Orbital ordering phenomena in d- and f-electron systems

Abstract

In recent decades, novel magnetism of d-and f-electron compounds has been discussed very intensively both in experimental and theoretical research fields of condensed matter physics. It has been recognized that these material groups are in the same category of strongly correlated electron systems, while the low-energy physics of d-and f-electron compounds has been separately investigated in rather different manners. One of the common features of both dand f-electron systems is certainly the existence of active orbital degree of freedom, but in f-electron materials, due to the strong spin-orbit interaction in rare-earth and actinide ions, the physics seems to be quite different from that of d-electron systems. In general, when the number of internal degrees of freedom and relevant interactions is increased, it is possible to obtain a rich phase diagram including large varieties of magnetic phases by using several kinds of theoretical techniques. However, we should not be simply satisfied with the reproduction of a rich phase diagram. It is believed that the more essential point is to seek a simple principle penetrating complicated phenomena in common with d-and f-electron materials, which opens the door to a new stage in orbital physics. In this sense, it is considered to be an important task of this paper to explain common features of magnetism in d-and f-electron systems from a microscopic viewpoint, using a key concept of orbital ordering, in addition to the review of the complex phase diagram of each material group. As a typical d-electron complex material exhibiting orbital order, we first focus on perovskite manganites, in which remarkable colossal magneto-resistance effect has been intensively studied. The manganites provide us with a good platform to understand that a simple mechanism works for the formation of complex spin, charge and orbital ordering. We also explain intriguing striped charge ordering on the orbitalordered background in nickelates and the effect of orbital ordering to resolve spin frustration in geometrically frustrated e g electron systems. Note that orbital ordering phenomena are also found in t 2g electron systems. Here we review recent advances in the understanding of orbital ordering phenomenon in Ca 2 RuO 4 . Next we discuss another spin-charge-orbital complex system such as the f-electron compound. After detailed explanation of the construction of microscopic models on the basis of a j -j coupling scheme, we introduce a d-electron-like

Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice

“…Furthermore, it is the interactions described by the Kanamori parameters that are responsible for Hund's rules in the e g manifold of a d-electron system [38,39]. Therefore, in transforming to the molecular orbital basis, we have explicitly derived Hund's rules for the E manifold of the molecule.…”

Magneto-orbital helices as a route to coupling magnetism and ferroelectricity in multiferroic CaMn7O12

“…O rbital ordering (OO) is one of the most striking manifestations of electronic correlations in a variety of materials, most notably in 3d transition-metal oxides 1 . In these systems, below a certain temperature T OO , a distinct anisotropic pattern of orbital occupation emerges from a nearly isotropic high-temperature state.…”

Microscopic Theory of Multipole Ordering in f-Electron Systems

“…When we compare this CEF energy diagram with that of the LS coupling scheme [38], we find that the shape of curves and the magnitude of excitation energy are different with each other. However, from the viewpoint of symmetry, the structure of the low-energy states is not changed between the LS and j-j coupling schemes [1]. Since we are interested in a possibility of Γ 3 quadrupole ordering, we choose the value of x as x = 0.0 in the following.…”

“…Recently, complex magnetism in rare-earth and actinide compounds has attracted much attention in the research field of condensed matter physics [1][2][3]. Since in general, spin-orbit coupling between electrons in 4 f and 5 f orbitals is strong, spin and orbital degrees of freedom are tightly coupled in f -electron materials.…”

“…It is true that several experimental results have been explained by those theoretical studies, but we believe that it is also important to promote microscopic approach for understanding of multipole phenomena in parallel with 2 Physics Research International phenomenological research. Based on this belief, the present author has developed a microscopic theory for multipolerelated phenomena with the use of a j-j coupling scheme [1,[20][21][22]. In particular, octupole ordering in NpO 2 has been clarified by the evaluation of multipole interaction with the use of the standard perturbation method in terms of electron hopping [6][7][8]23].…”