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

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 ${{\kappa }_1}^{-1\mathrm{}}$ and staggered susceptibility ${\chi }_s$. The values of the critical exponents $\nu$ and $\gamma$ in the power-law expressions ${\kappa }_1\sim {\left(\Delta T\right)}^{\nu }$ and ${\chi }_{s}T\sim {\left(\frac{\Delta T}{T}\right)}^{-\gamma }$ were found to be 0.61±0.02 and 1.16±0.04, respectively. These values are slightly lower than the theoretical estimates of 0.64 for $\nu$ and 1.25 for $\gamma$ for a fcc Ising model which DAG approximates reasonably well. In addition, the critical exponent $\eta$, introduced by Fisher in modifying the Ornstein-Zernike expression for the long-range behavior of the correlation function, was estimated to be 0.12±0.10.