Electrical conductivity of YBa2Cu3O7-δ single crystals under conditions of anionic ordering in Cu(1)O1-δ layers

The influence of thermocycling annealing processes on the oxygen ordering degree (order parameter) in YBa2Cu3O7-δ single crystals has been studied. It has been shown that an increase in the critical onset temperature of the transition to the superconducting state during thermocycling annealing procedures is consistent with the decrease of the σс/σаb parameter. This fact indicates a redistribution of the electronic density between the structurally inhomogeneous Cu(2)O2 and Cu(1)O1-δ planes, due to the formation of oxygen long-range order in the O(4)–Cu(1)–O(4) linear groups along the (b) crystal structure axis of the unit cell, and elimination of oxygen defects in the square nets of the Cu(2)O2 planes. The existence of the critical value of the conductivity anisotropy σс/σаb, below which its behavior does not correlate with the change of Тс, has been confirmed. In this case an increase in Тс and orthorhombic distortion of the crystal structure during isothermal annealing are caused by the amplification of the “interlayer” interaction between the Cu(2)О2 and Cu(1)О1-δ planes. As a result, the contribution of the Cu(1)О1-δ chain layers to the electron state density at the Fermi level increases. These layers can acquire superconducting properties due to tunneling of Cooper pairs from the Cu(2)О2 planes resulting in the formation of the induced superconductivity in these planes.


Introduction
An urgent task in the research of high-temperature superconductivity is to improve the technology of high-quality specimens including the YBa 2 Cu 3 O 7-δ compound having reproducible superconducting properties and to study their physico-chemical properties. One condition of the existence of the superconducting state in cuprate compounds is that planes perpendicular to the crystallographic С 4 axis and those parallel to that axis should contain virtually square nets with minor rhombic distortion. The sites of the squares should be occupied by О -2 oxygen anions and their centers should accommodate variable valence copper cations, i.e., Cu +1,+2,+3 , the average valence evaluated from the length of the Cu-O bond being ~2.33 [1,2]. Analysis of the dependence of the superconducting properties of YBa 2 Cu 3 O 7-δ on oxygen non-stoichiometry has shown that the critical temperature of the onset of the transition to the superconducting state (Т с ) is controlled by the density of electronic states N(E) at the Fermi level E F which are in turn associated with the concentration of oxygen vacancies (δ) and their distribution in the YBa 2 Cu 3 O 7-δ structure [3][4][5][6][7].
Т с is known to depend on the concentration of mobile oxygen distributed in the chain Сu(1)O 1-δ planes and may reach the highest level (~92 K) at δ = 0÷0.2 [8]. This correlation is however not definitive since Т с may vary at a constant δ due to the effect of not only the concentration of oxygen vacancies but also their ordering in the anionic sublattice of YBa 2 Cu 3 O 7-δ crystals [9][10][11][12][13][14]. The order parameter of oxygen vacancies (ηv 0 ) is in turn controlled by temperature and annealing time and therefore affects Т с [15][16][17][18]. Thus ordering of oxygen vacancies in YBa 2 Cu 3 O 7-δ can be considered as one method to change the carrier concentration in the square nets of the Сu(2)O 2 structural planes which determine the superconducting properties of the compound [19][20][21][22].
Despite the large number of works on the topic, the ordering conditions of oxygen vacancies between the (0 1/2 0) and (1/2 0 0) structural planes in the YBa 2 Cu 3 O 7-δ anionic sublattice, especially at δ → 0, have been studied insufficiently yet. It is therefore an important task to evaluate the threshold temperature (Т thr , K) at which the energy of the thermal atomic oscillations becomes higher than the oxygen bond energy in the -Сu(1)-О(4)-Сu(1)-О(4)chains and starts to violate the order of oxygen vacancies in the anionic sublattice.

