The origin of the 60 K plateau in YBa₂Cu₃O_6+x

Abstract

A model for the charge transfer mechanism in YBa2Cu3O6+x high-Tc cuprate based on the critical chain length concept is proposed to account for the 60 and 90 K plateaus in the Tc(x) dependence. It has been shown that, when the statistics of CuO chain formation was described in terms of the two-dimensional asymmetric next-to-nearest neighbor Ising (ASYNNNI) model, at any constant temperature below the top of ortho-II phase there exists a uniquely defined value of critical chain length lcr(T) that yields a constant doping p(x)≈const over the regime of ortho-II phase (related to the 60 K plateau of Tc(x)), while the 90 K plateau coincides with the monotonically increasing p(x) over the optimal doping level p = 0.16 in the regime of the ortho-I phase. Short length chains (l<lcr(T)), together with the first lcr(T)−2 holes in longer chains (l≥lcr(T)), are taken as not capable of attracting electrons from CuO2 planes. It is shown that only a part (≈41%) of the remaining l−lcr(T)+1 holes in the long chains can capture electrons. The results obtained indicate that the ASYNNNI model and two-plateau-like behavior of Tc(x) in YBa2Cu3O6+x are closely connected.

Charge transfer mechanism andTc(x) dependence in Y0.8(Ca)0.2Ba2Cu3O6+x

“…Such behavior of length distributions ensures a rapid convergence of summations in equation (2). Although theoretical study has shown that a certain departure from geometric-like behavior of f(l)s can be expected in narrow interval Δx≈0.07 around critical point of the OI-to-OII phase transition, due to increased fluctuations of energy of the ASYNNNI model [18], our extended analysis has inferred that such departures are nevertheless compensated by sums in (2) [26], so that the doping can be expressed in the following integrated form ( ) …”

“…from l=l min to l=∞, so that the number of transferred holes from a chain of length l≥l min appears to be equal to χ(l-l min +1) [22,26]. If f(l) denotes fraction of chains that have the same length l, the total number of transferred holes N would then be equal to , where…”

“…As far as l min is concerned, it should be noted that in our recent study [26] it has been shown that at any τ=const there exists a well defined value of l min , which we denoted by l opt (τ) (the so-called optimal chain length), for which p ch (x) remains constant as x increases beyond x≈0.5 over the region of ortho-II phase. From Figure 1 of reference [26] it can be seen that, at a given τ=const, if l min < l opt (τ) then p ch (x) is monotonically increasing function over the ortho-II phase region (and also in the whole interval 0<x<1).…”

“…From Figure 1 of reference [26] it can be seen that, at a given τ=const, if l min < l opt (τ) then p ch (x) is monotonically increasing function over the ortho-II phase region (and also in the whole interval 0<x<1). However, if l min >l opt (τ), then p ch (x), and, consequently, the concentration of active chain holes, both have a maximum at x≈0.5, that is followed by a decline when x increases beyond 0.5, to turn to be rising again after x enters into the regime of ortho-I phase [22,26]. Such a peaky behavior of p(x) at τ=const is clearly not what generates the T c (x) in Y 0.8 (Ca) 0.2 Ba 2 Cu 3 O 6+x system, but it is the monotonically increasing p(x) (and p ch (x)), as it can be straightforwardly verified by applying equation (1) on experimentally obtained T c (x) [8,9] (the so obtained p(x) is shown by open squares in Figure 1).…”

“…In situation like this, we relied on the following strategy: Firstly, we retained the LMTO values of in-plane O-O interactions that were successfully used in YBa 2 Cu 3 O 6+x [19] (although we were well aware that the effective V 1 , V 2 , and V 3 interactions might indeed be of different values in Y 0.8 (Ca) 0.2 Ba 2 Cu 3 O 6+x ), because we primarily wanted to examine applicability of the model (3) when combined with the ASYNNNI model of inplane oxygen ordering, and, secondly, given the fact that l opt (τ) rapidly increases with τ lowering (as shown in Figure 1 of reference [26] -the results of our the most recent analyses show that l opt (τ) scales with ≈exp(2│V 2 │/k B B T)), we attached to τ RT a lower value than in YBa 2 Cu 3 O 6+x system in order to open a way for a broader range of l min values to produce monotonically increasing p ch (x) and p(x)=(b eff /2)+p ch (x). We thus arrived at τ RT =0.38 that might be adopted as a relatively acceptable estimation for τ RT as it opens a way for l min =3, 4, or 5 to be producing a monotonic behavior of p ch (x), since at τ=0.38 the l opt (τ) falls at some point between 6 and 7 (as shown in Figure 1 of reference [26] , and yet such a development has not been grounded, at least in a persuasive way, upon available experimental data [16] (although the ortho-II phase has indeed been clearly detected in Y 0.8 (Ca) 0.2 Ba 2 Cu 3 O 6+x , as mentioned previously). Furthermore, taking into account that l min =4, or, alternatively, l min =5, have recently been shown to successfully account for both 60K and 90K plateaus in the YBa 2 Cu 3 O 6+x system [22,26], we were of opinion that introduction of ≈20% of Ca ions would not affect that drastically the chain's ability to trigger the charge transfer process, i.e.…”