Spin Pseudogap in Ni-Doped ${\mathrm{SrCuO}}_2$

The $S=1/2$ spin chain material ${\mathrm{SrCuO}}_2$ doped with 1% $S=1$ Ni impurities is studied by inelastic neutron scattering. At low temperatures, the spectrum shows a pseudogap $\Delta \approx 8\mathrm{meV}$, absent in the parent compound, and not related to any structural phase transition. The pseudogap is shown to be a generic feature of quantum spin chains with dilute defects. A simple model based on this idea quantitatively accounts for the experimental data measured in the temperature range from 2 to 300 K, and allows us to represent the momentum-integrated dynamic structure factor in a universal scaling form.

Figure 1

(a) Background-subtracted time-of-flight (TOF) neutron spectrum measured in ${\mathrm{SrCu}}_{0.99}{\mathrm{Ni}}_{0.01}{\mathrm{O}}_2$ on SEQUOIA, as a function of momentum transfer along the spin chains and energy transfer. Arrows indicate the spin pseudogap. (b) Momentum-integrated dynamic structure factor measured in ${\mathrm{SrCu}}_{0.99}{\mathrm{Ni}}_{0.01}{\mathrm{O}}_2$ at several temperatures, using TOF (solid symbols) and three-axis (open symbols) spectroscopy. The lines are calculated using Eq. (4), assuming $x=0.017$.

Figure 2

Symbols: energy dependence of the momentum-integrated dynamic structure factor measured in ${\mathrm{SrCu}}_{0.99}{\mathrm{Ni}}_{0.01}{\mathrm{O}}_2$ at $T=2$ and 6 K. The thin solid and dotted lines are the theoretical expectation for a defect-free spin chain at $T=0$ and 6 K, respectively. The solid and dashed curves are theoretical predictions for doped chains, assuming $x=0.01$, $x=0.017$, and $x=0.02$, as discussed in the text.

Figure 3

(a) The imaginary part of generalized susceptibility measured at several temperatures (symbols). The plot is in coordinates where ${\chi }^{\prime \prime }$ of a simple spin chain is a universal scaling form given by Eq. (1) (solid line) after correcting by population factor. (b) Collapse obtained for the same data, but normalized by the envelope function given by Eq. (5) with $x=0.017$. Open and solid symbols correspond to three-axis and TOF data, respectively.