Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides
The electronic structure and x-ray magnetic circular dichroism (XMCD) spectra of US, USe,
 and UTe are investigated theoretically from first principles, using the fully relativistic Dirac
 LMTO band structure method. The electronic structure is obtained with the local spin-density ap...
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| author | Antonov, V.N. Harmon, B.N. Andryushchenko, O.V. Bekenev, L.V. Yaresko, A.N. |
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| citation_txt | Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides / N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, A.N. Yaresko // Физика низких температур. — 2004. — Т. 30, № 4. — С. 411-426. — Бібліогр.: 89 назв. — англ. |
| collection | DSpace DC |
| container_title | Физика низких температур |
| description | The electronic structure and x-ray magnetic circular dichroism (XMCD) spectra of US, USe,
and UTe are investigated theoretically from first principles, using the fully relativistic Dirac
LMTO band structure method. The electronic structure is obtained with the local spin-density approximation
(LSDA), as well as with a generalization of the LSDA+U method which takes into account
that in the presence of spin–orbit coupling the occupation matrix of localized electrons becomes
non-diagonal in spin indexes. The origin of the XMCD spectra in the compounds is
examined.
|
| first_indexed | 2025-12-07T18:21:54Z |
| format | Article |
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Fizika Nizkikh Temperatur, 2004, v. 30, No. 4, p. 411–426
Electronic structure and x-ray magnetic circular
dichroism in uranium monochalcogenides
V.N. Antonov* and B.N. Harmon
Ames Laboratory, Iowa State University, Iowa 50011, USA
E-mail: antonov@ameslab.gov; antonov@imp.kiev.ua
O.V. Andryushchenko and L.V. Bekenev
Institute of Metal Physics, 36 Vernadsky Str., Kiev 03142, Ukraine
A.N. Yaresko
Max Planck Institute for Physics of Complex Systems, Dresden D-01187, Germany
Received August 7, 2003, revised October 21, 2003
The electronic structure and x-ray magnetic circular dichroism (XMCD) spectra of US, USe,
and UTe are investigated theoretically from first principles, using the fully relativistic Dirac
LMTO band structure method. The electronic structure is obtained with the local spin-density ap-
proximation (LSDA), as well as with a generalization of the LSDA+U method which takes into ac-
count that in the presence of spin–orbit coupling the occupation matrix of localized electrons be-
comes non-diagonal in spin indexes. The origin of the XMCD spectra in the compounds is
examined.
PACS: 71.28.+d, 71.25.Pi, 75.30.Mb
1. Introduction
The uranium compounds US, USe, and UTe belong
to the class of uranium monochalcogenides that crys-
tallize in the NaCl structure and order ferromag-
netically (on the uranium sublattice) at Curie temper-
atures of 178, 160, and 102 K, respectively (see, e.g.,
the review [1]). These uranium compounds exhibit
several unusual physical phenomena, which are the
reason for a continuing ongoing interest in these com-
pounds. Despite their relatively simple and highly
symmetrical NaCl structure, it has been found that the
magnetic ordering on the uranium atoms is strongly
anisotropic [2,3], with the uranium moment favoring
a [111] alignment. The magnetic anisotropy in US,
e.g., is one of the largest measured in a cubic material,
with a magnetic anisotropy constant K1 of more than
2 108• erg/cm3 [4]. Also the magnetic moment itself
is unusual, consisting of an orbital moment that is
about twice as large as the spin moment, and of oppo-
site sign [5–7]. A bulk magnetization measurement [3]
yields an ordered moment of 1.55 �B per unit formula,
and neutron scattering measurements [8] show a
slightly larger value of 1.70 �B , which is assigned to
the 5f magnetic moment. These values are far smaller
than that expected for the free ion, indicating
that some sort of «solid state effect» takes place with
the 5f states. From several experimental results (for
instance, photoemission [9], electrical resistivity [10],
pressure dependence of Curie temperature [11], and
specific heat measurements [12,13],) the 5f electrons
of US are considered to be itinerant.
It has been suggested that uranium monochalco-
genides are mixed valence systems [14]. Low-tempera-
ture ultrasonic studies on USe and UTe were per-
formed in the context of questioning the possibility of
the coexistence of magnetism and intermediate va-
lence behavior [15]. They found a monotonic trend of
the Poisson’s ratio, which decreases with increasing
chalcogenide mass and is positive in US, negative in
USe, and UTe. This indicates the possibility of inter-
mediate valence in the last two compounds. Indeed, a
© V.N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, and A.N. Yaresko, 2004
* Permanent address: Institute of Metal Physics, 36 Vernadsky Str., Kiev 03142, Ukraine
negative Poisson’s ratio, i.e. a negative C12 elastic
constant, is quite common for intermediate valence
systems, and its occurrence seems to be due to an an-
omalously low value of the bulk modulus. A negative
C12 means that it costs more energy to distort the crys-
tal from cubic to tetragonal structure than to modify
the volume. Thus, when uniaxially compressed along
a [100] direction, the material will contract in the
[010] and [001] directions, trying to maintain a cubic
structure. An explanation for a negative C12 may be
given through a breathing deformability of the acti-
nide ion due to a valence instability [16].
The dependence of the Curie temperatures TC of
US, USe and UTe on hydrostatic pressure up to
13 GPa has been determined in Ref. 17. For USe and
UTe, TC initially increases with applied pressures,
passing through maxima at pressure of about 6 GPa
and 7 GPa, respectively. For US, TC decreases mo-
notonically with pressure, which is consistent with
pressure-dependent itinerant electron magnetism.
Pressure increases the bandwidth and correspondingly
decreases the density of states at the Fermi level,
which leads to a decrease of TC. The behavior of USe
and UTe is suggestive of localized interacting 5f mo-
ments undergoing Kondo-type fluctuations, which be-
gin to exceed the magnetic interaction when TC passes
through a maximum. A theoretical analysis of these
experiments is given in Ref. 18. On the basis of band
structure calculations it is argued that the nonmo-
notonic behavior of TC under pressure is solely the re-
sult of pressure-driven increased 5f itineracy.
It must be remarked that the behavior of uranium
monochalcogenides cannot be explained entirely by a
simple trend of increasing localization with increasing
chalcogen mass [19]. Whereas such a trend is evident
in the dynamic magnetic response, in the pressure de-
pendence of the Curie temperatures and in the value of
the ordered moment, the behavior of Poisson’s ratio
and of the Curie temperature is the opposite from
what one would naively expect.
There are several band structure calculations
of uranium monochalcogenides in the literature [7,
20–28]. Kraft et al. [23] have performed the local
spin–density approximation (LSDA) calculation with
the spin–orbit interaction (SOI) in a second varia-
tional treatment for ferromagnetic uranium monochal-
cogenides (US, USe, and UTe) using the ASW me-
thod, and have shown that the magnitude of the
calculated orbital magnetic moment Ml is larger than
that of spin moment Ms and they couple to each other
in an antiparallel way. However, the magnitude of the
total magnetic moment ( Ms + Ml) is too small com-
pared to the experimental data, indicating that the
calculated Ml is not large enough.
The optical and magnetooptical (MO) spectra of
uranium monochalcogenides have been investigated
theoretically in Refs. 20,21,23,25. These theoretical
spectra are all computed from first principles, using
Kubo linear-response theory, but it appears that there
are large differences among them. Cooper and co-
workers [22] find good agreement with experiment for
the real part of the diagonal conductivity (� xx
( )1 ) of
UTe, but the much more complicated off-diagonal
conductivity (� xy
( )2 ) of US and UTe is about 4 times
larger than experiment, and also the shape of their
spectrum is different from the experimental one.
Halilov and Kulatov [20] also find an off-diagonal
conductivity which is much larger than the experi-
mental one, but they additionally obtain a diagonal
conductivity � xx
( )1 that differs substantially from ex-
periment. Gasche [21] find a Kerr rotation spectrum
of US that is quite different from experiment, and
subsequently consider the effect of an orbital polariza-
tion term to improve the ab initio Kerr spectra. Kraft
et al. [23] obtained for US, USe, and UTe reasonable
agreement with experiment for the absolute value of
the Kerr spectra. However, the shape of the Kerr spec-
tra is not reproduced by LSDA theory, since the theo-
retical spectra exhibit a double-peak structure but the
experimental spectra have only a one-peak structure.
The LSDA+U calculations presented in Ref. 25 take
into account the strong Coulomb correlations among
the 5f orbitals and are greatly improve the agreement
between theory and experiment for all three materials.
This finding appears to be consistent with the qua-
silocalized nature of the 5f electrons in these com-
pounds.
X-ray magnetic circular dichroism (XMCD) tech-
nique has developed in recent years into a powerful
magnetometry tool to investigate orbital and spin con-
tributions to magnetic moments. XMCD measures the
difference in absorption of a compound for x rays with
the two opposite (left and right ) states of circular po-
larization. The study of the 5f electron shell in ura-
nium compounds is usually performed by tuning
the energy of the x-ray close to the M45, edges of ura-
nium (located at 3552 and 3728 eV, respectively)
where electronic transitions between 3d3 25 2/ , / and
5 5 27 2f / , / states are involved. Recently XMCD mea-
surements have been successfully performed on US at
the M45, edges [29]. The XMCD spectrum for U
3 5d f� transitions in US has been calculated in Ref.
27 on the basis of the HF approximation for an ex-
tended Hubbard model. The parameters involved in
the tight-binding model were determined by fitting
the energy of Bloch electrons in the paramagnetic
state obtained in LDA band structure calculation.
412 Fizika Nizkikh Temperatur, 2004, v. 30, No. 4
V.N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, and A.N. Yaresko
There are no XMCD calculations for USe and UTe in
the literature.
With the aim of undertaking a systematic investi-
gation of the trends in uranium compounds we present
the theoretically calculated electronic structure and
XMCD spectra at M45, edges for the UX (X — S, Se,
and Te) compounds.
The paper is organized as follows. Section 2 pre-
sents a description of the crystal structure of the U
monochalcogenides and the computational details.
Section 3 is devoted to the electronic structure and
XMCD spectra of US, USe, and UTe calculated in the
LSDA and LSDA+U approximations. The XMCD the-
oretical calculations are compared to the experimental
measurements. Finally, the results are summarized in
Sec. 4.
2. Computational details
Magnetooptical effects refer to various changes in
the polarization state of light upon interaction with
materials possessing a net magnetic moment, includ-
ing rotation of the plane of linearly polarized light
(Faraday, Kerr rotation), and the complementary dif-
ferential absorption of left and right circularly polar-
ized light (circular dichroism). In the near-visible
spectral range these effects result from excitation of
electrons in the conduction band. Near x-ray absorp-
tion edges, or resonances, magnetooptical effects can
be enhanced by transitions from well-defined atomic
core levels to transition symmetry selected valence
states. There are at least two alternative formalisms
for describing resonant soft x-ray MO properties. One
uses the classical dielectric tensor [30]. Another uses
the resonant atomic scattering factor including charge
and magnetic contributions [31,32]. The equivalence
of these two descriptions (within the dipole approxi-
mation) is demonstrated in Ref. 33.
For the polar Kerr magnetization geometry and a
crystal of tetragonal symmetry, where both the four-
fold axis and the magnetization M are perpendicular
to the sample surface and the z axis is chosen parallel
to them, the dielectric tensor is composed of the diago-
nal �xx and � zz components and the off-diagonal �xy
component in the form
�
� �
�� �
� � �
�
�
�
�
xx xy
xy xx
zz
0
0 . (1)
A complete description of MO effects in this for-
malism is given by the four nonzero elements of the di-
electric tensor or, equivalently, by the complex refrac-
tive index n( )�
n i( ) ( ) ( ) ( )� � � � � � �� � � �1 (2)
for several normal modes corresponding to the propa-
gation of pure polarization states along specific direc-
tions in the sample. The solution of Maxwell’s equa-
tions yields these normal modes [34]. One of these
modes is for circular components of opposite (�)
helicity with wave vector h M| | having indexes
n i ixx xy� � �� � � � �1 � � � � . (3)
The two other cases are for linear polarization with
h M� [33]. One has electric vector E M| | and index
n i zz| | | | | |� � � �1 � � � . The other has E M� and
n i xx xy xx� � �� � � � �1 2 2� � � � �( ) / .
At normal light incidence the complex Faraday an-
gle is given by [33,35]
� � � � � �
�
F F Fi
l
c
n n( ) ( ) ( ) ( )� � � �� �2
. (4)
where c is the speed of light, and � �F ( ) and � �F ( )
are the Faraday rotation and the ellipticity. The com-
plex Faraday response describes the polarization
changes to the incident linear polarization on propa-
gation through the film of thickness l. (The incident
linearly polarized light is a coherent superposition of
two circularly waves of opposite helicity.)
