Low-temperature heat transport of ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ single crystals

We report a study of the Ce doping effect on the thermal conductivity $\left(\kappa \right)$ of ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ (NCCO) at low temperatures down to 0.3 K and in magnetic fields up to 14 T. It is found that with Ce doping, the electronic thermal conductivity increases; at the same time, the $a$-axis field-induced changes in $\kappa \left(H\right)$, associated with the spin flop and spin polarization of the ${\mathrm{Nd}}^{3+}$ sublattice, and the spin flop of the ${\mathrm{Cu}}^{2+}$ sublattice, gradually disappear. These are clearly due to the electron doping and the destruction of the antiferromagnetic orders. In the superconducting NCCO with $x$ = 0.14 and 0.18, although the electronic thermal conductivity shows sizable field dependencies with $H\parallel c$, the paramagnetic scattering of phonons is still playing the dominant role in the heat transport, which is different from many other cuprates. In the lightly doped samples $(x$ = 0.03 and 0.06), the low-$T$ $\kappa \left(H\right)$ isotherms with $H\parallel c$ show a steplike anomaly and are likely related to the spin/charge stripes.

Figure 1

(a) The $a$-axis thermal conductivity of ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ single crystals in zero field in a log-log plot. Inset: the ratios of the phonon mean-free path $l$ to the averaged sample width $W$ at $T<$ 1 K for nonsuperconducting samples of $x$ = 0, 0.03, and 0.06. (b) The low-temperature data plotted in $\kappa /T$ vs $T^2$.

Figure 2

Comparison of $\kappa \left(T\right)$ between the $x$ = 0 and 0.03 ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ single crystals with the zero field and 14-T field applied along the $a$ or the $c$ axis. The insets show the ratio of the phonon mean-free path $l$ to the averaged sample width $W$ at $T<$ 1 K and in different fields.

Figure 3

Comparison of the magnetic-field dependencies of thermal conductivity between the $x$ = 0 and 0.03 ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ single crystals with the field applied along the $a$ or the $c$ axis.

Figure 4

Thermal conductivity of two $x$ = 0.06 ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ single crystals, which were annealed with different processes. The one labeled by “$x$ = 0.06” was annealed in the same way as other NCCO samples, while the other one labeled by “$x$ = 0.06 $\left(Q\right)$” was annealed in flowing Ar and at 900${}^{\circ }$C but quenched to the liquid-nitrogen temperature. (a) The $\kappa \left(T\right)$ in linear plot. Inset: the magnetic susceptibilities measured in 10 Oe along the $c$ axis after cooling the samples in zero field. The data show that the $x$ = 0.06 sample is not superconducting above 2 K and the $x$ = 0.06 $\left(Q\right)$ sample has $T_c=$ 9 K. (b) The log-log plot of $\kappa \left(T\right)$ in both zero and 14-T fields along the $a$ axis. (c)–(f) Low-temperature $\kappa \left(H\right)$ isotherms for two samples in magnetic fields along either the $a$ or the $c$ axis.

Figure 5

Magnetic-field dependencies of thermal conductivity for two superconducting ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ single crystals with $x$ = 0.14 and 0.18.

Figure 6

Comparison of the lowest-$T$ $\kappa \left(H\right)$ data among differently doped ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ single crystals.

Figure 7

The $a$-axis thermal conductivity of ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ $(x=$ 0.14) single crystal in the zero field, plotted in $\kappa /T$ vs $T^2$. The size of this sample is 2.00 $\times$ 0.83 $\times$ 0.069 ${\mathrm{mm}}^3$. Inset: the zoom-in of the plot at very low temperatures.