Electronic structure and magneto-optical Kerr effect in the compound UCuP₂
The optical and magneto-optical (MO) spectra of the fernary compound UCuP₂ are investigated from first principles, using the fully relativistic Dirac linear-muffin-tin-orbital band structure method and density-functional theory in the local spin-density approximation. Within a band-like description...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Цитувати: | Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ / O. Horpynyuk, V.V. Nemoshkalenko, V.N. Antonov, B.N. Harmon, A.N. Yaresko // Физика низких температур. — 2002. — Т. 28, № 7. — С. 745-751. — Бібліогр.: 51 назв. — англ. |
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| author | Horpynyuk, O. Nemoshkalenko, V.V. Antonov, V.N. Harmon, B.N. Yaresko, A.N. |
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| citation_txt | Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ / O. Horpynyuk, V.V. Nemoshkalenko, V.N. Antonov, B.N. Harmon, A.N. Yaresko // Физика низких температур. — 2002. — Т. 28, № 7. — С. 745-751. — Бібліогр.: 51 назв. — англ. |
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| container_title | Физика низких температур |
| description | The optical and magneto-optical (MO) spectra of the fernary compound UCuP₂ are investigated from first principles, using the fully relativistic Dirac linear-muffin-tin-orbital band structure method and density-functional theory in the local spin-density approximation. Within a band-like description of the 5f electrons, good agreement with the measured MO spectra is obtained. The origin of the Kerr rotation in the compound is examined.
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Fizika Nizkikh Temperatur, 2002, v. 28, No. 7, p. 745–751
Electronic structure and magneto-optical Kerr effect
in the compound UCuP2
O. Horpynyuk and V. V. Nemoshkalenko
Institute of Metal Physics, 36 Vernadsky Str., 252142 Kiev, Ukraine
V. N. Antonov* and B. N. Harmon
Ames Laboratory, Iowa State University, Iowa, 50011
E-mail: anton@caskad.imp.kiev.ua
A. N. Yaresko
Max Planck Institute CPFS, 40, Nöthnitzer Str., D-01187 Dresden, Germany
Received November 12, 2001
The optical and magneto-optical (MO) spectra of the ternary compound UCuP2 are inves-
tigated from first principles, using the fully relativistic Dirac linear-muffin-tin-orbital
band structure method and density-functional theory in the local spin-density approximation.
Within a band-like description of the 5f electrons, good agreement with the measured MO
spectra is obtained. The origin of the Kerr rotation in the compound is examined.
PACS: 71.28.+d, 75.30.Mb
1. Introduction
Actinide compounds occupy an intermediate po-
sition between itinerant 3d and localized 4f systems
[1,2], and one of the fundamental questions con-
cerning the actinide materials is whether their f
states are localized or itinerant. This question is
most frequently answered by comparison between
experimental spectroscopies and the different theo-
retical descriptions. Optical and magneto-optical
(MO) spectroscopy, like photoelectron spectroscopy
and bremsstrahlung isochromat spectroscopy, sup-
ply direct information about the energy states
(both occupied and unoccupied) around the Fermi
energy [3] and can provide a means of discrimina-
tion between the two theoretical limits.
Intensive experimental and theoretical study
over more than two decades [4–8] has revealed that
5f magnetism is quite complex because Coulomb,
spin–orbit, crystalline field, and exchange energies
in 5f systems are of the same order of magnitude.
Today it is well established that many unusual
physical properties of the light actinide metals are a
reflection of the particular nature of the 5f elec-
trons. Friedel [9] proposed many years ago that the
bonding in these materials must involve the 5f elec-
trons. The argument for 5f bonding can be under-
stood as a consequence of the extended nature of
the 5f wave function relative to the rare-earth 4f
wave functions. This causes them to form in
bandlike states [10].
The itinerant nature of the 5f electrons in the
light actinide metals is well known [4]. Their elec-
tronic structure and optical properties is well
described by local spin-density approximation
(LSDA) band structure calculations [11,12]. On the
other hand, the decreasing f-band width (W) and
the increasing intra-atomic Coulomb energy (U) re-
sults in a Mott localization between plutonium and
americium [5,13,14], and the correlation effects are
not properly described in the LSDA [7,15].
