Electrical properties of yttrium iron garnet at high temperatures

The dc electrical conductivity ($\sigma$) and the Seebeck coefficient ($\alpha$) have been measured on $n$- and $p$-type single crystals of yttrium iron garnet (YIG) in the temperature range 600-1500 K. The temperature dependence of $\sigma$ and $\alpha$ at an oxygen partial pressure ($P_{O_2}$) of 1 atm shows extrinsic behavior of $\sigma$ for both $n$- and $p$-type samples with a thermal generation of charge carriers as the main cause of the temperature dependence of $\sigma$. The intrinsic conductivity was studied at various temperatures by measurements on $p$-type samples under a low $P_{O_2}$. A compilation of the experimental data in an $\alpha$-$\sigma$ plot shows consistency between the measurements on different samples. An analysis of the experimental results leads to the temperature-independent relations ${\mu }_{+}{N}_{+}{e}^{A_{+}}=3.0\mathrm{}\times {10}^{21}$ ${\mathrm{}\left(\mathrm{V}\sec \mathrm{cm}\right)\mathrm{}}^{-1\mathrm{}}$ and ${\mu }_{-}{N}_{-}{e}^{A_{-}}=5.2\mathrm{}\times {10}_{20}$ ${\mathrm{}\left(\mathrm{V}\sec \mathrm{cm}\right)\mathrm{}}^{-1\mathrm{}}$ for holes (+) and electrons (-), where $\mu$, $N$, and $A$ are the drift mobility, the effective density of states, and the transport coefficient, respectively. Further results are the relations $\frac{\beta }{k}+A_{+}+A_{-}=-5.4\mathrm{}$, and $A_{-}+\ln \left(g_{-}\right)=2.7\mathrm{}$, where the constant $\beta$ determines the temperature dependence of the band-gap energy, and $g_{-}$ is the spin degeneracy factor of Si impurities in YIG. The results are discussed in terms of the localized hopping model for YIG, the small-polaron model, and the large-polaron model. For both $n$- and $p$-type YIG the large-polaron model is in best agreement with the results.