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

本项目旨在扩展我们提出的关于金属镨及其金属间化合物的超导和核磁理论。在我们的理论中，吸引相互作用来自于晶体场单线态基态的虚激发。我们首先证明了米格达尔定理适用于这一过程，并建立了Eliashberg方程。通过线性化，我们得到了Q=0和布里渊带边界处导电电子磁化率最大值的超导转变温度Tc。对于前者，我们发现了p波对，由于晶体场的各向异性，其自旋三重态的简并度在Tc处被提升。对于后者，发生d波配对。诱导引力的机制也诱导了传导电子的质量增强，从而强烈地降低了Tc。虽然s-f交换相互作用和/或Van Vleck磁化率的增加增加了Tc，但它也诱导自发磁化超过临界值。在这种情况下，由于质量增强效应，超导性只出现在磁阶以下。这表明它与UPt3相似，UPt3被称为晶体场单线态系统。得到相图。我们还扩展了研究，从(4f) <@D12@>D1具有强Hund和LS耦合的Anderson hamilton量中推导出s-f交换相互作用。在此基础上推导了核自旋的RKKY相互作用。与这些研究相关，我们还研究了核在超低温下的自旋弛豫。在接近核有序时，弛豫偏离了Korringa定律，变得缓慢。另一项研究是关于电四极场中的核自旋，其中lz=(]SY.+-。I态是最低的态。磁弛豫表现为一个激活过程，在超低温下转动非常缓慢。

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.