Use of an AX₃ close-packing description of layered perovskites in understanding the role of various A ions in cuprate superconductors

Abstract

The layered perovskite oxide systems have been modelled on the basis of two types of AX₃ close-packing found, for example, in the Ll₂ and DO₂₂ structure types of Cu₃Au and TiAl₃, respectively. The former is known to give the ABX₃ perovskite structure. It is proposed that the latter gives the AX rock-salt structure upon the loss of XX rows for which the ionic radius ratio rA/rX > 0.73. The lower limit of the tolerance factor is also justified in such a packing scheme based on this geometrical constraint of rA/rX > 0.73 or a minimum r_Asim;1.02 Å. An admixture of the two kinds of packing yields the layered perovskite structure. The AX^#₃ packing (X^# includes the anion vacancy) may be modelled in terms of pseudo-spins in the axial next-nearest-neighbor-Ising (ANNNI) model. The pseudo-spins correspond to the two relative orientations of the AX^# rows instead of the lengths of the domains as in the usual description of long period intermetallic superlattices using antiphase boundary (APB) structures. Just as the intermetallic compounds, the layered cuprate perovskites in general have the m, 1ⁿ Fisher-Selke notation where m is the number of spins in "ferromagnetic" ...AX#.B.X^#X^#.AX^#... (perovskite) domains and n is the number of spins in the "antiferromagnetic" ...AX^#.X^#X^#.X^#A...(or rock-salt) domains. Three sites for the A ions may then be distinguished. The 3, 1 notation has the sequence ...A_PX^#.X^#X^#.B.A_FX^#.X^#X^#.B.A_PX^#.X^#X^#.X^#A_R.X^#X^#.ARX^#.X^# X^#..., where A_P are large cations such as La³⁺, Ba²⁺, Sr²⁺ in nine-fold coordination; A_F are cations with eight-fold coordinations such as Ca²⁺ and Y³⁺. TlBa₂CaCu₂O₇ is an example of such a notation. The A_R ions with six-fold coordination are ions such as Tl, Bi, Pb etc. It is proposed that the constraints of the close-packing model require the average size of the A_R ions to have an average radius of 1.02 Å. This is due to an admixture of various valence states in the A_R ions such as Bi, Tl, Pb to provide epitaxial stabilization. The possible role of an admixture of the valence skipping states of the A_R ions in enhancing the superconducting transition temperatures is discussed.