In this one page document recent experiments on spontaneous nuclear magnetic ordering in copper and silver are discussed. In copper, below the critical field of 250 microTesla earlier susceptibility measurements had revealed three antiferromagnetic phases at spin temperatures below 60 nanoKelvin. The experimental results for the phase diagram and the ordered spin structures are in excellent agreement with experiment. In silver, the spin-spin interactions are dominated by exchange forces, and therefore this material is an ideal model for a spin one-half Heisenberg system in an fcc lattice. Experimentally, the critical magnetic field is 80 microTesla and anitferromagnetic order was found by susceptibility measurements below 560 picoKelvin. The record lowest temperature produced was 500 picoKelvin. The field versus entropy diagram of silver shows a single ordered phase. By rapid field reversal the silver nuclei have been cooled to negative spin temperatures. The reality of spin temperatures, both positive and negative, have been clearly demonstrated by these experiments. 2 refs.