Abstract
We report comprehensive Cu NMR studies on single crystals of which contain simple chains and two-leg ladders. From measurements of the NMR shift, it is clear that the spin gap in the ladders decreases with isovalent Ca substitution from K for (Sr14) to K, K, and K for (Ca6), (Ca9), and (Ca11.5), respectively. The exponential decrease of the nuclear spin-lattice relaxation rate below ∼130 K is consistent with the presence of the spin gap in the spin excitation spectrum. In the range higher than K, we observed the following dependences: and the square of Gaussian spin-echo decay time, which are consistent with the scaling theory for the one-dimensional (1D) Heisenberg model. The value of is compatible with the theoretical prediction of an exchange constant along the leg K for Ca6 and K for Ca9 and Ca11.5. A notable finding is that the magnitude of the spin gap remains nearly constant and characteristics of novel 1D-like spin dynamics are maintained in the content varying from Ca9 to Ca11.5. On the other hand, the charge transport changes with increasing Ca content so that the more conductive Ca11.5 exhibits pressure-induced superconductivity exceeding 3.5 GPa. We have found that , which is proportional to the inverse spin correlation length , deviates from a linear dependence upon cooling and is described by , regardless of the Ca substitution. We point out that the value of is proportional to the finite value of where is the spin-wave velocity. From the result that the values of for Ca6, Ca9, and Ca11.5 are significantly reduced compared to that for Sr14, it is suggested that is dominated at low by an average distance among mobile holes obeying the relation From an estimate of 5.2 for Sr14, where is the Cu-Cu distance along the leg, is obtained as , 2.3, and 2.0, and hole content as , 0.22, and 0.25 per ladder for Ca6, Ca9, and Ca11.5, respectively. These values were consistent with 0.14, 0.2, and 0.22 for Ca6, Ca9, and Ca11 estimated from the optical conductivity experiment by Osafune et al. [Phys. Rev. Lett. 78, 1980 (1997)]. The compounds are thus hole-doped two-leg spin-ladder systems which reveal the metallic behavior dominated by the 1D-like spin dynamics at high and accompanied by the spin gap formation at low . For Ca11.5, as the spin gap is formed upon cooling below K, the resistivity increases in the direction perpendicular to the ladder, whereas the conductivity along the ladder remains metallic, followed by the localization of mobile holes in both directions below K. We point out that preformed pairs are confined in each ladder and localized below K at an ambient pressure.
- Received 2 May 1997
DOI:https://doi.org/10.1103/PhysRevB.57.11533
©1998 American Physical Society