Fermi Surfaces of Magnetic Uranium Compounds

为了有效地定量计算稀土和锕系化合物的电子能带结构，提出了一种相对论线性化增强平面波（RLAPW）方法。将RLAPW方法应用于价涨落态的立方Laves相铈化合物CeRu_2、CeCo_2和CeRh_2。计算了能带结构，构造了费米曲面。每种化合物的费米表面都由不同的薄片组成，这很好地解释了除了回旋加速器有效质量之外的德哈斯-范阿尔芬（dHvA）效应的实验结果。用同样的方法计算了重费米子U化合物UPt_3的能带结构和费米面。虽然dHvA效应的实验结果定性地得到了很好的解释，但仍有一些dHvA分支的起源不清楚。这一结果暗示了该方法的局限性，因为它忽略了现实中UPt_3中存在的反铁磁结构。然后，为了计算相对论性和自旋极化能带结构，将通常的密度泛函理论推广到外部电磁场中相互作用电子系统的相对论性电流和自旋密度泛函理论。用数密度、自旋密度和轨道电流密度作为描述系统哈密顿量的基本变量。证明了广义Hohenberg-Kohn定理成立，并导出了Kohn-Sham-Dirac型单粒子方程。单粒子方程以适合于孤立原子或离子的形式表示，并且具有类似于自旋和轨道角动量与有效磁场耦合的塞曼项的磁相互作用。单粒子方程也可以用于晶体中的电子，RLAPW方法的应用目前正在进行中。

In order to carry out quantitative calculations of the electronic energy band structure for rare-earth and actinide compounds efficiently, a relativistic linearized augmented-plane-wave (RLAPW) method is made. The RLAPW method is applied to the cubic Laves phase Ce compounds such as CeRu_2, CeCo_2 and CeRh_2 which belong to the valence fluctuation regime. The energy band structures are calculated, and the Fermi surface is constructed. The Fermi surface consists of various sheets in each compound, which explain reasonably well the experimental results for the de Haas-van Alphen (dHvA) effect except the cyclotron effective masses. The same method is applied to calculate the energy band structure and the Fermi surface for the heavy-fermion U compound UPt_3. Although the experimental results for the dHvA effect are explained qualitatively well, there remain some dHvA branches whose origins are not clear. This result implies the limitations of the method, because it neglects the antiferromagnetic structure which exists in UPt_3 in reality. Then, in order to calculate the relativistic and spin-polarized energy band structure, the usual density-functional theory is extended to a relativistic current-and spin-density-functional theory for the system of interacting electrons in an external electromagnetic field. The number density, the spin density and the orbital current density are used as basic variables to describe the Hamiltonian of the system. A generalized Hohenberg-Kohn theorem is shown to hold, and a single-particle equation of the Kohn-Sham-Dirac type is derived. The single-particle equation is represented in the form which is appropriate to an isolated atom or ion, and has the magnetic interaction similar to the Zeeman term in which the spin and the orbital angular momenta couple with an effective magnetic field. The single-particle equation can be formulated also for the electrons in a crystal, and the application of the RLAPW method to it is now in progress.