Magnetic circular dichroism is of first order in M
(or �xy) and is given by � �� �� or � � �� �, respec-
tively, the later representing the magnetooptical rota-
tion (MOR) of the plane of polarization (Faraday ef-
fect). Magnetic linear dichroism (MLD) n n� � | |
(also known as the Voigt effect) is quadratic in M.
The Voigt effect is present in both ferromagnets and
antiferromagnets, while the first-order MO effects in
the forward scattering beam are absent with the net
magnetization in antiferromagnets.
The alternative consideration of the MO effects is
based on the atomic scattering factor f q( , )� , which
provides a microscopic description of the interaction
of x-ray photons with magnetic ions. For forward scat-
tering (q � 0) f Z f if( ) ( ) ( )� � �� � � � �� , where Z is
the atomic number. f �( )� and ��f ( )� are the anomalous
dispersion corrections related to each other by the
Kramers–Kronig transformation. The general equiva-
lence of these two formalisms can be seen by noting
the one-to-one correspondence of terms describing the
same polarization dependence for the same normal
modes [33]. For a multicomponent sample they relate
to � and � through:
� �
�
�
�( ) ( )� ��
2 2
2
c r
Z f Ne
i
i
i i , (5)
Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides
Fizika Nizkikh Temperatur, 2004, v. 30, No. 4 413
� �
�
�
�( ) ( )� ���
2 2
2
c r
f Ne
i
i
i , (6)
where the sum is over atomic spheres, each having
number density Ni , and re is the classical electron ra-
dius. The x-ray absorption coefficient � ��( ) of polar-
ization � may be written in terms of the imaginary
part of f� �( ) as
� �
�
�
��
�( ) ( )� ��
4 r c
fe
�
, (7)
where � is the atomic volume. The x-ray MCD,
which is the difference in x-ray absorption for right-
and left-circularly polarized photons (� � �� �) can
be represented by ( �� � ��
� �f f ). Faraday rotation � �F ( )
of linear polarization measures the MCD in the real
part �f� of the resonant magnetic x-ray-scattering am-
plitude, i.e [36]
� �
� �
�
� �F
el
c
n n
lr
f f( ) [ ] ( ( ) ( )) .� � � � � �
� � � �2
Re
� (8)
Finally, the x-ray scattering intensity from an ele-
mental magnet at the Bragg reflection measured in the
resonant magnetic x-ray-scattering experiments is just
the squared modulus of the total scattering amplitude,
which is a linear combination of ( � � �� �� � ��
� �f if f ifz z, )
with the coefficients fully determined by the experi-
mental geometry [35]. Multiple scattering theory is
usually used to calculate the resonant magnetic x-ray
scattering amplitude ( � � ��f if ) [30,35,37].
We should mention that the general equivalence of
the dielectric tensor and scattering factor descriptions
holds only in the case considering dipole transitions
contributing to the atomic scattering factor f( )� .
Higher-order multipole terms have different polariza-
tion dependence [31].
Using straightforward symmetry considerations it
can be shown that all magnetooptical phenomena
(XMCD, MO Kerr and Faraday effects) are caused by
symmetry reduction, in comparison to the paramag-
netic state, caused by magnetic ordering [38]. XMCD
properties are manifested only when SO coupling
is considered in addition. To calculate the XMCD
properties one has to account for magnetism and SO
coupling at the same time when dealing with the elec-
tronic structure of the material considered. The theo-
retical description of magnetic dichroism can be cast
into four categories. On the one hand, there are
one-particle (ground-state) and many-body (excited-
state) theories; on the other hand, there are theories
for single atoms and those which take into account
the solid state. To name a few from each category,
for atomic one-particle theories we refer to Refs. 39
and 40, for atomic many-particle multiplet theory
to Refs. 41–44, for solid many-particle theories to
Ref. 45, and for solid one-particle theories (photoelec-
tron diffraction) to Refs. 46–49. A multiple-scattering
approach to XMCD, a solid-state one-particle theory,
has been proposed by Ebert et al. [50–52] and Tamura
et al. [53].
Within the one-particle approximation, the absorp-
tion coefficient � for an incident x ray of polarization �
and photon energy �� can be determined as the proba-
bility of electron transition from an initial core state
(with wave function� j and energy Ej ) to a final unoc-
cupied state (with wave function� nk and energy Enk)
� ��
�j
n
n j( ) | | | |� � � ��
k
k ! 2
� � � �� � �( ) ( )E E E En j n Fk k� . (9)
The ! � is the dipole electron–photon interaction op-
erator
! � �"� � e a , (10)
where " are the Dirac matrices, and a� is the � polar-
ization unit vector of the photon potential vector
[ ( , , )a / i� � �1 2 1 0 , az � ( , , )0 0 1 ]. (Here +/– de-
notes, respectively, left and right circular photon po-
larizations with respect to the magnetization direction
in the solid.) More detailed expressions of the matrix
elements for the spin-polarized fully relativistic
LMTO method may be found in Refs. 52,54.
While XMCD is calculated using equation (9), the
main features can be understood already from a simpli-
fied expression for paramagnetic solids. With restric-
tion to electric dipole transitions, keeping the integra-
tion only inside the atomic spheres (due to the highly
localized core sates) and averaging with respect to po-
larization of the right, one obtains the following ex-
pression for the absorption coefficient of the core level
with (l j, ) quantum numbers [55]:
� �
� � � �
lj
l j
l l j j l l jj
j
0 1 1 12 1
4 1
( )
,
, , ,
�
�
�
�
�
� �
� � � � � �
�
� �
�
, j
j
1
�
� �
�
�
� � �
� �
� �
� �l l j j
l j l j
l j
j j j
N E C E
, ,
, ,
,
( )( )
( ) ( )
1
1 2 1
. (11)
where N El j� �, ( ) is the partial density of empty sta-
tes and the C E
l j
l j
,
, ( )� � radial matrix elements [55].
Equation (11) allows only transitions with #l � �1,
#j � �0 1, (dipole selection rules) which means that
the absorption coefficient can be interpreted as a di-
rect measure for the sum of ( , )l j -resolved DOS curves
weighted by the square of the corresponding radial
matrix element (which usually is a smooth function of
energy). This simple interpretation is also valid for
the spin-polarized case [30].
