Metastability of the uniform magnetization in three-dimensional random-field Ising model systems. II. ${\mathrm{Fe}}_{0.47}$${\mathrm{Zn}}_{0.53}$${\mathrm{F}}_2$

Optical Faraday rotation was used to measure the uniform magnetization M versus temperature T, field H, and time t of the random-field Ising model system ${\mathrm{Fe}}_{0.47}$ ${\mathrm{Zn}}_{0.53}$ ${\mathrm{F}}_2$. The critical behavior of (∂M/∂T${)}_H$ versus T in fields up to 5 T confirms previous results at lower fields H≤1.9 T. The dynamical rounding temperature ${\varepsilon }^{\mathrm{*}}$ scales as $H^{2/\phi }$ with φ∼1.4, as predicted previously. Excess magnetization ΔM is found in the field-cooled or field-decreased metastable domain state, respectively. ΔM is concentrated at the domain walls and, hence, scales as $H^2$ at T∼$T_c$(H). On cooling ΔM approaches zero in the low-H, broad-wall limit, but ΔM is approximately constant for large H at all T<$T_c$(H), where vacancy pinning dominates. By decreasing from large H at constant low T, one subsequently finds ΔM∝[Tln(t/τ)${]}^{\mathrm{-}1}$. Both the behavior for T∼$T_c$ and for high H are essentially as predicted recently by Nattermann and Vilfan. The primary difference is that τ is not simply a constant attempt time, ${\tau }_0$∼${10}^{\mathrm{-}14}$–${10}^{\mathrm{-}10}$ s, but rather varies with T, approximately as τ=${\tau }_0$exp(DT), with D∼1.3 ${\mathrm{K}}^{\mathrm{-}1}$. This can be understood by considering the increasing influence of domain volume contributions to ΔM as T approaches $T_c$. ΔM>0 is also found on reversing the T scan of a zero-field cooled sample below but close to $T_c$. ΔM in this case is due to the freezing-in of very slow finite-size thermal fluctuations and does not indicate broken long-range order.