Analysis off−pmodel for octupole ordering inNpO2

Abstract

In order to examine the origin of octupole ordering in NpO2, we propose a microscopic model constituted of neptunium 5f and oxygen 2p orbitals. To study multipole ordering, we derive effective multipole interactions from the f -p model by using the fourth-order perturbation theory in terms of p-f hopping integrals. Analyzing the effective model numerically, we find a tendency toward Γ5u antiferro-octupole ordering.PACS numbers: 75.30. Et, 71.10.Fd, 75.40.Cx In the research field of condensed matter physics, it is one of currently important issues to unveil the mechanism of multipole ordering phenomena frequently observed in f -electron systems. It has been widely recognized that quadrupole ordering realizes in several felectron compounds, but recently, in addition to dipole and quadrupole ordering, a possibility of ordering of higher order magnetic multipoles, i.e., octupoles, has been discussed intensively.A typical candidate with octupole ordering is the lowtemperature ordered phase of NpO 2 , 1 since time reversal symmetry is broken in this phase, 2,3 but the detected internal field is too weak to be ascribed to dipole ordering.2,3,4 Indeed, several experimental facts 5,6,7,8 can be consistently explained by assuming longitudinal tripleq Γ 5u octupole ordering.9 In addition, recent experiments on the 17 O NMR also support the triple-q ordered state. 10,11In order to understand why such higher-order multipole order is realized in NpO 2 , it has been highly required to proceed to the microscopic research. In general, it is difficult to develop a microscopic theory for complex multipole ordering in f -electron systems beyond the phenomenological level, but it has been recently proposed to construct a microscopic f -electron model on the basis of a j-j coupling scheme.12 Following this proposal, we have studied the f -electron model on an fcc lattice composed of Np ions with hopping integrals via (f f σ) bonding, and actually found the triple-q octupole ordering.13 However, as shown in Fig. 1(a), oxygen anions exist between Np ions in actual crystal structure. Thus, it is important to clarify how the octupole ordering in the f -electron model is affected by oxygen anions.In this paper, we construct a more realistic model including also p orbitals of oxygen anions in addition to f orbitals of Np ions. We derive an effective multipole interaction model by evaluating the exchange of f electrons via p orbitals within the fourth-order perturbation with respect to p-f hopping integrals. By analyzing the effective model, we again find a tendency toward the triple-q octupole ordered phase, indicating that the f -electron model on the fcc lattice have grasped the essential point on the appearance of octupole ordering of NpO 2 .Let us discuss local f -electron states of actinide dioxides based on the j-j coupling scheme, in which we first include the spin-orbit interaction and consider only the states with total angular momentum j=5/2. From a quantitative viewpoint, this simplification may not be appropriate for actinid...

Effective Crystalline Electric Field Potential in a j– j Coupling Scheme

“…In addition, it is also possible to study complex multipole phenomena from a microscopic viewpoint by using the same f -electron model. [16][17][18][19][20][21] However, in the standard j-j coupling scheme in which j=7/2 states are simply discarded, only second-and fourthorder CEF parameters (B 6 ) are dropped. Thus, Γ + 3 doublet does not appear as a stable ground state in the j-j coupling scheme for O h symmetry.…”

Electronic properties of transuranium compounds with HoCoGa5-type tetragonal crystal structure

“…With increasing f -electron number, it has been pointed out that this two-orbital Hubbard model can be also applied to some neptunium and plutonium compounds. For instance, quite recently, magnetic structure of Np-115 [31] and octupole ordering of NpO 2 [32]- [34] have been discussed based on the two-orbital Hubbard model.…”

Microscopic Theory of Multipole Ordering in f-Electron Systems

“…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]. We have also discussed possible multipole states of filled skutterudites by analyzing multipole susceptibility of a multiorbital Anderson model based on the j-j coupling scheme [24][25][26][27][28][29].…”

“…In this sense, it seems to be natural to regard multipole as anisotropic spincharge density. This point has been emphasized in the visualization of multipole order [6][7][8]23]. Then, we have defined multipole as spin-charge density in the form of onebody operator from the viewpoint of multipole expansion of electromagnetic potential from charge distribution in electromagnetism [30,31].…”

“…In order to promote the research of multipole phenomena, felectron compounds crystallizing in the cubic structure with high symmetry are quite important. For instance, octupole ordering has been discussed in the phase IV of Ce 0.7 La 0.3 B 6 [4] and NpO 2 [3,[5][6][7][8] with cubic structure. As for NpO 2 , recently, a possibility of dotriacontapole ordering has been also pointed out [9,10].…”