Probe independence of hyperfine critical exponents

The critical exponent β for magnetically ordered materials has been obtained from a variety of hyperfine experiments, such as nuclear magnetic resonance, perturbed angular correlations, and M\"ossbauer effect. In this paper we discuss probe disturbance effects on hyperfine measurements of β. We consider both chemically pure substances and materials into which the hyperfine probe has been introduced as a dilute impurity, and emphasize the latter. From a theoretical point of view, we investigate several molecular-field models and present results of new calculations for an isolated nonmagnetic impurity in a three-dimensional Ising model. It is found that the disturbance produced by the impurity is substantially smaller in the latter case than for the corresponding molecular-field model. From an experimental point of view we present a survey of cases for which bulk and hyperfine measurements have been made on the same substance. We also report on a reanalysis of data in Ni, and present the results of power-law fits made for various ranges of reduced temperature. The cases studied include Ni ¹⁰⁰Rh, Ni ¹¹¹Cd, Ni ⁵⁷Fe, and Ni ¹⁸¹Ta, and are restricted to samples produced by diffusion or melting. On the available theoretical and experimental evidence, we conclude that values of β determined from hyperfine measurements involve probe-disturbance errors that are certainly smaller than 2% if the reduced temperature is restricted to t<10^-2 and care is taken to avoid source inhomogeneities and temperature gradients.