Nuclear Ferromagnetism in KMgF3
Ferromagnetism of the 19F spins in monocrystalline spherical samples of KMgF3 has been studied in high field and at negative spin temperature with the external field along either the  axis or the  axis. The methods of study of nuclear magnetic order axe described in Ref. (1).
KMgF3 is a cubic perovskite where the fluorine nuclei form three simple cubic lattices with anisotropic chemical shifts. For a general orientation of the external field, these lattices are magnetically inequivalent, both in chemical shift and in secular dipolar interactions. For dipolarly coupled nuclear spins, the transition temperature for magnetic ordering is in the microkelvin range. The cooling of the spins is produced by a two-step process: dynamic nuclear polarization (DNP) in high field through off- resonance ESR irradiation of paramagnetic centres at low concentration, followed by nuclear adiabatic demagnetization in the rotating frame (ADRF). The latter can be made so as to result in a spin temperature either positive or negative. The ordering takes place via the secular dipolar interactions. At negative spin temperature, theory predicts the occurrence of ferromagnetism with domains in the form of thin slices normal to the external field and carrying opposite magnetizations.
The most severe experimental problem is that of doping the cristals with proper paramagnetic centres so as to produce the largest possible nuclear polarization with the lowest possible concentration of centers. We have used F centers by bombarding the samples with 1.5 MeV electrons. The best results were obtained with an irradiation of 40 minutes at 230 K. The DNP, performed in a dilution refrigerator, in a field of 4.8 T and H.F. irradiation frequency of 135 GHz, yields a maximum polarization of about 70% after 12 hours. The paramagnetic center relative concentration, of the order of 10-4, produces a non-negligible magnetic perturbation of the fluorine spin sytem.
Most experiments were performed with the field parallel to the  axis for which two of the three cubic lattices of19 F are equivalent. At the average Larmor frequency of 192.8 MHz, their resonance frequency is about 2 kHz above that of the third 19F cubic lattice (σ⊥-σǁ ≃ 10 ppm). In the ordered state, the two kinds of spins experience different average dipolar field and the magnitudes of their polarizations are different: the ordering corresponds to a two-sublattice ferromagnetism. Furthermore, because of the different chemical shifts, the polarization magnitudes of each kind of spin are not the same in the domains of bulk opposite magnetization. The theoretical description of the ordering uses two different approaches: the Weiss-field approximation and the so-called ‘Physical model’ that takes partially into account the short-range correlation
between spins (2). The experimental observations are those of the absorption signal of the 19F spins and that of the 39K spins. The latter, of low gyromagnetic ratio, play a negligible part in the ordering and are mostly useful for ‘spying’ the fluorine spin system. The ferromagnetic ordering shows up from the variation of the transverse susceptibility as a function of dipolar energy, both quantities deduced from the fluorine absorption signal, and is also revealed by the splitting of the 39K resonance. The shape of the 19F NMR signal exhibits two remarkable features. Firstly, the existence of two peaks, both in the absorption and in the emission part of the signal, a result of the two-sublattice ferromagnetism where spins of different kinds have different polarizations and experience different Weiss field; secondly, the fact that the signal is not antisymmetric, reflecting the lack of symmetry between the domains of opposite magnetizations resulting from the different chemical shifts of the two kinds of 19F spins.
There is an overall agreement of the results with theoretical expectations which is, however, only qualitative. This is mostly due to the perturbation of the system by the dipolar field of the paramagnetic centres whose main effects are: a slower increase of transverse susceptibility with dipolar energy in the paramagnetic state, a decrease of the transition entropy and a broadening of the NMR signals.
With the external field parallel to the  axis, all 19F spins are equivalent. Ferromagnetism with domains is in that case very similar to that previously observed in CaF2, and in particular, gives rise to an antisymmetric NMR signal. It has been investigated mostly for comparison with the former field orientation. The evidence for the occurrence of ferromagnetism results much more clearly from the splitting of the 39K Zeeman signal than from the variation of the transverse susceptibility.