Concentration dependence of the random-field-crossover scaling in ${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{F}}_2$

The proportionality between the field-induced shifts Δ${\mathit{T}}_{\mathit{c}}$(H) and Δ${\mathit{T}}_{\mathrm{eq}}$(H) of the transition and equilibrium temperatures ${\mathit{T}}_{\mathit{c}}$(H) and ${\mathit{T}}_{\mathrm{eq}}$(H) and the root-mean-square random field ${\mathit{h}}_{\mathrm{RF}}$ was studied over a wide range of concentration (0.31≤x≤0.84) in the ideal random-field Ising model (RFIM) system ${\mathrm{Fe}}_{\mathit{x}}$ ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{F}}_2$. $T sub c (H)— and ${\mathit{T}}_{\mathrm{eq}}$(H) were determined experimentally from the optical birefringence Δn, for which d(Δn)/dT exhibits a peak at ${\mathit{T}}_{\mathit{c}}$(H) proportional to the magnetic specific heat. ${\mathit{T}}_{\mathrm{eq}}$(H) was determined from the point above which zero-field-cooled and field-cooled measurements gave identical results. For all x studied, ${\mathit{T}}_{\mathit{c}}$(H) and ${\mathit{T}}_{\mathrm{eq}}$(H) were found to shift from the H=0 transition at ${\mathit{T}}_{\mathit{N}}$ as [Δ${\mathit{T}}_{\mathit{c}}$(H),Δ${\mathit{T}}_{\mathrm{eq}}$(H)]=[c,${\mathit{c}}_{\mathrm{eq}}$] ${\mathit{T}}_{\mathit{N}}$ ${\mathit{h}}_{\mathrm{RF}}^{2/\mathrm{\phi }}$ as predicted, with φ=1.42±0.03, the universal random exchange to RFIM crossover exponent, after a mean-field correction ${\mathit{bH}}^2$. The nonuniversal quantities c and ${\mathit{c}}_{\mathrm{eq}}$ were found to be of order unity as expected, but slightly x dependent. An empirical x dependence for c and ${\mathit{c}}_{\mathrm{eq}}$ is suggested. This analysis is applied to existing data on ${\mathrm{Mn}}_{\mathit{x}}$ ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$