Nuclear ferromagnetic ordering in silver at negative nanokelvin temperatures

Abstract

Nuclear ferromagnetic ordering in silver, caused by the antiferromagnetic Ruderman-Kittel interactions, has been observed at negative absolute temperatures T>−1.9 nK. The ordered states, reached by adiabatic demagnetization after population inversion at initial entropies S<Sc=0.82 ℜ ln2, are described by a saturation of susceptibility to −1 and by nonhysteretic response to an external field. These observations are consistent with the domain configurations calculated by Viertio and Oja in the mean field theory. The experimental critical entropy, however, does not agree with theoretical calculations. In addition to our NMR measurements leading to these findings, we also discuss basic thermodynamics at T<0 and the theoretically calculated domain configurations in simple terms.