414 Fizika Nizkikh Temperatur, 2004, v. 30, No. 4
V.N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, and A.N. Yaresko
The application of standard LSDA methods to
f-shell systems meets with problems in most cases, be-
cause of the correlated nature of the f electrons. To ac-
count better for the on-site f-electron correlations, we
have adopted as a suitable model Hamiltonian that of
the LSDA+U approach [56]. The main idea is the same
as in the Anderson impurity model [57]: the separate
treatment of localized f electrons for which the Cou-
lomb f–f interaction is taken into account by a Hub-
bard-type term in the Hamiltonian
1
2
U n ni
i j
j
�
� (ni are
the f-orbital occupancies), and delocalized s p d, , elec-
trons for which the local density approximation for
the Coulomb interaction is regarded as sufficient.
Hubbard [58,59] was one of the first to point out
the importance, in the solid state, of Coulomb correla-
tions which occur inside atoms. The many-body crys-
tal wave function has to reduce to many-body atomic
wave functions as the lattice spacing is increased. This
limiting behavior is missed in the LDA/DFT. The
spectrum of excitations for the shell of an f-electron
system is a set of many-body levels describing pro-
cesses of removing and adding electrons. In the simpli-
fied case, when every f electron has roughly the same
kinetic energy � f and Coulomb repulsion energy U,
the total energy of the shell with n electrons is given
by E Un n /n fn� � �� ( )1 2 and the excitation spec-
trum is given by � �n n n fE E Un� � � ��1 .
Let us consider an f ion as an open system with a
fluctuating number of f electrons. The correct formula
for the Coulomb energy of f–f interactions as a func-
tion of the number of f electrons N given by the LDA
should be E UN N /� �( )1 2 [60]. If we subtract this
expression from the LDA total energy functional and
add a Hubbard-like term (neglecting for now ex-
change and non-sphericity) we will have the following
functional:
E E UN N / U n nLDA
i
i j
j� � � �
�
�( )1 2
1
2
. (12)
The orbital energies � i are derivatives of (12):
� �i
i
LDA
i
E
n
U n�
$
$
� � �( )
1
2
. (13)
This simple formula gives the shift of the LDA orbital
energy �U/2 for occupied orbitals (ni � 1) and
�U/2 for unoccupied orbitals (ni � 0). A similar for-
mula is found for the orbital dependent potential
V E/ ni i( ) ( )r r� � � , where the variation is taken not
on the total charge density %( )r but on the charge
density of a particular ith orbital ni ( )r :
V V U ni
LDA
i( ) ( ) ( )r r� � �
1
2
. (14)
Expression (14) restores the discontinuous behavior
of the one-electron potential of the exact density-
functional theory.
The functional (12) neglects exchange and non-
sphericity of the Coulomb interaction. In the most
general rotationally invariant form the LDA +U func-
tional is defined as [61,62]
E n E E n E nLDA U L S DA U dc� � � �[ ( ), �] [ ( )] ( �) ( �) ,% %r r( )
(15)
where E L S DA( ) [ ( )]% r is the LSDA (or LDA as in Ref.
60) functional of the total electron spin densities,
E nU( �) is the electron–electron interaction energy of
the localized electrons, and E ndc( �) is the so-called
«double counting» term which cancels approximately
the part of an electron–electron energy which is al-
ready included in E LDA. The last two terms are func-
tions of the occupation matrix �n defined using the lo-
cal orbitals � �� �lm .
The matrix � | | | |,n n m m� � �� � generally consists of
both spin-diagonal and spin-non-diagonal terms. The
latter can appear due to the spin–orbit interaction or a
noncollinear magnetic order. Then, the second term in
Eq. (15) can be written as [61–63]:
E n U nU
m
m m m m m m m m� �
�
� ��
1
2 1 2 1 2 3 4 3 4
(
, ,{ }
, ,
� �
� � � �
� � �n U nm m m m m m m m� � � �1 2 1 4 3 2 3 4, , ), (16)
where Um m m m1 2 3 4
are the matrix elements of the
on-site Coulomb interaction which are given by
U a Fm m m m m m m m
k
l
k
k
1 2 3 4 1 2 3 4
0
2
�
�
� , (17)
with F k being screened Slater integrals for a given l
and
a
k
lm Y lm lm Y lm
m m m m
k
kq kq
q k
k
1 2 3 4
4
2 1 1 2 3 4�
�
� �� �
�
�
�
| | | |* .
(18)
The � �lm Y lmkq1 2| | angular integrals of a product of
three spherical harmonics Ylm can be expressed in
terms of Clebsch–Gordan coefficients, and Eq. (18)
becomes
a C
m m m m
k
m m m m
l
k l1 2 3 4 1 2 3 4 0 0
0 2� �� �� , ( )
,
�
� �
C C
km m lm
lm
km m lm
lm
1 2 2
1
1 2 3
4
, , . (19)
Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides
Fizika Nizkikh Temperatur, 2004, v. 30, No. 4 415
The matrix elements Ummm m� � and Umm m m� � which
enter those terms in the sum in Eq. (16) which con-
tain a product of the diagonal elements of the occupa-
tion matrix can be identified as pair Coulomb and ex-
change integrals:
U Ummm m mm� � �� ,U Jmm m m mm� � �� . (20)
The averaging of the matrices Umm� and
U Jmm mm� �� over all possible pairs of m m, � defines the
averaged Coulomb U and exchange J integrals which
enter the expression for E dc. Using the properties of
the Clebsch–Gordan coefficients, one can show that
U
l
U Fmm
mm
�
�
��
�
�
1
2 1 2
0
( )
, (21)
U J
l l
U J
mm
mm mm� �
�
� �
�
�
� ��
1
2 2 1( )
( )
� � �
�
�
�F
l
C F
n l
l k
k
l
0 0
2
2
2
1
2 0 0,
, (22)
where the primed sum is over m m� & . Equations (21)
and (22) allow us to establish the following relation
between the average exchange integral J and Slater
integrals:
J
l
C Fn l
l k
l
k
�
�
�
1
2 0 0
0 2
2
2
( ), , (23)
or explicitly
J F F� �
1
14
2 4( ), for l � 2, (24)
J F F F� � �
1
6435
286 195 2502 4 6( ) for l � 3.
