Macroscopic phase separation in high-temperature superconductors

Abstract

High-temperature superconductivity is recovered by introducing extra holes to the Cu-O planes, which initially are insulating with antiferromagnetism. In this paper I present data to show the macroscopic electronic phase separation that is caused by either mobile doping or electronic instability in the overdoped region. My results clearly demonstrate that the electronic inhomogeneity is probably a general feature of high-temperature superconductors.

The mechanism of high-temperature superconductors, one of the challenging issues, has stimulated enormous effort in recent years. Connected with it is a widely accepted electronic phase diagram, which contains several important phases depending on the hole doping level: an insulator with three-dimensional antiferromagnetism at a low doping, a superconducting metal with non-Fermi liquid behavior (underdoped), and another superconducting metal with approximately the Fermi liquid behavior (overdoped) (1). In a paper by Kivelson and Emery (2) the dynamics of doped holes have been considered, and a picture named as phase separation has been proposed. This phase separation comprises two types: microscopic and macroscopic phase separations. The so-called microscopic phase separation is induced by the competition between the approaching tendency (attractive force) and the repulsive Coulomb force between doped holes, and thus as a compromise a stripe structure is anticipated (2). The evidence for static stripe has been found in La_(1.6-x)Nd_0.4 Sr_xCuO₄ with a hole doping level of 1/8 at which the superconductivity is strongly suppressed (3). Therefore it remains unclear whether this stripe phase is helpful or harmful to superconductivity. When the dopants in a neighboring layer are moving together with holes in the Cu-O planes, the long-range Coulomb force will be screened out, and the holes can approach together, leading to macroscopic clusters. In this paper I present data to show the evidence of the macroscopic phase separation.

Samples for this study are La-doped Bi₂Sr_2-xLa_xCuO_6+δ (Bi-2201) single crystals grown by the conventional self-flux method using CuO as flux. X-ray diffraction measurements show that only the (00l) peaks are observable and no extra peaks can be observed from the secondary phase even when the diffraction intensity is plotted logarithmically. The actual La content in my single crystals has been determined via a large area energy-dispersive x-ray analysis. For the sake of simplicity, in this paper I mention only the actual composition. The excellent quality of my single crystals has been confirmed by both the x-ray diffraction and the clear electron diffraction patterns based on transmission electron microscopy. The samples have been measured by using a superconducting quantum interference device (Quantum Design MPMS, 5.5 T). Because the results obtained from the two crystals are the same, in this paper I exclusively report the results from one single crystal with x = 0.25 (overdoped).

The temperature dependence of the DC magnetization measured at an external field of 20 Oe is presented in Fig. 1. Below about 16 K the zero field cooled (ZFC) and field cooled (FC) curves start to open, indicating an irreversibility effect induced by the flux pinning. It is difficult to find out any details around the transition temperature from this full-scale plot. An enlarged view of these two curves show, however, two transitions, one at about T_c1 ≈ 27 K, another one at about T_c2 ≈16 K. In the Inset to Fig. 1 an enlarged view of the FC and ZFC curves for 1 kOe is shown. Two transitions can be clearly seen here: one is still at about 27 K, another one already moves to about 8 K. Also for 1 kOe, the ZFC and FC curves open immediately when T_c2 is reached. It is found that for all of the fields (20 Oe to 20 kOe) applied here, the M(T) curves show two transitions. One transition is rather stable against the field, another one shifts very quickly to lower temperatures. For an underdoped sample with only one superconducting transition, the ZFC and FC curves merge at the irreversibility point and do not show a discontinuity, which is in sharp contrast to my observation here. In the Inset to Fig. 1, a sharp step appears at T_c2, showing a bulk superconducting transition.

Figure 1.

Temperature dependence of the diamagnetic moments measured in ZFC and FC processes at a field of 20 Oe. (Inset) An enlarged view for the curves measured in the same processes at a field of 1 kOe. Two transitions marked with T_c1 and T_c2 can be clearly seen here. Between T_c1 and T_c2 the ZFC and FC curves coincide with each other. The irreversibility appears when T_c2 is reached.

To investigate the influence of the external field on the two transitions, I measured the M(T) curves under various magnetic fields (20 Oe to 20 kOe). For each field, the FC and ZFC M(T) curves show two clear transitions, one is rather stable, at about 27 K, another one drops sharply from 16 K for 20 Oe to 4.5 K for 20 kOe. For the sake of simplicity, in Fig. 2 I show only the ZFC M(T) curves for magnetic fields from 20 Oe to 7 kOe, therefore all points above the second transitions are in the reversible region. The two transitions exhibit completely different reactions to the external field and thus may be categorized to different underlying physics. To uncover this difference, I enlarged the reversible magnetization around T_c1. As shown in the Inset to Fig. 2, a crossing point at (T*, M*) on the M(T) curves for nine different magnetic fields can be observed, despite the slight data scattering caused by the weak signal from my small crystal (≈1 mg). The similar common crossing point has been observed in many underdoped or optimally doped samples with only one transition (4–6), and the M(T) curves near that crossing point have been well described by the Ullah and Dorsey fluctuation theory (7) as delivering a rather high slope −dH_c2/dT ≈ 2 T/K. To check whether my data near T_c1 can be described by the critical fluctuation theory, I treat the data by following the scaling law

1

where A and B are independent on temperature and magnetic field, g(x) is a unknown function, α takes 1/2 for two dimensions and 2/3 for three dimensions. For both two and three dimensions I can find nice scaling for the nine M(T) curves with 1T/K ≤ −dH_c2/dT ≤ 2 T/K. The nice scaling shown in the Inset to Fig. 3 gives strong evidence that the transition near T_c1 has the same feature as that observed in some underdoped or optimally doped samples and thus may reflect the intrinsic property of H_c2(T) in high-T_c cuprates. By taking −dH_c2/dT = 1 T/K, as shown in Fig. 3 by the filled triangles, the H_c2(T_c1) curve shows a rather steep slope, which is in sharp contrast to that corresponding to the second transition at T_c2 shown in Fig. 3 by the filled circles.

Figure 2.

A selection of temperature dependence of the magnetic moments measured in the ZFC process at a field from 20 Oe to 7 kOe. Two transitions are clear here: one is stable, another one shifts quickly with the applied field. (Inset) An enlarged view of the same curves. A crossing point marked with (T*, M*) is evident here.

Figure 3.

Critical fields corresponding to the two transitions: ▴ mark the vicinity of superconductivity in individual clusters, i.e., the real H_c2; ● correspond to the phase coherence between clusters showing a bulk superconductivity. (Inset) The a scaling to the M(T) data as shown in the Inset to Fig. 2. The dashed line was drawn with a slope of −dH_c2/dT = 1 T/K.

So far I have presented the data determined in the magnetic measurement to show two distinct transitions. The transition at T_c1 is attributed to the superconductivity occurring on separate clusters, whereas that at T_c2 is caused by the phase coherence between the clusters (8). These clusters are formed by macroscopic phase separation of excess oxygen atoms. It is interesting to note that in overdoped LaSrCuO single crystals, recently I also have observed this type of macroscopic phase separation (9) although in this system to incorporate oxygen is very difficult. This discovery, together with the anomalous H_c2(T) found in overdoped Tl-2201 (10) and Y_1-xCa_xBa₂Cu₃O₇ (11) may indicate an intrinsic and universal behavior for the overdoped samples in which the electronic instability will inevitably lead to the macroscopic phase separation.

In conclusion, two distinct superconducting transitions have been observed for overdoped Bi₂Sr_2-xLa_xCuO_6+δ single crystals. It is found that the transition behavior near T_c1 corresponding to the high-temperature phase obeys the critical fluctuation theory, which is similar to many observations in underdoped or optimal doped samples and thus is categorized to the intrinsic properties of high-T_c cuprates.

Abbreviations

FC

field cooled

ZFC

zero field cooled