Thermal Conductivity of Quasi-One-Dimensional Antiferromagnetic Spin-Chain Materials

We study heat transport in quasi-one-dimensional spin-chain systems by considering the model of one-dimensional bosonic spin excitations interacting with three-dimensional phonons and impurities in the limit of weak spin-lattice coupling and fast spin excitations. A combined effect of the phonon and impurity scatterings yields the following spin-boson thermal conductivity behavior: ${\kappa }_s\propto T^2$ at low, ${\kappa }_s\propto T^{-1}$ at intermediate, and ${\kappa }_s=\mathrm{\text{const}}$ at higher temperatures. Our results agree well with the existing experimental data for ${\mathrm{S}\mathrm{r}}_2\mathrm{C}\mathrm{u}{\mathrm{O}}_3$. We predict an unusual dependence on the impurity concentration for a number of observables and propose further experiments.

Figure 1

Normalized spin thermal conductivity ${\kappa }_s$ vs reduced temperature $T/T_m$. Diamonds are the experimental data for ${\mathrm{S}\mathrm{r}}_2\mathrm{C}\mathrm{u}{\mathrm{O}}_3$, $T_m=79.4\mathrm{K}$, and ${\kappa }_s^{\max }=36.7\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$; see Ref. 1. The solid line is the result of this work, Eq. (17), for ${\Theta }_D=11.6T_m$. Arrows mark the saturation value ${\kappa }_s^{\infty }$ for the solid line at $T\gg {\tilde{\Theta }}_D$ and the spin-phonon scattering crossover scale ${\tilde{\Theta }}_D$, respectively. Asymptotic behavior at $T\ll T_m$ ($\sim T^2$) and at $T\gg T_m$ ($\sim \mathrm{\text{const}}$) are shown by the dashed lines. Inset: same data on the log-log scale.