbauer data revealed that the reentrant C4 phase is characteristic of a double-Q magnetic structure below Tre, 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 (Ba1 − xKax)Fe2As2 below Tre2 (see Figure 3).However, the reentrant C4 phase is robust in (Ba1 − xNax)Fe2As2 [9,10] and (Sr1 − xNax)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].

Materials and Methods
Single crystals of (Ba1 − xKx)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 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 C 4 (HTT phase)-C 2 (LTO phase) phase via magnetoelastic coupling at T N [1,2].In the hole-doped (Sr 1 − x Na x )Fe 2 As 2 , Mössbauer data revealed that the reentrant C 4 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 C 2 phase could be restored in (Ba 1 − x Ka x )Fe 2 As 2 below T re2 (see Figure 3).However, the reentrant C 4 phase is robust in (Ba 1 − x Na x )Fe 2 As 2 [9,10] and (Sr 1 − x Na x )Fe 2 As 2 [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., C 4 phase) [24].The fact that the interplay between magnetic and lattice structures leads to reentrant phase transition is manifested in other compounds.For example, BaFe 2 (PO4) 2 undergoes a rare reentrant structural transition owing to the competition between uniaxial magnetism and the Jahn-Teller distortion [25,26].

Materials and Methods
Single crystals of (Ba 1 − x K x )Fe 2 As 2 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 )Fe 2 As 2 .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 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, δ = ( − )/( + ).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.

Conclusions
Large single crystals of (Ba1 − xKx)Fe2As2 were grown by self-flux method.Magnetization measurements were used to screen large pieces of (Ba1 − xKx)Fe2As2 single crystals, with homogeneous samples selected using superconducting transition width as a criterion.Samples with Tc of 25 K were used to study tetragonal-orthorhombic-tetragonal-orthorhombic transformation sequence using resistivity and polarized optical imaging.We found domain formation at TN = 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.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 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, δ = (a O − b O ) / (a O + b O ).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.

Conclusions
Large single crystals of (Ba 1 − x K x )Fe 2 As 2 were grown by self-flux method.Magnetization measurements were used to screen large pieces of (Ba 1 − x K x )Fe 2 As 2 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.
)-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 1 .
Figure 1.(a) Temperature dependence of magnetization for the (Ba1 − xKx)Fe2As2 single crystal (x = 0.24) used in resistivity and polarized optics studies.The sample was cooled in zero magnetic field from above Tc to 3 K (ZFC) and with an applied field of 10 Oe (FC).The data were collected during the warming of the sample from 3 K to 35 K. (b) Normalized temperature-dependent resistivity of a sample, cut from part of magnetization crystal after polarized optics study.The derivate of the normalized resistivity (inset in panel b) shows a clear dip as the sample undergoes structure and magnetic transition at TN = 80.8 K.

Figure 1 .
Figure 1.(a) Temperature dependence of magnetization for the (Ba 1 − x K x )Fe 2 As 2 single crystal (x = 0.24) used in resistivity and polarized optics studies.The sample was cooled in zero magnetic field from above T c to 3 K (ZFC) and with an applied field of 10 Oe (FC).The data were collected during the warming of the sample from 3 K to 35 K; (b) Normalized temperature-dependent resistivity of a sample, cut from part of magnetization crystal after polarized optics study.The derivate of the normalized resistivity (inset in panel b) shows a clear dip as the sample undergoes structure and magnetic transition at T N = 80.8 K.

Figure 2 .
Figure 2. Temperature evolution of polarized optical images of the (Ba1 − xKx)Fe2As2 (x = 0.24) single crystal.Scale bar corresponds to 100 μm.The sequence shows the appearance of orthorhombic/magnetic domains at 80 K, highlighted with dashed lines to guide the eyes (horizontal lines in the center of the image panels).The domains are clearly visible on cooling down to 30 K, but disappear at 25 K.They reappear at 15 K.The scratch-like lines running at approximately 45° inclination in the left-bottom corner of the image panels correspond to growth terraces and faults.

Figure 2 .
Figure 2. Temperature evolution of polarized optical images of the (Ba 1 − x K x )Fe 2 As 2 (x = 0.24) single crystal.Scale bar corresponds to 100 µm.The sequence shows the appearance of orthorhombic/magnetic domains at 80 K, highlighted with dashed lines to guide the eyes (horizontal lines in the center of the image panels).The domains are clearly visible on cooling down to 30 K, but disappear at 25 K.They reappear at 15 K.The scratch-like lines running at approximately 45 • inclination in the left-bottom corner of the image panels correspond to growth terraces and faults.

Figure 3 .
Figure 3. Composition-temperature phase diagram of reentrant C2-C4-C2 transformation in (Ba1 − xKx)Fe2As2 (after Refs.[7,8]).The data of this study are shown with stars and highlighted by arrows.They are in reasonable agreement with the diagram, within possible error bars of composition determination.

Figure 3 .
Figure 3. Composition-temperature phase diagram of reentrant C 2 -C 4 -C 2 transformation in (Ba 1 − x K x )Fe 2 As 2 (after Refs.[7,8]).The data of this study are shown with stars and highlighted by arrows.They are in reasonable agreement with the diagram, within possible error bars of composition determination.
Ba1 − xKx)Fe2As2.The crystallization processes from the top of a liquid melt helps to expel impurity phases crystal growth, as shown in Figure4.

Figure 4 .
Figure 4. (a) Photos of (Ba1 − xKx)Fe2As2 single crystals grown by a self-flux method.(b) The disk-like crystals (~1 mm in thickness and 10 mm in diameter) are formed in the top of the ingot.

Figure 4 .
Figure 4. (a) Photos of (Ba 1 − x K x )Fe 2 As 2 single crystals grown by a self-flux method; (b) The disk-like crystals (~1 mm in thickness and 10 mm in diameter) are formed in the top of the ingot.