(25)
The meaning of U has been carefully discussed by
Herring [64]. For example, in an f-electron system
with n f electrons per atom,U is defined as the energy
cost for the reaction
2 1 1( )f f fn n n� �� � , (26)
i.e., the energy cost for moving an f electron between
two atoms which both initially had n f electrons. It
should be emphasized that U is a renormalized quan-
tity which contains the effects of screening by fast s
and p electrons. The number of these delocalized elec-
trons on an atom with n � 1 f electrons decreases
whereas their number on an atom with n � 1 f elec-
trons increases. The screening reduces the energy cost
for the reaction given by Eq. (26). It is worth noting
that because of the screening the value of U in
L(S)DA +U calculations is significantly smaller then
the bareU used in the Hubbard model [58,59].
In principle, the screened CoulombU and exchange
J integrals can be determined from supercell LSDA
calculations using Slater’s transition state technique
[65] or from constrained LSDA calculations [66–68].
Then, the LDA+U method becomes parameter-free.
However, in some cases, as for instance for bcc iron
[65], the value of U obtained from such calculations
appears to be overestimated. Alternatively, the value
of U estimated from the photoemission spectroscopy
(PES) and x-ray bremsstrahlung isochromat spectros-
copy (BIS) experiments can be used. Because of the
difficulties with unambiguous determination of U it
can be considered as a parameter of the model. Then
its value can be adjusted so as to achieve the best
agreement of the results of LDA+U calculations with
PES or optical spectra. While the use of an adjustable
parameter is generally considered an anathema among
first-principles practitioners, the LDA+U approach
does offer a plausible and practical method for the ap-
proximate treatment of strongly correlated orbitals in
solids. It has been fond that many properties evalu-
ated with the LDA+U method are not sensitive to
small variations of the value ofU around some optimal
value. Indeed, the optimal value ofU determined em-
pirically is often very close to the value obtained from
supercell or constrained density functional calcula-
tions.
All three chalcogenides, namely, US, USe, and
UTe, considered in the present work crystallize in the
NaCl type structure (B1) with space group symmetry
Fm m3 . The uranium atom is positioned at (0,0,0) and
the chalcogen at (1/2, 1/2, 1/2).
The details of the computational method are de-
scribed in our previous papers [69,70], and here we
only mention several aspects. The calculations were
performed using the fully relativistic LMTO method
for the experimentally observed lattice constants a �
= 5.86, 6.06, and 6.436 � for US, USe, and UTe, re-
spectively. To improve the potential we include addi-
tional empty spheres in the (1/4, 1/4, 1/4) posi-
tions. We used the von Barth–Hedin parametrization
[71] for the exchange-correlation potential. Brillouin
zone (BZ) integrations were performed using the im-
proved tetrahedron method [72] and the charge was
obtained self-consistently with 1330 irreducible k
points. The basis consisted of U s, p, d, f and g;
chalcogen s, p and d; empty spheres s and p LMTOs.
We have adopted the LSDA+U method [56] as a
different level of approximation to treat the elec-
tron–electron correlation. We used a generalization of
the LSDA+U method which takes into account that in
the presence of spin–orbit coupling the occupation
416 Fizika Nizkikh Temperatur, 2004, v. 30, No. 4
V.N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, and A.N. Yaresko
matrix of localized electrons becomes nondiagonal in
spin indexes [61]. Screened CoulombU and exchange
J integrals enter the LSDA+U energy functional as ex-
ternal parameters and have been set to U = 2 eV de-
rived from XPS measurements and J = 0.5 eV.
3. Results and discussion
3.1. Band structure and magnetic moments
In our band structure calculations we have per-
formed two independent fully relativistic spin-polar-
ized calculations. We consider the 5f electrons as:
itinerant electrons using the local spin-density ap-
proximation; and partly localized using the LSDA+U
approximation.
Figure 1 shows the energy band structure of US for
both the approximations. The LSDA energy band
structure of US can be subdivided into three regions
separated by energy gaps. The bands in the lowest re-
gion around –15 eV have mostly S s character with a
small amount of U sp character mixed in. The next six
energy bands are S p bands separated from the s bands
by an energy gap of about 6 eV. The width of the S p
band is about 4 eV. U 6d bands are broad and extend
between –2.5 and 10 eV. The sharp peaks in the DOS
just below and above the Fermi energy are due to the
5 5 2f / and 5f7 2/ states, respectively. Figure 1 also
shows the energy bands and total density of states of
US in the LSDA+U approximation [61,62]. The Cou-
lomb repulsion splits partially occupied U 5f5 2/
states and the LSDA+U calculations give a solution
Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides
Fizika Nizkikh Temperatur, 2004, v. 30, No. 4 417
0
0
5
5
X W K L W U X 0 4 8
US
X W K L W U X 0 4 8
– 5
– 5
– 10
– 10
– 15
– 15
E
n
e
rg
y,
e
V
E
n
e
rg
y,
e
V
DOS
LSDA+U
�
�
�
�
LSDA
Fig. 1. Self-consistent fully relativistic energy band structure and total DOS (in states/(unit cell·eV)) of US calculated
within the LSDA and LSDA+U approximations with U = 2 eV and J = 0.5 eV.
with three localized 5f electrons in US. U 5f states
just above the Fermi level are formed by the remain-
ing 5f5 2/ states, whereas the peak of 5f7 2/ states is
pushed about 1 eV upward from its LSDA position.
Figure 2 shows the calculated fully relativistic
spin-polarized partial 5f density of states of fer-
romagnetic uranium monochalcogenides calculated
in the LSDA and LSDA+U approximations. Because
of large spin–orbit interaction of 5f electrons, the
j /� 5 2 and j /� 7 2 states are fairly well separated
and the occupied states are composed mostly of the
j /� 5 2 states. The 5f7 2/ states are almost empty.