© O. Horpynyuk, V. V. Nemoshkalenko, V. N. Antonov, B. N. Harmon, and A. N. Yaresko, 2002
* Permanent address: Institute of Metal Physics, 36 Vernadsky Str., 252142 Kiev, Ukraine
Actinide compounds are excellent subjects for
MO research. The participation of the 5f states in
bonding is reflected in strongly hybridized bands
near the Fermi level, with a high density of states
and significant d�f oscillator strengths for optical
transitions. The 5f delocalization favors higher
magnetic ordering temperatures. In fact, many ura-
nium compounds have ordering temperatures which
are one order of magnitude higher than those in
similar lanthanide compounds [3,16]. Regarding
the magnitude of the MO effects compared to
rare-earth materials, an enhancement due to the
larger spin–orbit energy can be expected and is in
part experimentally verified [3,16]. For actinide
compounds the figure of merit R K K( º )�2 2� ,
where R is the optical reflectivity and �K and ºK
are the Kerr angle and Kerr ellipticity, respec-
tively, is one order of magnitude larger than for the
best transition or rare-earth compounds [3]. Be-
sides the issue of radioactivity (minimal for de-
pleted uranium) a hindrance for successful applica-
tion of actinide compounds in storage devices is
that the typical Curie temperatures are below room
temperature. This is not a fundamental problem,
and can probably be overcome by suitable alloying.
For actinide materials much of the MO experi-
mental effort up to now [3,16] has been focused on
binary UX NaCl-type uranium chalcogenides (X =
= S, Se, Te) and pnictides (X = P, As, Sb), uranium
compounds U3X4 (X = P, As) with the Th3P4 crys-
tal structure, and some ternary compounds such as
UAsTe, the tetragonal compounds UCuP2 and
UCuAs2, and the hexagonal compounds UCu2P2,
UMn2Si2, and UMn2Ge2.
There are quite a few first-principle calculations
of the MO spectra of uranium compounds [17–22].
The MO spectra of such compounds as UAsSe [19]
and U3P4 [20,22] are well described in the LSDA,
and we can conclude that they have at least par-
tially itinerant electron behavior. On the other
hand the MO spectra in US, USe, and UTe can be
well described only in the LSDA+U approximation
[21] supporting the localized description for their
5f electrons.
In the present work we report a detailed theo-
retical investigation of the electronic structure and
the optical and MO Kerr properties of the ternary
compound UCuP2. The paper is organized as fol-
lows. The computational details are explained in
Sec. 2. Section 3 presents the theoretical electronic
structure and MO spectra of UCuP2. The results
are then compared to the experimental data.
Finally, the results are summarized in Sec. 4.
2. Theoretical framework
Using straightforward symmetry considerations
it can be shown that all MO phenomena are caused
by the symmetry reduction — compared to the
paramagnetic state — caused by magnetic ordering
[23]. Concerning the optical properties this symme-
try reduction only has consequences when spin-or-
bital (SO) coupling is considered in addition. To
calculate the MO properties one therefore has to
take into account the magnetism and SO coupling
while at the same time dealing with the electronic
structure of the material considered. In performing
the corresponding band structure calculations it is
normally sufficient to treat the SO coupling in a
perturbative way. A more rigorous scheme, how-
ever, is obtained by starting from the Dirac equa-
tion set up in the framework of relativistic spin
density functional theory [24]:
[ ] ºc p mc IV Vsp z n n n� � �� � �� � � �2
k k k , (1)
with Vsp(r) the spin-polarized part of the
exchange-correlation potential corresponding to the
z quantization axis. All other parts of the potential
are contained in V( )r . The 4�4 matrices α β, , and I
are defined by
α
σ
σ
�
�
�
�
0
0
, β �
�
�
�
�
1
1
0
0
, I
1
1
�
�
�
�
0
0
, (2)
Where σ represents the standard Dirac matrices,
and 1 is the 2�2 unit matrix.
