Singlet-ground-state Magnets Coupled with Nuclear Spins. Systems with Singlet-doublet and Singlet-triplet Ions

Magnetic properties are studied of a system having two types of electronic singlet-ground-state ions, d-ion (singlet-doublet) and t-ion (singlet-triplet), by taking account of the hyperfine coupling. It is shown that the exchange interaction between the d-ion and the t-ion electronic spins affects crucially the magnetic properties. The results are discussed in connection with the experimental results of Pr metal. Double-hexagonal-close-packed (DHCP) Pr metal has attracted much interest as an electronic singletground-state (SGS) system. It contains two kinds of SGS ions, hexagonal-site and cubic-site ions. The first excited state is doublet a t the hexagonal site whereas it is triplet at the cubic site. From now on the hexagonalsite and the cubic-site ions will be called simply d-ion and t-ion, respectively. From analysis of the magnetic excitations in Pr at T 5 K Houmann et al. [l] evaluated the energy separation between the ground and the first excited states: A d ~ 3 . 5 meV for the d-ion and At& meV for the t-ion. It is believed [l-31 that the magnitude of the exchange couplings between electronic moments is insufficient to induce spontaneous ordering and that the magnetic ordering at low temperatures in Pr [2] can occur with a help of the nuclear spins. Furthermore, since At is much larger than Ad, it has been considered that the t-ions would hardly contribute to the magnetic ordering in Pr and hence little attention has been paid to the interaction between the dand tions (inter-sublattice interaction). Fkcently, however, Kawarazaki et al. [4] observed evidence for nuclearspin order at both the d-ion and the t-ion sites by neutron diffraction measurements, which indicates importance of the inter-sub-lattice coupling. The aim of the present report is to elucidate effects of the coupling between the two types of SGS ions on the magnetic properties. We assume the following two-sublattice model Hamiltonian: