195 research outputs found
A theory of the electric quadrupole contribution to resonant x-ray scattering: Application to multipole ordering phases in Ce_{1-x}La_{x}B_{6}
We study the electric quadrupole (E2) contribution to resonant x-ray
scattering (RXS). Under the assumption that the rotational invariance is
preserved in the Hamiltonian describing the intermediate state of scattering,
we derive a useful expression for the RXS amplitude. One of the advantages the
derived expression possesses is the full information of the energy dependence,
lacking in all the previous studies using the fast collision approximation. The
expression is also helpful to classify the spectra into multipole order
parameters which are brought about. The expression is suitable to investigate
the RXS spectra in the localized f electron systems. We demonstrate the
usefulness of the formula by calculating the RXS spectra at the Ce L_{2,3}
edges in Ce_{1-x}La_{x}B_{6} on the basis of the formula. We obtain the spectra
as a function of energy in agreement with the experiment of
Ce_{0.7}La_{0.3}B_{6}. Analyzing the azimuthal angle dependence, we find the
sixfold symmetry in the \sigma-\sigma' channel and the threefold onein the
\sigma-\pi' channel not only in the antiferrooctupole (AFO) ordering phase but
also in the antiferroquadrupole (AFQ) ordering phase, which behavior depends
strongly on the domain distribution. The sixfold symmetry in the AFQ phase
arises from the simultaneously induced hexadecapole order. Although the AFO
order is plausible for phase IV in Ce_{1-x}La_{x}B_{6}, the possibility of the
AFQ order may not be ruled out on the basis of azimuthal angle dependence
alone.Comment: 12 pages, 6 figure
Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB
A minimal model for multipole orders in CeB shows that degeneracy of the
quadrupole order parameters and strong spin-orbit coupling lead to peculiar
temperature and magnetic-field dependences of the X-ray reflection intensity at
superlattice Bragg points. Furthermore, the intensity depends sensitively on
the surface direction. These theoretical results explain naturally recent X-ray
experiments in phases II and III of CeB. It is predicted that under weak
magnetic field perpendicular to the (111) surface, the reflection intensity
should change non-monotonically as a function of temperature.Comment: 4 pages, 5 figure
Neutron scattering study of magnetic ordering and excitations in the ternary rare-earth diborocarbide Ce^{11}B_2C_2
Neutron scattering experiments have been performed on the ternary rare-earth
diborocarbide CeBC. The powder diffraction experiment confirms
formation of a long-range magnetic order at K, where a
sinusoidally modulated structure is realized with the modulation vector . Inelastic excitation spectra in the
paramagnetic phase comprise significantly broad quasielastic and inelastic
peaks centered at and 65 meV.
Crystalline-electric-field (CEF) analysis satisfactorily reproduces the
observed spectra, confirming their CEF origin. The broadness of the
quasielastic peak indicates strong spin fluctuations due to coupling between
localized spins and conduction electrons in the paramagnetic phase. A
prominent feature is suppression of the quasielastic fluctuations, and
concomitant growth of a sharp inelastic peak in a low energy region below
. This suggests dissociation of the conduction and localized
electrons on ordering, and contrasts the presently observed incommensurate
phase with spin-density-wave order frequently seen in heavy fermion compounds,
such as Ce(RuLa)Si.Comment: accepted for publication in Phys. Rev.
