Carrier doping effects on spin dynamics in ${\mathrm{Sr}}_{14-x}{A}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ ( $A=\mathrm{Ca}$, Y, and La) are investigated by Cu NMR and NQR. The energy gaps in the spin excitation spectra (spin gap) are confirmed to be $\Delta =140\mathrm{}\mathrm{K}$ for the Cu${\mathrm{O}}_2$ chain and $\Delta =470\mathrm{}\mathrm{K}$ for the C${\mathrm{u}}_2$${\mathrm{O}}_3$ ladder in S${\mathrm{r}}_{14}$C${\mathrm{u}}_{24}$${\mathrm{O}}_{41}$. The spin gap for the ladder increases with the Y and La substitutions for Sr (up to $x=3\mathrm{}$), while it decreases with increasing x in ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ and seems to collapse around $x=13\mathrm{}$ of the Ca substitution. Hole-doping effects on the spin gaps for the ladder configuration are interpreted in terms of magnon and hole-depairing excitations for the spin $S=\frac{1}{2}$ ladder.

• Received 2 August 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.1992