Superconductivity and magnetism in ladder and chain compounds physics of (Sr,Ca)₁₄Cu041O₄₁

The study of ladder materials has in recent years become one of the central issues in the field of condensed matter physics. Ladder materials, which contain a structural unit composed of coupled arrays of one-dimensional (1D) chains, are considered to be an interesting intermediate step between one- and two-dimensional (2D) systems [1-5]. In fact, it is now recognized that the crossover from 1D to 2D is far from straightforward and that ladder materials by themselves exhibit a variety of new physics. Historically, studies on ladder material were motivated by the discovery of hightransition- temperature (high-Tc) superconductors occurring in 2D spin-1/2 (S=1/2) Heisenberg antiferromagnets [6]. Two theoretical predictions have particularly triggered extensive research [1,2]. First, ladders made from an even number of spin-1/2 Heisenberg chains (even-leg ladders) are expected to have a unique spin-liquid ground state with short range spin correlation, where there exists a finite energy gap ("spin gap") to the lowest excited state. The spin gap, more frequently called the pseudogap, is a key feature of high-T_c superconductors, particularly in the low carrier concentration region. Ladder materials are in this context considered to be good references to gain insights into the pseudogap physics of high-T_c superconductors. Second, and a more intriguing hypothesis, is the possible occurrence of superconductivity in even-leg ladders when they are doped with holes, similar to the high-Tc materials in which holes are doped into 2D copper-oxygen (CuO₂) planes. The symmetry of pairing is predicted to be d-wave like [7], adding to the similarities between doped ladders and doped 2D planes. Stimulated by these theoretical suggestions, intensive experimental studies have been carried out, with a variety of cuprate ladder materials having been newly discovered. For instance, (i) the existence of a spin gap was confirmed for SrCu ₂O₃, a prototype of a twoladder compound [8,9], (ii) hole-doping into two-legged ladders was first achieved on LaCuO_2.5 by replacing La with Sr [10], and (iii) superconductivity at 12.5 K was observed in Sr_14-xCa_xCu₂₄O₄₁ under a pressure of 3 GPa [11]. Here, we review experimental results on cuprate spin ladder materials, emphasizing those for Sr_14-xCa_xCu ₂₄O₄₁. In Sec. 1.2, brief theoretical background is provided, while Sec. 1.3 introduces typical cuprate spin ladder materials. In Chap. 2, we review the magnetic properties of hole-doped edge-sharing S=1/2 chains, a constituent of (Sr,Ca)₁₄Cu₂₄O₄₁, after which the normal state properties of (Sr,Ca)14Cu24O41 are considered in Chap. 3, with emphasis on the effect of Ca substitution on charge dynamics of hole-doped two-leg ladders. Superconducting properties are then discussed in Chap. 4, being followed by Chap. 5 which discusses the consistency between theory and experiments of ladder and summarizes novel physical insights obtained by a series of experiments on (Sr,Ca)₁₄Cu₂₄O ₄₁. Readers should note that our review is in addition to other excellent reviews on spin ladder system [3-5].