Spin gap in the single spin-$\frac{1}{2}$ chain cuprate ${\mathrm{Sr}}_{1.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_3$

We report ${}^{63}\mathrm{Cu}$ nuclear magnetic resonance and muon spin rotation measurements on the $S=1/2$ antiferromagnetic Heisenberg spin chain compound ${\mathrm{Sr}}_{1.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_3$. An exponentially decreasing spin-lattice relaxation rate $T_1^{-1}$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound ${\mathrm{Sr}}_{0.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_2$, and it confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling $J^{\prime }$. Our results therefore suggest that the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain is induced by a local bond disorder of the intrachain exchange coupling $J$. A low-temperature upturn of $T_1^{-1}$ evidences growing magnetic correlations. However, zero-field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound, which is most likely suppressed by the opening of the spin gap.

Figure 1

Chain structure of ${\mathrm{Sr}}_2$${\mathrm{CuO}}_3$ and double-chain structure of ${\mathrm{SrCuO}}_2$ including the main exchange couplings $J$ (intrachain) and $J^{\prime }$ (interchain). Gray spheres represent the copper ions, red spheres represent the oxygen ions.

Figure 2

Temperature-dependent $T_1^{-1}$ for ${\mathrm{Sr}}_{1.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_3$ measured along the $b$ (black squares) and $a$ (green dots) direction, in comparison to $T_1^{-1}$ of ${\mathrm{Sr}}_{0.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_2$ measured along $b$ (open red dots, taken from Ref. [9]). Note that the $b$ direction of ${\mathrm{SrCuO}}_2$ is crystallographically equivalent to $a$ of ${\mathrm{Sr}}_2$${\mathrm{CuO}}_3$ (see Fig. 1). The inset shows the temperature evolution of the stretching exponent $\lambda$ of the relaxation function [see Eq. (1)].

Figure 3

(a) ${}^{63}\mathrm{Cu}$ NMR spectra of ${\mathrm{Sr}}_{1.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_3$ for $H\parallel b$ measured at different temperatures (see labels). All three resonance lines of the quadrupolar split ${}^{63}\mathrm{Cu}$ NMR spectrum are visible. Additionally, the high field satellite of the ${}^{65}\mathrm{Cu}$ isotope is visible at $\sim$6.52 T. (b) Temperature-dependent full width at half-maximum (FWHM) of the ${}^{63}\mathrm{Cu}$ central line and the ${}^{63}\mathrm{Cu}$ satellite at high field values, which is not disturbed by an overlapping ${}^{65}\mathrm{Cu}$ resonance line. The almost parallel temperature dependence of the FWHM of the satellite and the central transition evidences a magnetic broadening effect.

Figure 4

ZF $\mu$SR asymmetries of ${\mathrm{Sr}}_{1.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_3$ measured at 100 K (gray squares), 5 K (orange diamonds), and 1.5 K (blue dots), respectively. The inset shows the temperature dependence of the initial asymmetry $A_0$ (green squares) and the Gaussian decay rate $\sigma$ (brown dots) obtained by fitting the asymmetry time spectra to Eq. (2).