The Hall Effect in Yttrium, Lanthanum, Cerium, Praseodymium, Neodymium, Gadolinium, Dysprosium, and Erbium

The Hall effect has been studied from 300°K to 20.3°K in metallic yttrium, lanthanum, cerium, praseodymium, and neodymium. The ferromagnetic rare earth metals, gadolinium, dysprosium, and erbium have been studied quantitatively only above their respective Curie temperatures with gadolinium being measured to 350°C. The measurements have been made at many temperatures using an alternating current method. Yttrium, lanthanum, gadolinium, and erbium are found to have negative Hall effects at all temperatures studied. Cerium, praseodymium, and neodymium show positive Hall effects throughout the temperature range investigated. Dysprosium metal exhibits a negative Hall effect from 300°K down to about 130°K, but below that temperature the effect is positive. This reversal is interpreted as being due to a change in the sign of the extraordinary Hall effect. The Hall coefficient of cerium is found to go through a thermal hysteresis loop in a manner similar to the electrical resistivity and other properties. Values for the ordinary Hall coefficients are obtained where necessary from the temperature variation of the Hall effect. The Hall coefficients are used to calculate for each metal the effective number of carriers, $n^{*}$, ($n^{*}=\frac{1}{\mathrm{Ne}{R}_0}$), on a simple one-band model. In addition, the two-band model, assuming electron conduction in the $5d$ band and hole conduction in the $6s$ band, is used to understand the positive effect in three of the metals and to obtain curves for the number of holes in the $6s$ band as a function of the ratio of $d$-electron mobility to $s$-hole mobility. No ordered change in the magnitude and sign of the effect along the rare earth series is observed.