In magnets, the atomic spin Ms and orbital Ml
magnetic moments are basic quantities and their sepa-
rate determination is therefore important. Methods of
their experimental determination include traditional
gyromagnetic ratio measurements [73], magnetic form
factor measurements using the neutron scattering [74],
and magnetic x-ray scattering [75]. In addition to
these, the recently developed x-ray magnetic circular
dichroism combined with several sum rules [76,77]
has attracted much attention as a method of site- and
symmetry-selective determination of Ms and Ml . Ta-
ble presents the comparison between calculated and
experimental magnetic moments in uranium mono-
chalcogenides. For comparison, we also list the results
of previous band structure calculations. Our LSDA re-
sults obtained by the fully relativistic spin-polarized
LMTO method are in good agreement with the ASW
results of Kraft et al. [23]. The LSDA calculations for
ferromagnetic uranium monochalcogenides (US, USe,
and UTe) give a magnitude of the total magnetic mo-
ment Mt too small compared to the experimental
418 Fizika Nizkikh Temperatur, 2004, v. 30, No. 4
V.N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, and A.N. Yaresko
U 5f5/2
U 5f7/2
0
5
0
5
– 2 – 1 0 1 2 3 4
0
5
10
10
10
5
5
– 2 – 1 0 1 2 3 4
5
1 0
Energy, eV Energy, eV
LSDA LSDA+U
US
USe
UTe
Fig. 2. The partial 5f5 2/ and 5f7 2/ density of states (in states/(atom·eV)) within US, USe, and UTe calculated in the
LSDA and LSDA+U approximations.
data, indicating that the calculated Ml is not large
enough.
It is a well-known fact, however, that the LSDA
calculations fail to produce the correct value of the or-
bital moment of uranium compounds [7,78,80–82]. In
LSDA, the Kohn-Sham equation is described by a lo-
cal potential including the spin-dependent electron
density. The electric current, which describes Ml , is,
however, not included. This means that although Ms
is self-consistently determined in LSDA, there is no
framework to simultaneously determine Ml self-con-
sistently.
Numerous attempts have been made to better esti-
mate Ml in solids. They can be roughly classified into
two categories. One is based on the so-called current
density functional theory [83–85] that is intended to
extend density functional theory to include the orbital
current as an extra degree of freedom, which describes
Ml . Unfortunately the explicit form of the current
density functional is at present unknown. The other
category includes the orbital polarization (OP) [7,78,
81,82], self-interaction correction (SIC) [86], and
LSDA+U [61,62] approaches, which provide a means
beyond the LSDA scheme to calculate Ml .
For a better description of Ml , the OP functional
form of BLz
2 with the Racah parameter B has been de-
duced [7] from an atomic multiplet ground state with-
out SOI, whose S and L are given by Hund’s rules.
However, the OP method does not assure us that it
will give a good description when the SOI is included
and thus S and L are no longer good quantum num-
bers. Using the LSDA+OP method Brooks [7] ob-
tained larger magnitude of Ml and improvement in
Mt . However, they have stated that the individual
magnitudes of Ms and Ml are considered to be too
large from the analysis of the magnetic form factor,
and the ratio Ml/ Ms is still far from the experimen-
tal value for all the three uranium monochalcogenides
(Table).
Solovyev et al. [62] argue that the key parameter
responsible for the exchange-correlation enhancement
of the orbital magnetic moments in solids is the «Hub-
bard U» rather than the intra-atomic Hund’s second
rule coupling, being consistent with a more general
concept of the orbital polarization. This leads to a uni-
fied rotationally invariant LSDA+U prescription for
the orbital magnetism. Table presents the calculated
magnetic moments in uranium monochalcogenides us-
ing a generalization of the LSDA+U method [61,62].
In this calculations we usedU � 2 0. eV and J � 0 5. eV.
Table presents also the LSDA+U calculated magnetic
moments withU J� � 0 5. eV. Since in that caseUeff =
= 0 the effect of LSDA+U comes from non-spherical
terms which are determined by F2, F 4, and F6 Slater
integrals. Since the basic idea of such an approach is
similar to the OP method [7,81], we denote the last
approximation as LSDA+U(OP). The LSDA+U(OP)
approximation describes the correlations between spin
and orbital magnetic moment directions.
Figure 3 shows the 5f5 2/ partial density of states in
US calculated within the LSDA, LSDA+U(OP) and
LSDA+U approximations. The LSDA+U(OP) approx-
imation strongly affects the relative energy positions
of mj projected 5f density of states and substantially
improves their orbital magnetic moments (Table). For
example, the ratio M /Ml s in the LSDA+U(OP) cal-
culations is equal to –2.17 and –2.14 for US and UTe,
respectively. The corresponding experimental value
Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides
Fizika Nizkikh Temperatur, 2004, v. 30, No. 4 419
Table
The experimental and calculated spin Ms, orbital Ml, and
total Mt magnetic moments at uranium site (in �B) of US,
USe, and UTe.
Compound Method Ms Ml Mt – Ml/Ms
LSDA –1.53 2.14 0.60 1.41
LSDA+U(OP) –1.48 3.21 1.72 2.17
LSDA+U –1.35 3.42 2.07 2.53
US LSDA [23] –1.6 2.5 0.9 1.6
LSDA+OP [7] –2.1 3.2 1.1 1.5
OP scaled HF [78] –1.51 3.12 1.61 2.07
HF(TB) [27] –1.49 3.19 1.70 2.14
exper. [8] –1.3 3.0 1.7 2.3
exper. [3] — — 1.55 —
LSDA –1.75 2.54 0.79 1.45
LSDA+U(OP) –1.65 3.65 2.00 2.21
LSDA+U –1.96 4.61 2.65 2.35
USe LSDA [23] –1.8 2.8 1.0 1.5
LSDA+OP [7] –2.4 3.4 1.0 1.4
exper. [8] — — 2.0 —
exper. [3] — — 1.8 —
LSDA –2.12 3.12 1.00 1.47
LSDA+U(OP) –1.91 4.09 2.17 2.14
LSDA+U –2.13 4.95 2.81 2.32
UTe LSDA [23] –2.2 3.4 1.2 1.5
LSDA+OP [7] –2.6 3.4 0.8 1.3
exper. [79] –1.57 3.48 1.91 2.21
exper. [8] — — 2.2 —
exper. [3] — — 1.9 —
are –2.3 for US from the neutron measurements [8]
and –2.21 for UTe from the magnetic Compton profile
measurements [79].
The 5f spin Ms and orbital Ml magnetic moments
in US have been also calculated in Ref. 27 on the basis
of the HF approximation for an extended Hubbard
model. The tight-binding model includes the int-
ra-atomic 5f–5f multipole interaction and the SOI in
the 5f state. The parameters involved in the model
were determined by fitting with the energy of Bloch
electrons in the paramagnetic state obtained in the
LDA band structure calculation. The calculated ratio
of the moments M /Ml s of –2.14 and Ml of –3.19�B
are in good agreement with available experimental re-
sults (Table).
