Single-crystal Mössbauer measurement of the critical exponent β in the random-exchange Ising system ${\mathrm{Fe}}_{0.9}$${\mathrm{Zn}}_{0.1}$${\mathrm{F}}_2$

Mössbauer measurements of the hyperfine field, $H_{\mathrm{hf}\left(\mathrm{T}\right)}$, for the random-exchange Ising system ${\mathrm{Fe}}_{0.9}$ ${\mathrm{Zn}}_{0.1}$ ${\mathrm{F}}_2$ are reported for the critical region. Concentration gradients were minimized by choosing a single crystal with its growth axis perpendicular to the plane of the absorber. Inhomogeneous broadening was treated by fitting with four magnetic sites, using a procedure that explicitly diagonalizes the Hamiltonian. This indicates that residual short-range order is negligible, demonstrates that $H_{\mathrm{hf}}$ is aligned with a principal axis of the electric-field gradient, and gives excellent fits. Rounding of the transition was determined via constant-velocity thermal scanning, and implies that residual concentration variability was <0.03 at. %. After corrections to scaling, the data yield a critical exponent β=0.350(9) in the reduced-temperature range of 3×${10}^{\mathrm{-}4}$<t${<10\mathrm{}}^{\mathrm{-}1}$. This result is consistent with the most recent theoretical prediction, β=0.3494(15).