Superconductivity and Nuclear Magnetism due to the Virtual Excitation of the Singlet Ground State

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This project aimed to extend the theory of superconductivity and nuclear magnetism which we had proposed for praseodimium metal and its intermetallic compounds. In our theory an atractive interaction comes from the virtual excitation of the crystal field singlet ground state. We first proved that the Migdal theorem holds for this process and set up the Eliashberg equation. By linearizing it, we obtained the superconducting transition temperature Tc for the cases where the maximum of the conduction electron susceptibility occurs at Q=0 and at the Brillouin zone boundary. For the former, we found p-wave pairing, whose degeneracy of the spin triplet states is lifted at Tc due to the crystalline field anisotropy. For the latter, d-wave pairing occurs. The mechanism to induce the attractive force also induces the mass-enhancement for the conduction electrons, which works to reduce Tc strongly. Although the increase of the s-f exchange interaction and/or the Van Vleck susceptibility augments Tc, it also induces spontaneous magnetization beyond a critical value. In this case, due to the mass enhancement effect, the superconductivity appears only below the magnetic order. This suggests a similarity with UPt3, which is known as a crystal field singlet state system. The phase diagram is obtained. We are also extending the study to derive the s-f exchange interaction from the Anderson Hamiltonian for (4f) <@D12@>D1 with strong Hund and LS couplings. On the basis of it the RKKY interaction is derived for nuclear spins. Relating to these studies we also study the nuclear spin relaxation in ultralow temperatures. In approaching the nuclear ordering, the relaxation deviates from the Korringa law and turns slow. Another study is concerning nuclear spins in the electric quadrupole field, where lz=(]SY.+-。[)I states are the lowest states. The magnetic relaxation behaves as an activation process and turns very slow inultralow temperatures.