We should mention that the results of the
LSDA+U(OP) calculations are in close agreement
420 Fizika Nizkikh Temperatur, 2004, v. 30, No. 4
V.N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, and A.N. Yaresko
5 f
5/2
m j =
m j =
m j =
m j =
0
1
2
3
0
1
2
3
–1 0 1 2
1
2
3
LSDA+U
other
US
LSDA
LSDA+U(OP)
P
ar
tia
lD
O
S
,s
ta
te
s/
(a
to
m
·e
V
)
Energy, eV
– 5/2
–3/2
–1/2
+1/2
Fig. 3. The partial 5f5 2/ density of states (in states/(atom·eV)) in US, USe, and UTe calculated within the LSDA,
LSDA+U(OP), and LSDA+U approximations.
with the results obtained using the HF approximation
for an extended Hubbard model [27] (Table). Both
the approximations take into account the SOI and the
intra-atomic 5f–5f Coulomb interaction in the Hub-
bard model. The small differences in magnetic mo-
ments are due to slightly different values of Ueff . In
our calculations we used U J� � 0 5. eV, which gives
Ueff = 0. The authors of Ref. 27 usedU � 0 76. eV and
J � 0 5. eV, which givesUeff = 0.26 eV. Besides, there
are some small differences in the F2, F 4, and F6 Slat-
er integrals in two the calculations.
Figure 3 also shows the mj projected 5f /5 2 density
of states in US calculated in the LSDA+U approxima-
tion with U � 2 0. eV and J � 0 5. eV. The correspond-
ing partial DOSs for USe and UTe are presented in
Fig. 4. The degree of localization of occupied 5f /5 2
states is increasing from US to UTe. In US the 5f /5 2
f /5 2 states with m /j � �5 2 is strongly hybridized with
other occupied states, while the hybridization in USe
and particularly in UTe almost vanishes. The 5f /5 2
states with m /j � �5 2 are responsible for the narrow
single peak in UTe (Fig. 4). The orbital magnetic mo-
ments calculated in the LSDA+U approximation are
larger than calculated in the LSDA+U(OP) approxi-
mation, which leads to a slightly overestimated ratio
M /Ml s in comparison with the experimental data for
the LSDA+U calculations (Table).
3.2. XMCD spectra
The XMCD measurements on the U M45, edges of
US have been presented in Ref. 29. The measured
dichroic M4 line consists of a simple nearly symmetric
negative peak that has no distinct structure. Such a
Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides
Fizika Nizkikh Temperatur, 2004, v. 30, No. 4 421
5f 5/ 2
m j =
m j =
m j =
m j =
0
1
2
3
–2 –1 0 1 2
1
2
3
4
P
ar
tia
lD
O
S
,s
ta
te
s/
(a
to
m
·e
V
)
USe
UTe
other
Energy, eV
– 5/2
–3/2
–1/2
+1/2
Fig. 4. The partial 5f /5 2 density of states (in states/(atom·eV)) in US, USe, and UTe calculated within the LSDA+U
approximation.
peak is characteristic of the M4 edge of all uranium
systems. The dichroic line at the M5 edge has an asym-
metric s shape with two peaks — a stronger negative
peak and a weaker positive peak. The dichroism at the
M4 edge is more than one order of magnitude larger
than at the M5 edge.
We recall that the M4 (M5) edge corresponds to
3 3 53 2 5 2d d f/ /( )� transitions. The created 3d core
hole has electrostatic interaction with the 5f shell.
However, in a first approximation, this interaction
can be neglected since no clear multiplet structure is
distinguished in the absorption spectra. This approxi-
mation is supported theoretically since the Slater
integrals F d fk( , )3 5 andG d fk( , )3 5 are small compared
to the F f fk( , )5 5 integrals and 3d spin-orbit interac-
tion [29]. In neglect of the core-level splitting the
measured spectra reflect the density of states above
the Fermi level EF weighted by the dipole transition
probabilities. Since the XMCD technique uses circu-
larly polarized x rays, the dichroism contains informa-
tion about the character of the magnetic sublevels in
the DOS.
Because of the electric dipole selection rules
(#l � �1; #j � �0 1, ) the major contribution to the ab-
sorption at the M4 edge stems from the transitions
3 53 2 5 2d f // � and that at the M5 edge originates pri-
marily from 3 55 2 7 2d f/ /� transitions, with a weaker
contribution from 3 55 2 5 2d f/ /� transitions. For the
later case the corresponding 3 55 2 5 2d f/ /� radial ma-
trix elements are only slightly smaller than for the
3 55 2 7 2d f // � transitions. The angular matrix ele-
ments, however, strongly suppress the 3 55 2 5 2d f // �
contribution. Therefore the contribution to the
XMCD spectrum at the M5 edge from the transitions
with #j � 0 is 15 times smaller than the transitions
with #j � 1 (see Eq. 11).
Figure 5 shows the XMCD spectra of US, USe, and
UTe at the uranium M45, edges calculated within the
LSDA and LSDA+U approximations. It is clearly seen
that the LSDA calculations give inappropriate results.
The major discrepancy between the LSDA calculated
and experimental XMCD spectra is the size of the M4
XMCD peak. The LSDA underestimates the integral
intensity of the XMCD at M4 edge. As the integrated
XMCD signal is proportional to the orbital moment
[76] this discrepancy could be related to an underesti-
mation of the orbital moment by LSDA-based compu-
tational methods (Table). On the other hand, the
LSDA+U approximation produces good agreement
with the experimentally measured intensity for the
M4 XMCD spectrum. In the case of the M5 XMCD
spectrum, the LSDA strongly overestimates the value
of the positive peak. The LSDA+U(OP) approxima-
tion gives good agreement in the shape and intensity
of the XMCD spectrum at the M5 edge.
The behavior of the 5f electrons ranges from nearly
delocalized to almost localized: US is considered to be
nearly itinerant [88], while UTe is considered to be
quasilocalized [89]. So the failure of LSDA descrip-
tion of XMCD spectra in US comes as a surprise, be-
cause, if the 5f electrons are itinerant, one would ex-
pect the delocalized LSDA approach to be applicable.
However, as the integrated XMCD signal is propor-
tional to the orbital moment [76], this discrepancy
could be related to an underestimation of the orbital
moment by LSDA-based computational methods.
