Electrical properties of yttrium iron garnet at high temperatures

Abstract

The dc electrical conductivity ($\ensuremath{\sigma}$) and the Seebeck coefficient ($\ensuremath{\alpha}$) 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 $\ensuremath{\sigma}$ and $\ensuremath{\alpha}$ at an oxygen partial pressure (${P}_{{O}_{2}}$) of 1 atm shows extrinsic behavior of $\ensuremath{\sigma}$ for both $n$- and $p$-type samples with a thermal generation of charge carriers as the main cause of the temperature dependence of $\ensuremath{\sigma}$. 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 $\ensuremath{\alpha}$-$\ensuremath{\sigma}$ plot shows consistency between the measurements on different samples. An analysis of the experimental results leads to the temperature-independent relations ${\ensuremath{\mu}}_{+}{N}_{+}{e}^{{A}_{+}}=3.0\ifmmode\times\else\texttimes\fi{}{10}^{21}$ ${(\mathrm{V}\mathrm{sec}\mathrm{cm})}^{\ensuremath{-}1}$ and ${\ensuremath{\mu}}_{\ensuremath{-}}{N}_{\ensuremath{-}}{e}^{{A}_{\ensuremath{-}}}=5.2\ifmmode\times\else\texttimes\fi{}{10}_{20}$ ${(\mathrm{V}\mathrm{sec}\mathrm{cm})}^{\ensuremath{-}1}$ for holes (+) and electrons (-), where $\ensuremath{\mu}$, $N$, and $A$ are the drift mobility, the effective density of states, and the transport coefficient, respectively. Further results are the relations $\frac{\ensuremath{\beta}}{k}+{A}_{+}+{A}_{\ensuremath{-}}=\ensuremath{-}5.4$, and ${A}_{\ensuremath{-}}+\mathrm{ln}({g}_{\ensuremath{-}})=2.7$, where the constant $\ensuremath{\beta}$ determines the temperature dependence of the band-gap energy, and ${g}_{\ensuremath{-}}$ 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.