There are quite a few band structure methods
available now that are based on the above Dirac
equation [25]. In the first scheme the basis func-
tions are derived from the proper solution to the
Dirac equation for the various single-site potentials
[26,27]. In the second one, the basis functions are
obtained initially by solving the Dirac equation
without the spin-dependent term [28–30] and then
this term is taken into account only in the
variational step [26,31,32]. In spite of this approxi-
mation used, the second scheme nevertheless gives
results in very good agreement with the first one
[25], while being very simple to implement.
Phenomenologically, optical and magneto-opti-
cal properties of solids are treated by means of a di-
electric tensor. The dielectric tensor is composed of
the diagonal component �xx and � zz and the off-di-
agonal component �xy in the form
�
� �
� �
�
� �
�
�
�
�
�
�
�
xx xy
xy xx
zz
0
0
0 0
. (3)
746 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7
O. Horpynyuk et al.
In the polar geometry, where the z axis is chosen
to be perpendicular to the solid surface and parallel
to the magnetization direction, the expression for
the Kerr angle can be obtained easily for small an-
gles and is given by [3]
� � �
� �
� �
�
�
� �
K K
xy
xx xx
i
i
( ) º ( )
( )
( ) ( )
� �
�
�1
4
, (4)
where �K is the Kerr rotation and ºK is the
so-called Kerr ellipticity. � � ���( , , , )� x y z is the
optical conductivity tensor, which is related to the
dielectric tensor ��� through
� � �
�
�
� ��� �� ��( ) ( )� �
4 i
. (5)
The optical conductivity tensor, or equivalently,
the dielectric tensor is the important spectral quan-
tity needed for the evaluation of the Kerr effect
[33]. The optical conductivity can be computed
from the energy band structure by means of the
Kubo–Greenwood [34] linear-response expression
[35]:
� �� �
�
��
�
� � �
�
� �
��
���
ie
m Vuc
f fn n
nnnn
n n
2
2�
(º ) (º )
( )
(k k
k k
� k k
k
) ( )
( )
,
� nn
nn i
�
�� �
�
� � �
(6)
where f nk(º ) is the Fermi function,
� ���nn n n� �� �k k kº º is the energy difference of the
Kohn–Sham energies ºnk , and � is the lifetime
parameter, which is included to describe the finite
lifetime of excited Bloch electron states. The � nn�
�
are the dipole optical transition matrix elements,
which in a fully relativistic description are given by
[36]
P nn n nm c� ��( )k k k� � �α , (7)
where � nk is the four-component Bloch electron
wave function.
Equation (6) for the conductivity contains a
double sum over all energy bands, which naturally
separates into the so-called interband contribution,
i.e., n n� �, and the intraband contribution, n n� '.
The intraband contribution to the diagonal compo-
nents ofσ may be rewritten for zero temperature as
� �� �
�
� � ���
�
�
�
( ),p
D
i
i
2
4
, (8)
where � �p, are the components of the plasma
frequency, which are given by
( ) (º ) ,,�
�
��
�
p
uc n
n F nn
e
m V
E2
2
2
24
� ��
k
k � (9)
and EF is the Fermi energy. For cubic symmetry,
we furthermore have � � � �p p x p y p z
2 2 2 2� � �, , , .
Equation (8) is identical to the classical Drude
result for the ac conductivity, with � �D D�1/ ,
where �D is the phenomenological Drude electron
relaxation time. The intraband relaxation time
parameter �D may be different from the interband
relaxation time parameter �. The latter can be
frequency dependent [37], and, because excited
states always have a finite lifetime, will be
nonzero, whereas �D will approach zero for very
pure materials. Here we adopt the perfect crystal
approximation, i.e., �D � 0. For the interband
relaxation parameter, on the other hand, we shall
use, unless stated otherwise, � � 0 4. eV. This value
has been found to be on average a good estimate of
this phenomenological parameter. The contribution
of intraband transitions to the off-diagonal
conductivity usually is not considered. Also, we did
not study the influence of local field effects on the
MO properties.