Experimental
The YBa 2 Cu 3 O 7-δ single crystals were zone melt grown with directional mass transport in the system of {Ba 3 Cu 5 O 8 + хBaCuO 2 }/Y 2 BaCuO 5 diffusion pairs due to the component concentration gradient between the contacting layers [23,24]. The Y 2 BaCuO 5 and BaCuO 2 compounds were synthesized using high purity grade Y 2 O 3 , BaO and CuO oxides. The compounds were synthesized in thermal plants at 1220 K, 1270 K and pO 2 = 0.21 × 10 5 Pa for BaCuO 2 and Y 2 BaCuO 5 , respectively. The temperature in the thermal plants was maintained using a RIF-101 high-precision temperature controller and was monitored with a Pt-Pt/Rh(10%) thermocouple accurate to ± 0.5 K. The as-grown single crystals had sizes of 1 × 1 × 0.5 ÷ 5 × 4 × 2 mm 2 , δ = 0.6-0.7 and the superconducting parameters Т с = 31-36 K and ∆Т с = 11-18 K, where ∆Т с = 90÷10 % is the width of the temperature transition to the superconducting state. The structure of the single crystals was studied on a DRON-3 diffractometer in СuК α radiation. The lattice parameters were determined using the asymmetrical method accurate to ± 5 × 10 -5 nm for YBa 2 Cu 3 O 7-δ powders.
Since the saturation rate and subsequent oxygen ordering in YBa 2 Cu 3 O 7-δ triple cuprate are far lower for single crystals and dense ceramics (ρ = 6.0-6.2 g/cm 3 ) than for moderate density ceramic specimens (ρ = 4.4-4.7 g/cm 3 ), the parameter value δ ≤ 0.1 was achieved using three stage thermocycling annealing [25][26][27]. At the initial stage the YBa 2 Cu 3 O 7-δ crystals were annealed at 820 K for 25 h, and the second stage, at Т = 1020 K for 2 h and at the third stage they were stepwise cooled at a 40-50 K/h rate within the 1020-870 K range and at a 1-5 K/h rate in the 870-720 K range. The electrical conductivity of the YBa 2 Cu 3 O 7-δ crystals was measured in the 77-800 K range using the four-probe method with platinum contacts.

