Magnetic X-ray scattering study of random field effects in Mn0.75Zn0.25F2

Abstract

We report a detailed synchrotron X-ray scattering study of the magnetic correlations in two samples of Mn0.75Zn0.25F2 as a function of temperature and applied field. The critical behavior of this system is believed to be isomorphic with that of the three-dimensional random field Ising model (RFIM). On cooling in an external magnetic field (FC), the first sample exhibits a transition to long range order (LRO) in the near-surface region, at a field dependent temperature,T N (H). In contrast, bulk neutron scattering studies show a long lived metastable domain state forming below a metastability boundary,T M (H). The transition temperatureT M (H), lies below the metastability boundary,T M (H). The temperature difference,T M (H)−T M (H), increases with increasing field and agrees closely with the value deduced from an extrapolation from aboveT M (H) of earlier, equilibrium neutron scattering results on the spin-spin correlation length. On cooling, the order parameter exponent is found to be large, β=0.30±0.05. We speculate that there is an imbalance in the random fields in the neighborhood of linear surface defects (scratches) in this sample, and that the consequent net staggered field initiates a regular random Ising transition. The second sample was cut from the first and underwent a more extensive polishing process, resulting in a smoother surface with a small density of visible defects. Interestingly, it does not attain a LRO state on cooling, but rather it forms a domain state consistent with that observed by neutron diffraction. Both samples may be prepared in a LRO state, either by cooling in zero field and subsequently applying a field (ZFC) or, at high fields, by heating from the XY phase (FHXY). We have studied the evolution of the metastable LRO state in each sample on warming. We find universal behavior in both samples at all fields studied. Specifically there is a powerlaw-like decay of the order parameter with exponent β=0.20±0.05, and a rounded transition region which may be described by a Gaussian distribution of transition temperatures. The width of this distribution scales asH2. A scaling plot of all the warming data as a function of the scaling variable (T−T C (H)/H2 is constructed. We label this non-equilibrium pseudo-critical behavior, “trompe l'oeil critical behaviour.” Phenomenologically, these results enable us to explain many previous, apparently contradictory, results in the literature.