We mention, lastly, that the Kramers–Kronig
transformation has been used to calculate the
dispersive parts of the optical conductivity from
the absorptive parts.
3. Crystal structure and computational details
Self-consistent energy band-structure calcula-
tions of UCuP2 were performed by means of the
fully relativistic, spin-polarized linear-muffin-tin-
orbital (SPR LMTO) method using the atomic
sphere approximation with combined corrections
included [26,29–32]. The LSDA part of the energy
band structure calculations were based on the
spin-density-functinal theory with von Barth–Hedin
parameterization [38] of the exchange-correlation
potential. Core charge densities were recalculated
at every iteration of the self-consistency loop. The
k-space integrations were performed with the im-
proved tetrahedron method [39] and the charge
was obtained self-consistently with 349 irreducible
k points. The basis consisted of U s, p, d, f, and g;
Cu s, p, d, and f ; P s, p, and d LMTOs.The energy
expansion parameters E Rl� were chosen at the cen-
ters of gravity of the occupied parts of the partial
state densities; this gives high accuracy for the
charge density.
Electronic structure and magneto-optical Kerr effect in the compound UCuP2
Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 747
UCuP2 belongs to the layered tetragonal ZrAl3
type crystal structure (Fig. 1) with the space group
I4/mmm (No. 139) with U at the 4e position, Cu
at the 4d position, and P at the 4c and 4e positions.
The phosphorus atoms have two nonequivalent po-
sitions: the plane with P1 atoms is situated between
uranium planes, while the plane containing the P2
atoms lies between uranium and copper planes (see
Fig. 1). The lattice constants are a = 3.803 Å, c =
= 18.523 Å [40]. The corresponding Brillouin zone is
shown in Fig. 2. The unit cell of UCuP2 contains
8 atoms.
4. Results and discussion
The uranium pnictide ternary compounds with
copper or nickel crystallize in a high-symmetry
structure: UCuP2, UCuAs2, and UNiAs2 are
tetragonal [41] and UCu2P2 and UCu2As2 are
hexagonal [42]. The U–Cu ternaries order ferro-
magnetically, in contrast to the U–Ni ternaries,
which are all antiferromagnets [3]. The magnetic
ordering temperatures are among the highest
known so far for uranium compounds, reaching
216 K for UCu2P2 [43]. The magnetic and trans-
port properties of UCuP2 were investigated by
Kaszorowski et al. [44] on single-crystal specimens.
They found that the compound is ferromagnetic be-
low 75 K, with a spontaneous magnetic moment of
0.98 �B , and in the magnetically ordered region it
exhibits large magnetocrystalline anisotropy con-
stants. The electrical resistivity of UCuP2 at low
temperature behaves as T2, while in the tempera-
ture range above TC the observed negative slope of
( )T may point to Kondo lattice behavior [44].
The energy dependence of the Kerr rotation and
ellipticity of UCuP2 have been measured by
Funagalli et al. [45]. The measurements were done
on a natural grown surface perpendicular to the c
axis. Although UCuP2 has a lower uranium con-
centration in comparison with UX and U3X4
(X = P, As) compounds, its Kerr rotation reaches
1.6° (Ref. 45).
748 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7
O. Horpynyuk et al.
Fig. 1. Crystal structure of tetragonal UCuP2.
Fig. 2. Brillouin zone of tetragonal UCuP2.
Fig. 3. Self-consistent fully relativistic, spin-polarized
energy band structure and total DOS (in states/(unit
cell eV)) of UCuP2 .
The fully relativistic spin-polarized energy band
structure of ferromagnetic UCuP2, shown in Fig. 3,
is rather complicated. It may, however, be under-
stood from the total and partial density of states
(DOS) presented in Fig. 4. The bands in the lowest
region between �13.4 and �7.2 eV have mostly a P s
character with some amount of U and Cu spd char-
acter mixed in. The energy bands between �7.2 and
�0.4 eV are P 3p states strongly hybridized with the
Cu 3d and U 6d states. There is a quasi-gap be-
tween P s and p states. The Cu 3d states are fully
occupied and situated around 5.0 eV below the
Fermi level. The U 5f energy bands are located
above and below EF at about �0.4 to 3.0 eV. The
highest region above the Fermi energy can be charac-
terized as anti-bonding U 6d states. It is interesting
to note that the 3p partial density of states for P1
and P2 sites differ from each other significantly.
