Complex-Orbital Order in Fe_3O_4 and Mechanism of the Verwey Transition

Electronic state and the Verwey transition in magnetite (Fe_3O_4) are studied using a spinless three-band Hubbard model for 3d electrons on the B sites with the Hartree-Fock approximation and the exact diagonalisation method. Complex-orbital, e.g., 1/sqrt(2)[|zx> + i |yz>], ordered (COO) states having noncollinear orbital moments ~ 0.4 mu_B on the B sites are obtained with the cubic lattice structure of the high-temperature phase. The COO state is a novel form of magnetic ordering within the orbital degree of freedom. It arises from the formation of Hund's second rule states of spinless pseudo-d molecular orbitals in the Fe_4 tetrahedral units of the B sites and ferromagnetic alignment of their fictitious orbital moments. A COO state with longer periodicity is obtained with pseudo-orthorhombic Pmca and Pmc2_1 structures for the low-temperature phase. The state spontaneously lowers the crystal symmetry to the monoclinic and explains experimentally observed rhombohedral cell deformation and Jahn-Teller like distortion. From these findings, we consider that at the Verwey transition temperature, the COO state remaining to be short-range order impeded by dynamical lattice distortion in high temperature is developed into that with long-range order coupled with the monoclinic lattice distortion.Comment: 16 pages, 13 figures, 6 tables, accepted for publication in J. Phys. Soc. Jp

Critical Scaling of the Magnetization and Magnetostriction in the Weak Itinerant Ferromagnet UIr

The weak itinerant ferromagnet UIr is studied by magnetization and magnetostriction measurements. Critical behavior, which surprisingly extends up to several Tesla, is observed at the Curie temperature $T_C\simeq45$ K and is analyzed using Arrott and Maxwell relations. Critical exponents are found that do not match with any of the well-known universality classes. The low-temperature magnetization $M_s\simeq0.5$ $\mu_B \cong const.$ below 3 T rises towards higher fields and converges asymptotically around 50 T with the magnetization at $T_C$. From the magnetostriction and magnetization data, we extract the uniaxial pressure dependences of $T_C$, using a new method presented here, and of $M_s$. These results should serve as a basis for understanding spin fluctuations in anisotropic itinerant ferromagnets.Comment: 4 pages, 3 figure