Heat Transport as a Probe of Electron Scattering by Spin Fluctuations: The Case of Antiferromagnetic ${\mathrm{CeRhIn}}_5$

Heat and charge conduction were measured in the heavy-fermion metal ${\mathrm{CeRhIn}}_5$, an antiferromagnet with $T_N=3.8\mathrm{K}$. The thermal resistivity is found to be proportional to the magnetic entropy, revealing that spin fluctuations are as effective in scattering electrons as they are in disordering local moments. The electrical resistivity, governed by a ${\mathbf{q}}^2$ weighting of fluctuations, increases monotonically with temperature. In contrast, the difference between thermal and electrical resistivities, characterized by a ${\omega }^2$ weighting, peaks sharply at $T_N$ and eventually goes to zero at a temperature $T^{\star }\simeq 8\mathrm{K}$. $T^{\star }$ thus emerges as a measure of the characteristic energy of magnetic fluctuations.

Figure 1

Thermal conductivity of ${\mathrm{CeRhIn}}_5$, for a current in the basal plane (open circles). The dashed line is the estimated phonon conductivity (${\kappa }_{\mathrm{ph}}$), and the solid line the electronic contribution (${\kappa }_e\equiv \kappa -{\kappa }_{\mathrm{ph}}$).

Figure 2

Electronic thermal resistivity $w_e$ (circles) and electrical resistivity $\rho$ (squares), compared to the magnetic entropy $S_{\mathrm{mag}}$ (line) obtained from published specific heat data [12]. Inset: low-temperature data as a function of $T^2$. Lines are linear fits.

Figure 3

Difference between thermal ($w_e\equiv L_{0}T/{\kappa }_e$) and electrical ($\rho$) resistivities: $\delta (T)\equiv w_e(T)-\rho (T)$. The vertical dash-dotted line marks the Néel temperature $T_N$. Note how abruptly the onset of static antiferromagnetic order cuts off the growth in $\delta (T)$ with decreasing temperature. Note also that $\delta (T)$ vanishes above $T\simeq 8\mathrm{K}$, revealing that temperature has by then exceeded the characteristic energy of magnetic fluctuations. The solid line is a fit to $a{T}^2+b{T}^5$ below $T_N$.

Figure 4

Temperature dependence of normalized Lorenz ratio, $L(T)/L_0\equiv {\kappa }_e/L_0\sigma T=\rho (T)/w_e(T)$. The solid line is a fit to the Fermi-liquid expression, $L/L_0=({\rho }_0+A{T}^2)/(w_0+B{T}^2)$.