Nernst-Ettingshausen Effect in Elemental Rare-Earth Single Crystals

The transverse Nernst-Ettingshausen (N-E) coefficient $N $measurements of the elemental rare-earth (R-E) single-crystal are for the first time presented from 80 to 420 K. Since they have mainly hexagonal symmetry at room temperature, measurements are given with the heat flux along the [100] and the [001] axes. Due to their complex band structure and Fermi surface, their small thermopower (S) and their multicarrier systems involving electron (e) and hole (h) pockets, their $N$ are expected to be large. Indeed, for such systems, both $S $and $N$ can be expressed as$^{1} \quad S=(S_{e}$\textit{$\sigma $}$_{e}+ S_{h}$\textit{$\sigma $}$_{h}$\textit{)/( $\sigma $}$_{e}$\textit{+$\sigma $}$_{h})$ while $N=[(N_{e}$\textit{$\sigma $}$_{e}+ N_{h}$\textit{$\sigma $}$_{h}$\textit{)( $\sigma $}$_{e}$\textit{+$\sigma $}$_{h})+(S_{h}-S_{e})(R_{Hh}$\textit{$\sigma $}$_{h}- R_{He}$\textit{$\sigma $}$_{e}$\textit{)$\sigma $}$_{e}$\textit{$\sigma $}$_{h}$\textit{]/( $\sigma $}$_{e}$\textit{+$\sigma $}$_{h})^{a}$, where \textit{$\sigma $} is the electrical conductivity and $R_{H}$ the Hall coefficient and the subscript correspond to either carriers. Since $S_{h}>$0 and$ S_{e}<$0, the resulting $S$ should be low thus leading to a large $N$ . These solids are useful in single-material thermoelectric N-E coolers. They create a large temperature differences using thermomagnetic effects, without having to be cascaded. This would resolve th problem of contact resistances of actual multi-stage Peltier coolers, especially in the cryogenic temperature range. The dimensionless figure of merit of N-E coolers is \textit{zT}$_{N}=B^{2}N^{2}$\textit{$\sigma $(B)T/$\kappa $(B),} with $B$ is the magnetic field, $T$ the absolute temperature and \textit{$\kappa $} the thermal conductivity. a.E.H. Putley, \textit{The Hall Effect and Semiconductor Physics} , New York: Dover publication, 1968.