Large thermomagnetic effects in weakly disordered Heisenberg chains

The interplay of different scattering mechanisms can lead to novel effects in transport. We show theoretically that the interplay of weak impurity and umklapp scattering in spin-1/2 chains leads to a pronounced dip in the magnetic field dependence of the thermal conductivity $\kappa$ at a magnetic field $B\sim T$. In sufficiently clean samples the reduction in the magnetic contribution to heat transport can easily become larger than 50%, and the effect is predicted to exist even in samples with a large exchange coupling, $J⪢B$, where the field-induced magnetization is small. Qualitatively, our theory might explain dips at $B\sim T$ observed in recent heat transport measurements on copper pyrazine dinitrate, but a fully quantitative description is not possible within our model.

Figure 1

(Color online) Upper figure: field-dependent thermal conductivity $\kappa \left(B,T\right)-\kappa \left(0,T\right)$ in the spin-1/2 compound CuPzN taken from Ref. 7. The downturn at large fields arises as the spinon band is considerably depleted. For $T=0$ the magnetization saturates at $B\approx 15\text{T}$. Lower figure: the normalized magnetic part of the thermal conductivity, ${\kappa }_{\text{mag}}\left(B,T\right)/{\kappa }_{\text{mag}}\left(0,T\right)$, as a function of $h={\mu }_{B}gB/\left(k_{B}T\right)$ shows a dip at $h\sim 3$. Note that there might be a considerable error in the size of the dip as ${\kappa }_{\text{mag}}\left(B=0,T\right)$ could not be measured directly due to a large phonon background, see text and Ref. 7 for details.

Figure 2

(Color online) Field dependence of the of the normalized thermal conductivity as a function of the rescaled field, $h=g{\mu }_{B}B/k_{B}T$. For moderate disorder $\alpha \left(T\right)$, Eq. (15), $10\gtrsim \alpha \left(T\right)\gtrsim 1$, a pronounced dip in ${\kappa }_{\text{mag}}\left(B\right)$ is predicted for $g{\mu }_{B}B\sim 4k_{B}T$. For even smaller values of $\alpha \left(T\right)$ the dip gets broader and deeper, approximating the asymptotic behavior [Eq. (17)] (solid black line), up to larger and larger fields.