Critical magnetic field dependence of thermally activated surface processes.

Abstract

Activated processes at surfaces such as desorption or sublimation may exhibit a thermal anomaly at the Curie point of a magnetic substrate. We propose to measure this anomaly with an applied magnetic field H, and we predict a decrease in the reaction rate proportional to H with x(T) T, ) =2, x(T & T, ) =1, and x(T=T, ) =2/6~, where 6~=1.9 is an exponent for ordinary phase transitions. In the case of a surface transition, or if the substrate is a film with two-dimensional Ising behavior, the anomaly is significantly enhanced. PACS numbers: 68.35.Rh, 82.65.Yh In this Letter we examine the behavior of thermally activated surface processes in an applied magnetic field. In the vicinity of a continuous magnetic phase transition these processes may exhibit anomalies in their reaction rate, r(T), known as the Hedvall effect. ' The experimentally observed deviation from the Arrhenius law r(T) =k exp( — Q/ktt T) depends not only on the type of the processdesorption, sublimation, oxidation, or catalytic reaction — but also on the specific substrate-adsorbate combination and on features such as oxide-layer thickness or on details of the surface preparation. This variety complicates the theoretical understanding of the Hedvall effect considerably. An important contribution was made by Suhl and co-workers some years ago. ' Combining the Kramers to activated processes with linear-response theory, these authors expressed the activation energy Q and the attempt frequency k in Eq. (1) in terms of those static and dynamic degrees of freedom in the substrate which are coupled to the spin of the adsorbed particles. This coupling leads to a temperature dependence in k(T) and Q(T) which reAects the critical behavior of the substrate and thus causes deviations from a straight line in the Arrhenius plot ln(r) vs (1/T) near T,. It has recently been shown' that the anomaly in k, as well as in Q, is significantly weaker than predicted in earlier work for two reasons. (1) The relevant critical behavior of the substrate is that of its surface. ' In the case of the so-called ordinary transitions where the surface orders simultaneously with the bulk, the critical near-surface effects are weaker than those in the bulk. Only the bulk behavior was taken into account in Ref. 14. (2) The critical slowing down in the substrate invalidates a naive use of the Kramers approach since a clearcut separation in the time scales is no longer possible. Memory effects lead to a renormalized attempt frequency k which involves a dynamic correlation function at nonzero frequencies. Its anomaly turns out to be reduced compared to that of the zero-frequency limit employed in previous work. ' ' Such a weak anomaly appears to be in qualitative agreement with experiments. However, the uncertainties in the available data inhibit a quantitative comparison with the theory. Furthermore, these measurements of the rate, with temperature as the only control parameter, do not provide enough information to allow for stringent tests of crucial model assumptions. Therefore, we suggest Hedvall experiments be performed with an applied magnetic field H. This field is an additional parameter which can be varied reversibly in a controlled fashion during a measurement on a particular sample. We predict a decrease in the rate with increasing field as