Nuclear magnetic ordering in simple metals at positive and negative nanokelvin temperatures

This paper is a comprehensive review of almost twenty years of research on nuclear magnetic ordering, first in copper and later in silver and rhodium metals. The basic principles of nuclear magnetism and the measurement of positive and negative spin temperatures are discussed first. Cascade nuclear refrigeration techniques, susceptibility and nuclear-magnetic-resonance (NMR) measurements, and arrangements for neutron-diffraction experiments at nanokelvin and picokelvin temperatures are described next. Comprehensive magnetic-susceptibility and neutron-diffraction measurements on copper, which led to the discovery of at least three antiferromagnetic phases, one displaying the novel (0 ) spin structure and the other two showing the type-I order of the fcc system, are then described in detail. NMR data on silver, at T>0 and T<0, are presented next leading to the observation that silver orders antiferromagnetically at positive spin temperatures and ferromagnetically at negative spin temperatures. The authors discuss recent neutron-diffraction measurements that show that the antiferromagnetic structure at T>0 is in a single-k type-I state. NMR data on rhodium at T>0 and T<0 are also described. Results obtained on Tl, Sc, ${\mathrm{AuIn}}_2$, and metallic Pr compounds and on insulators like ${\mathrm{CaF}}_2$ are then discussed briefly. The paper is concluded by an extensive theoretical section. Calculations of conduction-electron mediated exchange interactions are described, and the mean-field theory of nuclear magnetic ordering is presented. The role of thermal and quantum fluctuations is then discussed, particularly in the selection of the antiferromagnetic ground state. Finally, theoretically calculated magnetic phase diagrams and ordered spin structures of copper and silver are presented in detail and compared with experimental results. The overall agreement is good, affirming the value of nuclear magnets in Cu and Ag as realizations of simple physical models.