It is interesting to note that the LSDA+U(OP) and
LSDA+U calculations give similar results for the
XMCD spectrum at the M5 edge in the case of US and
became relatively more different going through USe
and UTe, probably reflecting the increase of degree of
422 Fizika Nizkikh Temperatur, 2004, v. 30, No. 4
V.N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, and A.N. Yaresko
X5
–2
–1
0
1
X2
–3
–2
–1
0
1
2
X2
–3
–2
–1
0
1 UTe
USe
LSDA
LSDA+U (OP)
LSDA+U
experiment
US
U
M
x-
ra
y
m
ag
n
e
tic
ci
rc
u
la
r
d
ic
h
ro
is
m
, a
rb
. u
n
its
4
,5
0 20 40 60 80 100
Energy, eV
Fig. 5. The XMCD spectra of US, USe, and UTe at the
uranium M45, edges calculated within the LSDA (dashed
lines), LSDA+U(OP) (dotted lines), and LSDA+U (solid
lines) approximations. Experimental spectra of US [87]
(open circles) were measured at magnetic field 2 T. The U
M4 spectra are shifted by –95 eV to include them in the
figure.
localization of the 5f electrons. Besides, the relative
intensity of the M5 and M4 XMCD spectra is strongly
increased going from US to UTe. Experimental mea-
surements of the XMCD spectra in USe and UTe are
highly desired.
4. Summary
We have studied by means of an initio fully-relativ-
istic spin-polarized Dirac linear muffin-tin orbital
method the electronic structure and the x-ray mag-
netic circular dichroism in US, USe, and UTe. We
found that the degree of localization of occupied 5f5 2/
states is increasing going from US to UTe. In US the 5
f5 2/ states with m /j � �5 2 is strongly hybridized
with other occupied states, while this hybridization in
USe and particularly in UTe almost vanishes. The 5
f5 2/ states with m /j � �5 2 form a narrow single peak
in UTe.
The LSDA calculations for ferromagnetic uranium
monochalcogenides (US, USe, and UTe) give the
magnitude of the total magnetic moment Mt too small
compared to the experimental data, indicating that
the calculated Ml is not large enough. On the other
hand, the LSDA+U method (with Ueff = 0, the so
called LSDA+U(OP) approximation) provides good
agreement with neutron and XMCD experimental
data. The orbital magnetic moments calculated in the
LSDA+U approximation are larger than calculated in
the LSDA+U(OP) approximation, which leads to a
slightly overestimated ratio M /Ml s in comparison
with the experimental data for the LSDA+U calcula-
tions.
The experimentally measured dichroic U M4 line
in US consists of a simple nearly symmetric negative
peak that has no distinct structure. The dichroic line
at the M5 edge has an asymmetric s shape with two
peaks — a stronger negative peak and a weaker posi-
tive peak. The major discrepancy between the LSDA
calculated and experimental XMCD spectra is the size
of the M4 XMCD peak. The LSDA underestimates
the integral intensity of the XMCD at the M4 edge.
As the integrated XMCD signal is proportional to the
orbital moment this discrepancy could be related to an
underestimation of the orbital moment by LSDA-
based computational methods. The LSDA calculations
also strongly overestimates the value of the positive
peak of the XMCD spectrum at the M5 edge. On the
other hand, the LSDA+U(OP) approximation gives
good agreement in the shape and intensity of the U
XMCD spectra at the M4 and M5 edges.
Acknowledgments
This work was carried out at the Ames Labora-
tory, which is operated for the U.S. Department of
Energy by Iowa State University under Contract
No. W-7405-82. This work was supported by the Of-
fice of Basic Energy Sciences of the U.S. Department
of Energy.
V.N. Antonov gratefully acknowledges the hospi-
tality at Ames Laboratory during his stay.
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Physics and Chemistry of the Actinides, A.J. Freeman
and G.H. Lander (eds.), North-Holland Amsterdam
(1985), V. 2, p. 29.
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|
| id | nasplib_isofts_kiev_ua-123456789-119511 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T18:21:54Z |
| publishDate | 2004 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Antonov, V.N. Harmon, B.N. Andryushchenko, O.V. Bekenev, L.V. Yaresko, A.N. 2017-06-07T07:35:19Z 2017-06-07T07:35:19Z 2004 Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides / N. Antonov, B.N. Harmon, O.V. Andryushchenko, L.V. Bekenev, A.N. Yaresko // Физика низких температур. — 2004. — Т. 30, № 4. — С. 411-426. — Бібліогр.: 89 назв. — англ. 0132-6414 PACS: 71.28.+d, 71.25.Pi, 75.30.Mb https://nasplib.isofts.kiev.ua/handle/123456789/119511 The electronic structure and x-ray magnetic circular dichroism (XMCD) spectra of US, USe,
 and UTe are investigated theoretically from first principles, using the fully relativistic Dirac
 LMTO band structure method. The electronic structure is obtained with the local spin-density approximation
 (LSDA), as well as with a generalization of the LSDA+U method which takes into account
 that in the presence of spin–orbit coupling the occupation matrix of localized electrons becomes
 non-diagonal in spin indexes. The origin of the XMCD spectra in the compounds is
 examined. This work was carried out at the Ames Laboratory,
 which is operated for the U.S. Department of
 Energy by Iowa State University under Contract
 No. W-7405-82. This work was supported by the Office
 of Basic Energy Sciences of the U.S. Department
 of Energy.
 V.N. Antonov gratefully acknowledges the hospitality
 at Ames Laboratory during his stay. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Низкотемпеpатуpный магнетизм Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides Article published earlier |
| spellingShingle | Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides Antonov, V.N. Harmon, B.N. Andryushchenko, O.V. Bekenev, L.V. Yaresko, A.N. Низкотемпеpатуpный магнетизм |
| title | Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides |
| title_full | Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides |
| title_fullStr | Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides |
| title_full_unstemmed | Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides |
| title_short | Electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides |
| title_sort | electronic structure and x-ray magnetic circular dichroism in uranium monochalcogenides |
| topic | Низкотемпеpатуpный магнетизм |
| topic_facet | Низкотемпеpатуpный магнетизм |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119511 |
| work_keys_str_mv | AT antonovvn electronicstructureandxraymagneticcirculardichroisminuraniummonochalcogenides AT harmonbn electronicstructureandxraymagneticcirculardichroisminuraniummonochalcogenides AT andryushchenkoov electronicstructureandxraymagneticcirculardichroisminuraniummonochalcogenides AT bekenevlv electronicstructureandxraymagneticcirculardichroisminuraniummonochalcogenides AT yareskoan electronicstructureandxraymagneticcirculardichroisminuraniummonochalcogenides |