Collective Spin and Charge Excitations in (Sr,La)14−xCaxCu24O41 Quantum Spin Ladders

In 1988, material research focussed around the study of high temperature superconducting copper-oxides brought about new phases of Cu-O based systems, the two-leg spin-ladders (2LL's), that have the general formula (A 1−x A' x) 14 Cu 24 O 41 , with A an alkaline earth metal and A' a trivalent (transition or lanthanoid) metal [1, 2]. There were well-founded hopes that these materials could provide useful insight for the unresolved problems posed by the 2D cuprates [3, 4] and from this perspective two main reasons triggered the interest of the scientific community. One of them was based on a number of physical properties that are common for both ladders and high T c 's. These include the presence of similar Cu-O-Cu antiferromagnetic (AF) correlations which give rise to a finite spin gap and were predicted to generate d-wave like pairing of doped carriers [5], the evidence for 'pseudogap' phenomena in optical absorption spectra [6] and, most importantly, the discovery of superconductivity under pressure evolving with hole doping in the AF environment [7, 8]. The second reason resides in the crystal similarities and more precisely the fact that one can imagine building the 2D square Cu-O lattice by gradually increasing the coupling between individual 2LL's [9], the simplicity of the latter making them more tractable for theoretical analysis. The unit cell of Sr 14 Cu 24 O 41 contains four formula units, 316 atoms in all, this large number of atoms being due to the presence of two nearly commensurate substructures: the CuO 2 chains and the Cu 2 O 3 2LL's. A better understanding of the two interacting blocks can be achieved by decomposing the chemical formula into (Sr 2 Cu 2 O 3) 7 (CuO 2) 10 : planes of CuO 2 chains are stacked alternately with planes of Cu 2 O 3 ladders and these are separated by Sr buffer layers, see Fig. 1. The lattice constants of the individual subsystems satisfy the approximate relation 7 c ladder ≈ 10 c chain. The b-axis is perpendicular to the Cu-O layers which define the (ac) plane, the c-axis being along the ladder/chain direction. A valence counting shows that Sr 2+ 14 Cu 24 O 2− 41 is intrinsically doped, the average valence per Cu atoms being +2.25. Optical conductivity [10], X-ray absorption [11], dc resistivity and magnetic susceptibility [12] measurements, as well as evaluations of the Madelung potential [13] …