This reflects the different positions for the two phos-
phorus atoms. As we mentioned above, the plane
with P1 atoms is situated between uranium planes,
whereas the plane with P2 atoms lies between ura-
nium and copper planes (see Fig. 1). The P1 atoms
have as neighbors four P1 atoms at a distance of
2.688 Å and four uranium atoms at 2.793 Å. On the
other hand, the P2 atoms have four Cu neighbor
atoms at a distance of 2.423 Å and four uranium
atoms at 2.898 Å. As a result, the 3p partial density
of states for the P1 site has one peak structure for
occupied states, reflecting strong hybridization
between the P1 3p and U 6d states, whereas the 3p
partial density of states for the P2 site has two
peaks due to the hybridization of P2 3p states with
both Cu 3d and U 6d states.
Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 749
Electronic structure and magneto-optical Kerr effect incompound the UCuP2
Fig. 4. Fully relativistic, spin-polarized total (in
states/(unit cell eV)) and partial densities of state (in
states/(atom eV)) calculated for UCuP2.
Fig. 5. Calculated and experimental [45] Kerr rotation
(�K) and Kerr ellipticity (º
K
) spectra of UCuP2 as
well as the theoretically calculated off-diagonal optical
conductivity �xy and function Im ! "�D �1 (see the
explanation in the text).
After consideration of the above band structure
properties we turn to the MO spectra. In Fig. 5 we
show the calculated and experimental [45] MO
Kerr spectra of UCuP2. There exists rather good
agreement between the experimental Kerr spectra
and the ab initio LSDA calculated one. Overall,
the experimental features are reasonably well re-
produced, except the theoretically calculated spec-
tra have sharper features in comparison with the
experimentally observed spectra. There is also a
small red energy shift by about 0.1 eV in the posi-
tion of the main Kerr rotation and ellipticity peaks
in comparison with the experiment. We can con-
clude, therefore, that the spectral behavior of the
MO Kerr spectra in UCuP2 is well described by
LSDA band-structure theory.
To investigate the origin of the Kerr spectra, we
consider the separate contributions of both the nu-
merator of Eq. (4), i.e., � �xy( ) and the denomina-
tor, D ixx xx( ) ( / )� � � � �� �1 4 . In Fig. 5 we
show how the separate contributions of numerator
and denominator bring about the Kerr angle and
Kerr ellipticity of UCuP2. The imaginary part of
the inverse denominator (times the photon fre-
quency), Im[�D]−1, displays a strong resonance
structure at about 0.2 eV. However, the imaginary
and real parts of �� xy , i.e. ��2xy and ��1xy , dis-
play a very small value at this energy. Therefore
the first minimum in the Kerr rotation and Kerr el-
lipticity at around 0.2 eV results from a deep reso-
nance structure of the denominator. Outside the in-
frared peak, for energies above 0.5 eV, the Kerr
rotation and ellipticity spectra are fully determined
by the shape of � xy , which in turn are known to be
due to the interplay of SO coupling and spin
polarization. The two peaks at about 0.7 and 2.0 eV
in the Kerr rotation spectrum originate mostly from
U 6 5d f� interband transitions (see Figs. 3 and
4). The interband transitions from the Cu 3d to the
U 5f band start above 4 eV. In the 1 to 5 eV energy
region the theoretical and experimental curves de-
viate from one another in some details.
The theoretically calculated figure of merit
R K K( º )�2 2� in UCuP2 has a maximum value of
1.2° at 0.7 eV, which is higher than that in
PtMnSb (0.83° at 1.57 eV) [46] but smaller
than that in U3As4 (6.0° at 0.35 eV) [22].