Resonant X-Ray Scattering from the Quadrupolar Ordering Phase of CeB_6
We theoretically investigate the origin of the resonant x-ray scattering
(RXS) signal near the Ce absorption edge in the quadrupolar ordering
phase of CeB, considering the intersite interaction between the
states in the initial state. The anisotropic charge distribution of the
states modulates the states through the intra-atomic Coulomb interaction
and thereby generates a large RXS superlattice intensity. The temperature and
magnetic field dependence indicates that the induced dipolar and octupolar
orders have little influence on the RXS spectra, in good agreement with the
recent experiment.Comment: 4 pages, 4 figure
Antiferro-quadrupole Ordering of CeB Studied by Resonant X-ray Scattering
Under zero magnetic field, a quadrupolar order parameter at q_Q=(1/2,1/2,1/2)
in a typical antiferro-quadrupole (AFQ) ordering compound CeB6 has been
observed for the first time by means of a resonant X-ray scattering (RXS) te\
chnique. The RXS is observed at the 2p->5d dipole transition energy of the Ce
L3-edge. Using this RXS technique to observe the pure order parameter of the
AFQ state, the magnetic phase diagram of Phase II is first determined.Comment: 7 pages, 4 figure
Metal-insulator transition in PrRuP and SmRuP investigated by optical spectroscopy
Electronic structures of the filled-skutterudite compounds PrRuP
and SmRuP, which undergo a metal-insulator transition (MIT) at
= 60 K and 16 K, respectively, have been studied by means of
optical spectroscopy. Their optical conductivity spectra develop an energy gap
of 10 meV below . The observed characteristics of the energy
gap are qualitatively different from those of the Kondo semiconductors. In
addition, optical phonon peaks in the spectra show anomalies upon the MIT,
including broadening and shifts at and an appearance of new peaks
below . These results are discussed in terms of density waves or
orbital ordering previously predicted for these compounds.Comment: 4pages, 4figures, submitted to Physical Review
Fluctuation Effects on the Quadrupolar Ordering in Magnetic Field
Effects of magnetic field on the quadrupolar ordering are investigated with
inclusion of fluctuation of order parameters. For the simplest model with the
nearest-neighbor quadrupolar interaction, the transition temperature and the
specific heat are derived by the use of the recently proposed effective medium
theory. It is shown that magnetic field H has two competing effects on the
quadrupolar ordering; one is to encourage the ordering by suppressing the
fluctuation among different components of order parameters, and the other is to
block the ordering as in antiferromagnets. The former is found to be of order
H^2 and the latter of order H^4. Hence the fluctuation is suppressed for weak
fields, and the transition temperature increases with magnetic field. The
fluctuation effect is so strong that the entropy released at the quadrupolar
ordering is only about half of the full value ln 4 even without the Kondo
effect.Comment: 10 pages including 3 Postscript figure
Magnetic phase diagram of antiferroquadrupole ordering in HoB2C2
The magnetic phase diagram for antiferro-quadrupole (AFQ) ordering in
tetragonal HoBC has been investigated by measurements of elastic
constants , and in fields along the basal -
plane as well as the principal [001]-axis. The hybrid magnet (GAMA) in Tsukuba
Magnetic Laboratory was employed for high field measurements up to 30 T. The
AFQ phase is no longer observed above 26.3 T along the principal [001] axis in
contrast to the relatively small critical field of 3.9 T in fields applied
along the basal [110] axis. The quadrupolar intersite interaction of
and/or is consistent with the anisotropy in the magnetic phase diagram
of the AFQ phase in HoBC.Comment: Phys. Rev. B. (2005) in press. approx 8 pages, 10 figure
Interpocket polarization model for magnetic structures in rare-earth hexaborides
The origin of peculiar magnetic structures in cubic rare-earth (R)
hexaborides RB_6 is traced back to their characteristic band structure. The
three sphere-like Fermi surfaces induce interpocket polarization of the
conduction band as a part of a RKKY-type interaction. It is shown for the
free-electron-like model that the interpocket polarization gives rise to a
broad maximum in the intersite interaction I(q) around q=(1/4,1/4,1/2) in the
Brillouin zone. This maximum is consistent with the superstructure observed in
R=Ce, Gd and Dy. The wave-number dependence of I(q) is independently extracted
from analysis of the spin-wave spectrum measured for NdB_6. It is found that
I(q) obtained from fitting the data has a similarly to that derived by the
interpocket polarization model, except that the absolute maximum now occurs at
(0,0,1/2) in consistency with the A-type structure. The overall shape of I(q)
gives a hint toward understanding an incommensurate structure in PrB_6 as well.Comment: 5 pages, 3 figures, submitted to J.Phys.Soc.Jp
Orbital Kondo Effect in CeLaB: Scaling Analysis
Peculiarity of the Kondo effect in CeLaB is investigated on
the basis of the scaling equations up to third order. For the case where the
- charge fluctuation enters in addition to the - one, the
effective exchange interaction becomes anisotropic with respect to the orbital
pseudospins which represent the two different orbitals in the ground
state. Because of different characteristic energies for electric and magnetic
tensors, scaling with the single Kondo temperature does not apply to physical
quantities such as the resistivity and magnetic susceptibility. Possibility of
a bizzare phase is pointed out where the RKKY interaction leads to the spin
ordering without orbital ordering. This phase serves as a candidate of the
phase IV which is observed to be isotropic magnetically.Comment: 10 pages, 4 eps figures, submitted to PR
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