Phase-transition behavior in the random-field antiferromagnetFe0.5Zn0.5F2s

We present a combined magnetic x-ray and neutron scattering study of the order parameter of the diluted antiferromagnet ${\mathrm{Fe}}_{0.5}$ ${\mathrm{Zn}}_{0.5}$ ${\mathrm{F}}_2$ in an applied field. This system is believed to be modeled by the three-dimensional random-field Ising model. A long range ordered (LRO) state is prepared through a zero-field-cooled procedure (ZFC). The evolution of this LRO state is studied on warming at fixed field. The x-ray order parameter data are well described by a power-law-like transition at all fields with an exponent ${\mathrm{{\rm B}}}_{\mathrm{ZFC}}$ varying from 0.21 to 0.12. The transition region is broadened and may be described by a Gaussian distribution of transition temperatures, centered at ${\mathrm{T}}_{\mathrm{C}}$ (H), of width ${\mathrm{\sigma }}_{\mathrm{ZFC}}$ (H). It is found that ${\mathrm{\sigma }}_{\mathrm{ZFC}}$ (H)=${\mathrm{AH}}^2$ +B. This rounding is attributed to anomalously slow dynamics, which prevents equilibrium being attained for experimentally relevant time scales for T${\mathrm{T}}_{\mathrm{M}}$ (H) where ${\mathrm{T}}_{\mathrm{M}}$ (H) is the temperature below which metastability effects occur. The apparent critical behavior in fact represents a continuous evolution from metastable behavior towards equilibrium behavior. Neutron scattering studies on the same sample allow identification of ${\mathrm{T}}_{\mathrm{C}}$ (H) with the temperature at which the correlation length of the zero-field-cooled fluctuations reaches a maximum value, equal to the corresponding field-cooled value. A qualitative finite size scaling argument is presented to explain the ${\mathrm{H}}^2$ width dependence. Data showing similar scaling of the width of the ZFC transition region inferred from the temperature derivative of the uniform magnetization as measured by superconducting quantum interference device magnetometry and from neutron scattering measurements of the pseudocritical scattering are also presented. These results lead to an interpretation of indirect specific heat measurements in which the ZFC peak structure, previously attributed to critical fluctuations, is seen instead to arise entirely from a LRO contribution to the measured quantity.