Results and discussion
The highest diamagnetic response was observed in the crystal after the fourth annealing stage. In that crystal the diamagnetic response was 3.7 times higher than after single-stage annealing. Therefore the superconducting transition temperature increases and the transition width decreases as indicated by the single crystal magnetization temperature functions (Fig. 1). Further increase of the number of annealing stages did not improve the superconducting parameters of the crystals.
These results combined with data on field functions of magnetization allowed evaluating the critical current of the crystal using the Bean model: where М + and Мare the magnetizations of the crystal for opposite magnetic induction vectors of the outer magnetic field. Analysis of the field functions of magnetization showed that the plateaus on the hysteresis loops are almost symmetrical (Fig. 2). It is therefore sufficient to substitute |-M + + M -| in Eq. (1) for the double residual moment of magnetization М res which equals to the crystal magnetization in a zero field after application of a strong magnetic field (14 T). Then the equation of the critical current density in the crystal takes on as follows: The magnetization curves M(B) at T = 7 K in magnetic field B parallel to the (c) axis show that with an increase in the number of annealing stages, the areas of the hysteresis loops and hence M res increase significantly (Fig. 2). In accordance with Eq. (2) the annealing process described above increases the critical current density J c ≈ 0.68; 1.21; 2.05; 2.59 × 10 4 A/cm 2 for the first, second, third and fourth annealing stages, respectively. The effect of gas thermal annealing of the YBa 2 Cu 3 O 7-δ crystal on the concentration and ordering of oxygen vacancies in the (ab) plane between different crystallographic positions (0 1/2 0) and (1/2 0 0) was determined by measuring the electrical conductivity in different crystal directions: along the с(σ с ) axis and in a direction parallel to the (ab) (σ ab ) plane. This study showed that thermocycling annealing of the crystals caused correlated changes in Т с and σ с /σ аb (Fig. 3). The decrease in the σ с /σ аb ratio due to a faster increase in σ аb , than in σ с is caused by different mechanisms of the effect of thermocycling annealing on the electrical conductivity of the crystal in different directions.
One can assume that the growth of σ с is caused by an increase in the degree of covalence of the bond along the c axis of the YBa 2 Cu 3 O 7-δ lattice leading to an increase in the overlapping of the wave functions of electrons located on the Cu3d z2 orbitals of copper and the О2р z orbitals of oxygen. This assumption is confirmed by a decrease in the lattice parameter along the (c) axis (Table 1).
The increase in the electrical conductivity σ аb after thermocycling annealing is caused by a redistribution of the electronic density from the square nets of the Сu(2)O 2 layers to the Сu(1)O 1-δ chain layers which leads to an increase of N(Е) F in Сu(2)O 2 . The redistribution of the electronic density is affected by the concentration and ordering of oxygen vacancies along (a) or an increase in the occupation density of (0 1/2 0) crystallographic positions by oxygen anions leading to an increase in the orthorhombic distortion ∆ (b-а) .
After constant Т с and σ с /σ аb were achieved we started isothermal annealing in the 720-560 K range at pO 2 = 5 × 10 5 Pa for 15 h. T c increased at ∆T с = const at temperatures below the threshold one T t = 600 K (Fig. 4). Furthermore σ с /σ аb remained constant during isothermal annealing in the 660-560 K range whereas T c increased. The increase in T c can be arbitrarily split in two regions I and II with T c increasing faster in the region I than in the region II (Fig. 4).
For determining T c as a function of oxygen vacancy concentration and ordering, the order parameter was introduced which depends linearly on the orthorhombic distortion ∆ (b-а) and is expressed analytically as ∆ (b-а) = αηv 0 , where α is the proportion coefficient. This latter proportion    coefficient is calculated for the maximum value max(∆ (b-а) ) = 0.00780 nm for the stoichiometric composition of YBa 2 Cu 3 O 7-δ corresponding to η max = 0.5 [28]. The T c parameters of the thermocycled crystals are more sensitive to the concentration of oxygen vacancies (δ) than to their ordering (ηv 0 ) ( Tables 1, 2 Analysis of the change in the anisotropy of the electrical conductivity after thermocycling and isothermal annealing showed that the increase in T c does not necessarily correlate with the changes in σ с /σ аb . On the one hand the increase in T c for the heat treated specimens can be accounted for by an increase in the free carrier concentration in the Cu(2)О 2 planes and an increase in the strength of the interlayer interaction (σ с /σ аb ) between the Cu(2)О 2 and Cu(1)О 1-δ .planes. On the other hand annealing at 660-560 K and pO 2 = 5 × 10 5 Pa increases T c of the crystals without changing their σ с /σ аb . This suggests that the anisotropy of the electrical conductivity of the YBa 2 Cu 3 O 7-δ single crystals depends on the oxygen nonstoichiometry parameter δ and is not determined by ηv 0 . It is safe to assume that annealing at 660-560 K and pO 2 = 5 × 10 5 Pa changes the mechanism that controls the superconducting properties of the crystals. Then the increases in σ аb and T c originate from the ordering of oxygen ions and are caused by the contribution of the Cu(1)O 1-δ chain layers to the electronic density of states at the Fermi level. The Cu(1)О 1-δ chain layers can be superconducting due to the proximity effects, and this fact makes possible the exi-stence of induced superconductivity in these layers due to tunneling of Cooper pairs from the Cu(2)О 2 planes.

Conclusion
Study of the regularities of oxygen interaction with yttrium/barium cuprate single crystals for the first time justified the necessity of using multistage gas thermal treatment in order to increase the superconducing parameters of YBa 2 Cu 3 O 7-δ due to intentional impact on oxygen sorption and ordering processes in its anionic sublattice.
An increase in the critical onset temperature of the transition to the superconducting state during this annealing is consistent with the decrease of the σ с /σ аb parameter. This fact indicates a redistribution of the electronic density between the structurally inhomogeneous Cu(2)O 2 and Cu(1)O 1-δ planes, due to the formation of oxygen longrange order in the O(4)-Cu(1)-O(4) linear groups along the (b) crystal structure axis of the unit cell, and elimination of oxygen defects in the square nets of the Cu(2)O 2 planes.
The existence of the critical value of the conductivity anisotropy σ с /σ аb , below which its behavior does not correlate with the change of Т с , was confirmed. In this case an increase in Т с and orthorhombic distortion of the crystal structure during isothermal annealing are caused by the amplification of the "interlayer" interaction between the Cu(2)О 2 and Cu(1)О 1-δ planes. As a result, the contribution of the Cu(1)О 1-δ chain layers to the density of electronic state at the Fermi level increases. These layers can acquire superconducting properties due to tunneling of Cooper pairs from the Cu(2)О 2 planes resulting in the formation of the induced superconductivity in these planes. Table 2. Dependence of the superconducting characteristics and crystal lattice parameters of the YBa 2 Cu 3 O 7-δ single crystal on the temperature of isothermal annealing.