In spite of the reasonably close correspondence
between the experimental and theoretical Kerr
spectra, we find that not all properties of UCuP2
are equally well represented. For example, the cal-
culated total magnetic moment of uranium in
UCuP2 is only 0.262�B (Table) (with spin moment
–0.886�B and orbital moment 1.148�B), which
is considerably smaller than the experimental mo-
ment of about 0.89 �B [44].
Table
The experimental and LSDA calculated spin, orbital
and total magnetic moments (in �B) of UCuP2.The
experimental data are from Ref. 44
Atom M
s
M
l
M
total
Experiment
.
U –0.886 1.148 0.262 0.89
Cu –0.009 –0.002 –0.011
P
1
0.012 0.001 0.013
P
2
–0.006 –0.001 –0.007
The calculated moment is dominated by 5f
states: the 5f components of the spin and orbital
moment are –0.845�B and 1.137�B , respectively.
It is a well-known fact, however, that within the
LSDA the total magnetic moment of uranium com-
pounds in general comes out too small [47–51].
Corrections which simulate Hund’s second rule in-
teractions in solids, describing orbital correlations
absent in the homogeneous electron gas, such as the
orbital polarization (OP), are needed to bring the
magnetic moment into better agreement with ex-
periment [48–51]. Interestingly, the fact that the
OP is too small within the LSDA does not preclude
a reasonable explanation of the MO Kerr spectrum.
The same conclusion was also reached previously
for UAsSe [19] and U3X4 (X = P, As, Sb, and Bi)
[22] compounds.
5. Summary
On the basis of the good agreement between ex-
perimental and theoretical MO characteristics we
conclude that the U 5f electrons in the ternary
UCuP2 compound are essentially itinerant. How-
ever, the difference in the main peak position of the
Kerr rotation and ellipticity spectra requires fur-
ther investigation of the electron self-energies.
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Electronic structure and magneto-optical Kerr effect incompound the UCuP2
|
| id | nasplib_isofts_kiev_ua-123456789-130231 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T17:07:30Z |
| publishDate | 2002 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Horpynyuk, O. Nemoshkalenko, V.V. Antonov, V.N. Harmon, B.N. Yaresko, A.N. 2018-02-09T10:45:31Z 2018-02-09T10:45:31Z 2002 Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ / O. Horpynyuk, V.V. Nemoshkalenko, V.N. Antonov, B.N. Harmon, A.N. Yaresko // Физика низких температур. — 2002. — Т. 28, № 7. — С. 745-751. — Бібліогр.: 51 назв. — англ. 0132-6414 PACS: 71.28.+d, 75.30.Mb https://nasplib.isofts.kiev.ua/handle/123456789/130231 The optical and magneto-optical (MO) spectra of the fernary compound UCuP₂ are investigated from first principles, using the fully relativistic Dirac linear-muffin-tin-orbital band structure method and density-functional theory in the local spin-density approximation. Within a band-like description of the 5f electrons, good agreement with the measured MO spectra is obtained. The origin of the Kerr rotation in the compound is examined. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Магнетизм Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ Article published earlier |
| spellingShingle | Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ Horpynyuk, O. Nemoshkalenko, V.V. Antonov, V.N. Harmon, B.N. Yaresko, A.N. Магнетизм |
| title | Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ |
| title_full | Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ |
| title_fullStr | Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ |
| title_full_unstemmed | Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ |
| title_short | Electronic structure and magneto-optical Kerr effect in the compound UCuP₂ |
| title_sort | electronic structure and magneto-optical kerr effect in the compound ucup₂ |
| topic | Магнетизм |
| topic_facet | Магнетизм |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/130231 |
| work_keys_str_mv | AT horpynyuko electronicstructureandmagnetoopticalkerreffectinthecompounducup2 AT nemoshkalenkovv electronicstructureandmagnetoopticalkerreffectinthecompounducup2 AT antonovvn electronicstructureandmagnetoopticalkerreffectinthecompounducup2 AT harmonbn electronicstructureandmagnetoopticalkerreffectinthecompounducup2 AT yareskoan electronicstructureandmagnetoopticalkerreffectinthecompounducup2 |