23 research outputs found
Effective Crystalline Electric Field Potential in a j-j Coupling Scheme
We propose an effective model on the basis of a - coupling scheme to
describe local -electron states for realistic values of Coulomb interaction
and spin-orbit coupling , for future development of microscopic
theory of magnetism and superconductivity in -electron systems, where
is the number of local electrons. The effective model is systematically
constructed by including the effect of a crystalline electric field (CEF)
potential in the perturbation expansion in terms of . In this paper,
we collect all the terms up to the first order of . Solving the
effective model, we show the results of the CEF states for each case of
=25 with symmetry in comparison with those of the Stevens
Hamiltonian for the weak CEF. In particular, we carefully discuss the CEF
energy levels in an intermediate coupling region with in the order
of 0.1 corresponding to actual -electron materials between the and
- coupling schemes. Note that the relevant energy scale of is the
Hund's rule interaction. It is found that the CEF energy levels in the
intermediate coupling region can be quantitatively reproduced by our modified
- coupling scheme, when we correctly take into account the corrections in
the order of in addition to the CEF terms and Coulomb interactions
which remain in the limit of =. As an application of the
modified - coupling scheme, we discuss the CEF energy levels of filled
skutterudites with symmetry.Comment: 12 pages, 7 figures. Typeset with jpsj2.cl
Multipole State of Heavy Lanthanide Filled Skutterudites
We discuss multipole properties of filled skutterudites containing heavy
lanthanide Ln from a microscopic viewpoint on the basis of a seven-orbital
Anderson model. For Ln=Gd, in contrast to naive expectation, quadrupole moments
remain in addition to main dipole ones. For Ln=Ho, we find an exotic state
governed by octupole moment. For Ln=Tb and Tm, no significant multipole moments
appear at low temperatures, while for Ln=Dy, Er, and Yb, dipole and
higher-order multipoles are dominant. We briefly discuss possible relevance of
these multipole states with actual materials.Comment: 5 pages, 3 figure
Multipole as -Electron Spin-Charge Density in Filled Skutterudites
It is shown that -electron multipole is naturally defined as spin-charge
one-electron density operator in the second-quantized form with the use of
tensor operator on the analogy of multipole expansion of electromagnetic
potential from charge distribution in electromagnetism. Due to this definition
of multipole, it is possible to determine multipole state from a microscopic
viewpoint on the basis of the standard linear response theory for multipole
susceptibility. In order to discuss multipole properties of filled
skutterudites, we analyze a seven-orbital impurity Anderson model by employing
a numerical renormalization group method. We show our results on possible
multipole states of filled skutterudite compounds.Comment: To appear in the Proceedings of International Conference on "New
Quantum Phenomena in Skutterudite and Related Systems" (September 2007, Kobe,
Japan
Microscopic Approach to Magnetism and Superconductivity of -Electron Systems with Filled Skutterudite Structure
In order to gain a deep insight into -electron properties of filled
skutterudite compounds from a microscopic viewpoint, we investigate the
multiorbital Anderson model including Coulomb interactions, spin-orbit
coupling, and crystalline electric field effect. For each case of
=113, where is the number of electrons per rare-earth ion, the
model is analyzed by using the numerical renormalization group (NRG) method to
evaluate magnetic susceptibility and entropy of electron. In order to make
further step to construct a simplified model which can be treated even in a
periodic system, we also analyze the Anderson model constructed based on the
- coupling scheme by using the NRG method. Then, we construct an orbital
degenerate Hubbard model based on the - coupling scheme to investigate
the mechanism of superconductivity of filled skutterudites. In the 2-site
model, we carefully evaluate the superconducting pair susceptibility for the
case of =2 and find that the susceptibility for off-site Cooper pair is
clearly enhanced only in a transition region in which the singlet and triplet
ground states are interchanged.Comment: 14 pages, 11 figures, Typeset with jpsj2.cl
Orbital ordering phenomena in - and -electron systems
In recent decades, novel magnetism of - and -electron compounds has
been discussed very intensively both in experimental and theoretical research
fields of condensed matter physics. It has been recognized that those material
groups are in the same category of strongly correlated electron systems, while
the low-energy physics of - and -electron compounds has been separately
investigated rather in different manners. One of common features of both -
and -electron systems is certainly the existence of active orbital degree of
freedom, but in -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 -electron systems. In general, when the number of
internal degrees of freedom and relevant interactions is increased, it is
possible to obtain 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 rich phase diagram. It is believed
that more essential point is to seek for a simple principle penetrating
complicated phenomena in common with - and -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 article to explain common features
of magnetism in - and -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.Comment: 112 pages, 38 figure
Construction of a Microscopic Model for Yb and Tm Compounds on the Basis of a \mib{j}-\mib{j} Coupling Scheme
We provide a prescription to construct a microscopic model for heavy
lanthanide systems such as Yb and Tm compounds by exploiting a - coupling
scheme. Here we consider a situation with a large spin-orbit coupling, in which
=5/2 sextet is fully occupied, while =7/2 octet is partially occupied,
where denotes total angular momentum. We evaluate crystalline electric
field potentials and Coulomb interactions among the states of the =7/2 octet
to construct a local Hamiltonian in the - coupling scheme. Then, it is
found that the local -electron states composed of the =7/2 octet agree
quite well with those of seven orbitals even for a realistic value of the
spin-orbit coupling. As an example of the application of the present model, we
discuss low-temperature multipole states of Yb- and Tm-based filled
skutterudites by analyzing multipole susceptibility of the Anderson model in
the - coupling scheme with the use of a numerical renormalization group
technique. From the comparison with the numerical results of the seven-orbital
Anderson model, it is concluded that the multipole state is also well
reproduced by the - coupling model, even when we include the
hybridization between conduction and electrons for the realistic value of
the spin-orbit coupling. Finally, we briefly discuss future applications of the
present prescription for theoretical research on heavy lanthanide compounds.Comment: 12 pages, 8 figures
Exciton Mediated Triplet Superconductivity in Th System PrOs4Sb12
In PrOs4Sb12, the lowest-lying singlet and triplet states in a Pr 4f^2
configuration hybridize with conduction electrons having local a_u and t_u
point-group symmetries. It is shown that for an attractive triplet pairing
interaction, the orbital degrees of freedom of the t_u component are important.
In addition, the Th point-group symmetry characteristic of skutterudites plays
an important role in stabilizing triplet superconductivity.Comment: 4 pages, 2 figure