Determination of the sign distribution of electric field gradient in amorphous yttrium iron garnet

An interpretation of the line-shape asymmetry for the ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ Mössbauer Zeeman spectrum in speromagnetically ordered amorphous yttrium iron garnet ($a$-YIG) at 4.2 K provides the first reported measurement of the distribution of electric-field-gradient (EFG) sign in an amorphous material. The number of iron sites with positive EFG ($n_{+}$) is found to exceed those with negative EFG ($n_{-}$) in $a$-YIG in the ratio $\frac{n_{+}}{n_{-}}\approx 1.16\pm 0.04$. This finding is in quantitative agreement with the prediction of a computer model of randomly packed spherical ions. Since $\frac{n_{+}}{n_{-}}=0\mathrm{}$ for crystalline YIG, the possibility that $a$-YIG retains any vestige of its crystalline local environment in distorted form can therefore be completely excluded.