Electron transport in heavily doped GdN

We report measurements of electron transport phenomena in the intrinsic ferromagnetic semiconductor GdN doped with $1.3\times {10}^{21}{\mathrm{cm}}^{-3}$ electrons. The conductivity, carrier concentration, and thermoelectric power are compared with expectations based on an LSDA+$U$ band structure. In the ferromagnetic state the carriers fill the majority-spin conduction band pockets to the bottom of the minority-spin band. The resistance implies an electron mobility of 18 ${\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at zero temperature, and in turn a mean-free path of 10–30 nm. Spin disorder scattering rapidly reduces the mobility near the 70 K Curie temperature ($T_{\text{C}}$). The thermoelectric power is negative in the paramagnetic phase, as expected for a $n$-type conductor, with a magnitude that is in agreement with the Fermi energy implied by the band structure. The thermopower reverses sign to be positive in the ferromagnetic phase, which correlates with a strongly temperature-dependent electron diffusion from spin-disorder scattering that increases rapidly as the temperature rises toward $T_{\text{C}}$.

Figure 1

The band structure of GdN calculated within the LSDA+$U$ approximation and tuned to optical measurements of the direct gap at the X point [10]. The expanded view shows the axes of the prolate spheroid in the majority-spin conduction-band pocket.

Figure 2

Temperature dependent resistivity in an epitaxial GdN film showing a strongly peaked resistivity at the Curie temperature. The inset shows the temperature derivative of the resistivity, which clearly peaks at a temperature lower than than $T_{\text{C}}$.

Figure 3

Hall resistance of a GdN film. The Hall effect is linear in the paramagnetic phase (300 and 90 K) but in the ferromagnetic phase it is augmented by the rise of the anomalous Hall effect as the magnetization rises to 2.1 T. The high-field slope is used to give a first approximation to the carrier concentration plotted in Fig. 4.

Figure 4

The electron concentration (a) and mobility (b) in the GdN film.

Figure 5

The Seebeck coefficient of an epitaxial GdN film measured from ambient temperature to 5 K.