Magnetic Neutron Scattering in Dysprosium Aluminum Garnet. II. Short-Range Order and Critical Scattering

Abstract

Critical magnetic scattering above ${T}_{N}$ has been studied in antiferromagnetic dysprosium aluminum garnet (DAG) to determine the temperature dependence of both the correlation length ${{\ensuremath{\kappa}}_{1}}^{\ensuremath{-}1}$ and staggered susceptibility ${\ensuremath{\chi}}_{s}$. The values of the critical exponents $\ensuremath{\nu}$ and $\ensuremath{\gamma}$ in the power-law expressions ${\ensuremath{\kappa}}_{1}\ensuremath{\sim}{(\ensuremath{\Delta}T)}^{\ensuremath{\nu}}$ and ${\ensuremath{\chi}}_{s}T\ensuremath{\sim}{(\frac{\ensuremath{\Delta}T}{T})}^{\ensuremath{-}\ensuremath{\gamma}}$ were found to be 0.61\ifmmode\pm\else\textpm\fi{}0.02 and 1.16\ifmmode\pm\else\textpm\fi{}0.04, respectively. These values are slightly lower than the theoretical estimates of 0.64 for $\ensuremath{\nu}$ and 1.25 for $\ensuremath{\gamma}$ for a fcc Ising model which DAG approximates reasonably well. In addition, the critical exponent $\ensuremath{\eta}$, introduced by Fisher in modifying the Ornstein-Zernike expression for the long-range behavior of the correlation function, was estimated to be 0.12\ifmmode\pm\else\textpm\fi{}0.10.