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The thermal Hall conductivity $\kappa_{xy}$ and Hall conductivity$\sigma_{xy}$ in CeCoIn$_5$ are used to determine the Lorenz number ${\calL}_H$ at low temperature $T$. This enables the separation of the observedthermal conductivity into its electronic and non-electronic parts. We uncoverevidence for a charge-neutral, field-dependent thermal conductivity, which weidentify with spin excitations. At low $T$, these excitations dominate thescattering of charge carriers. We show that suppression of the spin excitationsin high fields leads to a steep enhancement of the electron mean-free-path,which leads to an interesting scaling relation between the magnetoresistance,thermal conductivity and $\sigma_{xy}$.

The Lorenz number in CeCoIn$_5$ inferred from the thermal and charge Hall currents