Spin Gap in the Zigzag Spin-$1/2$ Chain Cuprate ${\mathrm{Sr}}_{0.9}{\mathrm{Ca}}_{0.1}{\mathrm{CuO}}_2$

We report a comparative study of ${}^{63}\mathrm{Cu}$ nuclear magnetic resonance spin lattice relaxation rates $T_1^{-1}$ on undoped ${\mathrm{SrCuO}}_2$ and Ca-doped ${\mathrm{Sr}}_{0.9}{\mathrm{Ca}}_{0.1}{\mathrm{CuO}}_2$ spin chain compounds. A temperature independent $T_1^{-1}$ is observed for ${\mathrm{SrCuO}}_2$ as expected for an $S=1/2$ Heisenberg chain. Surprisingly, we observe an exponential decrease of $T_1^{-1}$ for $T<90\mathrm{K}$ in the Ca-doped sample evidencing the opening of a spin gap. The data analysis within the $J_1\mathrm{\text{−}}{J}_2$ Heisenberg model employing density-matrix renormalization group calculations suggests an impurity driven small alternation of the $J_2$-exchange coupling as a possible cause of the spin gap.

Figure 1

Spin lattice relaxation rate $T_1^{-1}$ of ${\mathrm{SrCuO}}_2$ (a) and ${\mathrm{Sr}}_{0.9}{\mathrm{Ca}}_{0.1}{\mathrm{CuO}}_2$ (b) for different field directions. Inset: zigzag structure and main couplings.

Figure 2

Spin lattice relaxation rate $T_1^{-1}$ of ${\mathrm{Sr}}_{0.9}{\mathrm{Ca}}_{0.1}{\mathrm{CuO}}_2$ vs inverse temperature. Lines are fits of Eq. (2) with a fixed spin gap of $\Delta =50\mathrm{K}$ at low temperature (10–40 K). For clearness $T_{1,\mathrm{off}}^{-1}$ has been subtracted from the data and the fits. Inset: the same for $H\parallel b$ in $H=2\mathrm{T}$.

Figure 3

Spin gap as a function of $J_2/J_1$ in the AFM-AFM sector of the $J_1\mathrm{\text{−}}{J}_2$ HM. The experimental value of the spin gap in units of $J_1$ is depicted by dashed lines adopting $J_2=2000\mathrm{K}$.

Figure 4

The same as in Fig. 3 for an alternating AFM NNN exchange $J_2(1\pm \delta )$ at (a) zero and (b) weak arbitrary NN-exchange $J_1$. (c) Spin structure factor for several disorder strengths $D$ with $\delta =0.1$ and $J_1=0$. The inset of (a) shows $(\Delta /J_2{)}^{1.5}$ for small alternations $\delta$.