Analysis of Specific Heat Data in the Critical Region of Magnetic Solids

Abstract

A detailed analysis of specific heat data in the critical region of magnetic solids is presented. An inverse power law, whose strength is measured by the exponent α, is used to describe the temperature dependence of the magnetic specific heat. Other parameters used include the power law coefficient A, the critical temperature Tc, and a constant background term B. Advanced techniques of data analysis suitable for estimation of nonlinear parameters and their errors under conditions of realistically weighted experimental data were used to obtain the dependence of α, Tc, A, and B on the range of data points included in the fit. Those exponents and parameters that provide the best overall fit to the data have been found. Literature references to 49 experiments from 1935 to 1971 are given. We present in tabular form the values of α, A, and B for 24 different magnetic crystals. With some exceptions, the best fits to the data suggest that in the temperature range studied the magnetic specific heat is not symmetric; the exponent α depends on the range of data included in the fit, varies widely from material to material, and in many cases is definitely negative below the critical temperature; and that there is little evidence that the asymptotic region is being adequately sampled by experiment. These results have the implication that until such time as we can adequately account for departures from the expected sharp peak in the data at Tc (data rounding) and corrections to asymptotic scaling, then comparisons between magnetic specific heat experiments and lowest order scaling predictions are to this date still tenuous.