Journal of Magnetism and Magnetic Materials 100 (1991) 394-412 North-Holland Spontaneous nuclear magnetic ordering in copper and silver at nano- and picokelvin temperatures Pertti Hakonen, Olli V. Lounasmaa and Aarne Oja Low Temperature Laboratory, Helsinki University of Technology, 02150 Espoo, Finland Owing to the weak mutual interactions, spontaneous nuclear magnetic ordering in metallic copper and silver occurs at 60 nK and 560 pK, respectively. These extremely low spin temperatures can be reached by two-stage adiabatic nuclear demagnetization. Spin ordering has been investigated by employing magnetic susceptibility measurements on copper and silver and by using neutron diffraction techniques on copper. Three antiferromagnetic phases in the field-entropy plane have been discovered in copper, caused by competition between the dipolar and Ruderman-Kittel exchange interactions; only one ordered state has been found in silver. Negative spin temperatures have been produced in silver as well, and a clear ferromagnetic tendency was observed when T < 0. The theoretically calculated spin-spin interactions, ordering tempera- tures, magnetic phase diagrams and ordered spin structures are in good overall agreement with experimental data for these two metals. I. Introduction Nuclear spins in metals provide good models to investigate magnetism. The nuclei are well localized, their spins are isolated from the elec- tronic and lattice degrees of freedom at low tem- peratures, and the interactions between nuclear spins can be calculated from first principles. Therefore, nuclear magnets are particularly suit- able for testing theory against experiments. Be- cause the nuclear magneton is small, the critical temperatures for spontaneous magnetic ordering are in the submicrokelvin range. Much higher nuclear ordering temperatures, around 1 mK, have been observed in solid 3He [1], owing to the strong quantum mechanical exchange force en- hanced by the large zero-point motion, and in Van Vleck paramagnets [2], like PrNi 5 [3], in which considerable hyperfine enhancement of the magnetic field occurs. Experiments on nuclear magnetic ordering in metals are based on the pioneering studies of Kurti and his coworkers [4]. They established, in 1956, the feasibility of the nuclear demagnetiza- tion method. In spite of the limitations imposed by cryogenic techniques available at that time, the Oxford group succeeded in reaching 1 txK in the nuclear spin system of copper. The first studies of nuclear cooperative phenomena, on insulators like CaF 2 and LiH, were made by Abragam and Goldman and their coworkers at Saclay 15 years later [5,6]. Investigations of nuclear magnetic ordering in copper were started in Helsinki in the mid 1970's [7-9] by constructing a two-stage nuclear demag- netization cryostat, precooled by a dilution refrig- erator; the apparatus, the first of its kind, was specially designed for nuclear ordering experi- ments. The first important results were obtained, however, only in 1982 [10,11] when magnetic sus- ceptibility measurements showed that copper or- ders antiferromagnetically below its critical tem- perature of about 60 nK. Two years later, three antiferromagnetic phases were discovered [12,13] in a single crystal specimen of copper below the critical field B c = 0.25 mT. In order to determine the spin structures of antiferromagnetically ordered copper, neutron diffraction experiments were initiated in 1985, after a careful feasibility study [14], in a collabo- ration between the Riso National Laboratory in Denmark, the Hahn-Meitner Institute of Berlin, 0304-8853/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved