Effects of Crystal Structure and the On-Site Coulomb Interactions on the Electronic and Magnetic Structure of Pyrochlores $A_2$Mo$_2$O$_7$ (A= Y, Gd, and Nd)

摘要

Being motivated by recent experimental studies, we investigate magneticstructures of the Mo pyrochlores $A_2$Mo$_2$O$_7$ ($A$= Y, Nd, and Gd) andtheir impact on the electronic properties. The latter are closely related withthe behavior of twelve Mo($t_{2g}$) bands, located near the Fermi level andwell separated from the rest of the spectrum. We use a mean-field Hartree-Fockapproach, which combines fine details of the electronic structure for thesebands, extracted from the conventional calculations in the local-densityapproximation, the spin-orbit interaction, and the on-site Coulomb interactionsamongst the Mo(4d) electrons, treated in the most general rotationallyinvariant form. The Coulomb repulsion U plays a very important role in theproblem, and the semi-empirical value U$\sim$1.5-2.5 eV accounts simultaneouslyfor the metal-insulator (M-I) transition, the ferromagnetic (FM) - spin-glass(SG) transition, and for the observed enhancement of the anomalous Hall effect(AHE). The M-I transition is mainly controlled by $U$. The magnetic structureat the metallic side is nearly collinear FM, due to the double exchangemechanism. The transition into the insulating state is accompanied by the largecanting of spin and orbital magnetic moments. The sign of exchange interactionsin the insulating state is controlled by the Mo-Mo distances. Smaller distancesfavor the antiferromagnetic coupling, which preludes the SG behavior in thefrustrated pyrochlore lattice. Large AHE is expected in the nearly collinear FMstate, near the point of M-I transition, and is related with the unquenchedorbital magnetization at the Mo sites. We also predict large magneto-opticaleffect in the same FM compounds.