Bulk band structure and Fermi surface of nickel: A soft xray angleresolved photoemission study
ABSTRACT We study the bulk band structure and Fermi surface of nickel metal by soft xray angleresolved photoemission spectroscopy (SX ARPES). SX ARPES, using tunable photons from hν∼300 to 800 eV, facilitates depthsensitive inplane band mapping of Ni(100). Horizontal and verticalpolarizationdependent studies are used to selectively enhance dipoleallowed transitions. While lowtemperature (50 K) results provide band dispersions consistent with the direct transition model, roomtemperature (300 K) studies confirm and quantify significant intensity loss due to nondirect transitions. The band maps provide band dispersions and identify all the bands in the ΓXWWXΓ quadrant in momentum space. In particular, the results show that a hole pocket derived from the X2↓ downspin band exists in bulk Ni. This is in contrast to results of surfacesensitive ultraviolet ARPES studies but consistent with other bulksensitive measurements. The Z1↓ band is also shown to have depthsensitive band dispersion and Fermi surface crossings. In addition, the magnetically active Z2↓ downspin band shows nearly flatband behavior. The Fermi surface and band dispersions determined by the present ARPES measurements are in good agreement with local density approximation band structure calculations. SX ARPES is thus a valuable probe of the intrinsic momentumresolved electronic structure of solids.
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Article: Finitetemperature magnetism of transition metals: an ab initio dynamical meanfield theory.
[show abstract] [hide abstract]
ABSTRACT: We present an ab initio quantum theory of the finitetemperature magnetism of iron and nickel. A recently developed technique which combines dynamical meanfield theory with realistic electronic structure methods successfully describes the manybody features of the one electron spectra and the observed magnetic moments below and above the Curie temperature.Physical Review Letters 09/2001; 87(6):067205. · 7.94 Impact Factor  SourceAvailable from: I. V. Solovyev[show abstract] [hide abstract]
ABSTRACT: We discuss different methods of calculation of the screened Coulomb interaction U in transition metals and compare the socalled constraint localdensity approximation (LDA) with the GW approach. We clarify that they offer complementary methods of treating the screening and therefore should serve for different purposes. The analysis is illustrated by calculations for the ferromagnetic Ni. In the ab initio GW method, the renormalization of bare onsite Coulomb interactions between 3d electrons (being of the order of 20–30 eV) occurs mainly through the screening by the same 3d electrons, treated in the randomphase approximation (RPA). The basic difference of the constraintLDA method from the GW method is that it deals with the neutral processes, where the Coulomb interactions are additionally screened by the “excited” electron, since it continues to stay in the system. This is the main channel of screening by the itinerant (4sp) electrons, which is especially strong in the case of transition metals and missing in the GW approach, although the details of this screening may be affected by additional approximations, which typically supplement these two methods. The major drawback of the conventional constraintLDA method is that it does not allow us to treat the energy dependence of U, while the full GW calculations require heavy computations. We propose a promising approximation based on the combination of these two methods. First, we take into account the screening of Coulomb interactions in the 3delectronlike bands located near the Fermi level by the states from the orthogonal subspace, using the constraintLDA methods. The obtained interactions are further renormalized within the bands near the Fermi level in RPA. This allows the energydependent screening by electrons located near the Fermi level, including the same 3d electrons.Physical Review B 01/2005; 71(4):045103. · 3.77 Impact Factor  SourceAvailable from: Akinori IrizawaA. Sekiyama, S Kasai, M. Tsunekawa, Y Ishida, M. Sing, A. Irizawa, A. Yamasaki, S. Imada, T Muro, Y Saitoh, Y. Onuki, T Kimura, Y Tokura, S Suga[show abstract] [hide abstract]
ABSTRACT: We report the Fermi surfaces of the superconductor Sr2RuO4 and the nonsuperconductor Sr1.8Ca0.2RuO4 probed by bulksensitive highenergy angleresolved photoemission. It is found that there is one squareshaped holelike, one squareshaped electronlike and one circleshaped electronlike Fermi surface in both compounds. These results provide direct evidence for nesting instability giving rise to magnetic fluctuations. Our study clarifies that the electron correlation effects are changed with composition depending on the individual band. Comment: 5 pages, 3 figures including 2 color figuresPhysical Review B 02/2004; · 3.77 Impact Factor
Page 1
Bulk band structure and Fermi surface of nickel: A soft xray angleresolved
photoemission study
N. Kamakura,1,* Y. Takata,1T. Tokushima,1Y. Harada,1A. Chainani,1K. Kobayashi,2and S. Shin1,3
1Soft Xray Spectroscopy Laboratory, RIKEN/SPring8, Sayocho, Sayogun, Hyogo 6795148, Japan
2JASRI/SPring8, Sayocho, Sayogun, Hyogo 6795198, Japan
3Institute for Solid State Physics (ISSP), The University of Tokyo, Kashiwanoha, Kashiwa, Chiba 2778581, Japan
?Received 31 March 2006; revised manuscript received 25 June 2006; published 28 July 2006?
We study the bulk band structure and Fermi surface of nickel metal by soft xray angleresolved photoemis
sion spectroscopy ?SX ARPES?. SX ARPES, using tunable photons from h??300 to 800 eV, facilitates depth
sensitive inplane band mapping of Ni?100?. Horizontal and verticalpolarizationdependent studies are used to
selectively enhance dipoleallowed transitions. While lowtemperature ?50 K? results provide band dispersions
consistent with the direct transition model, roomtemperature ?300 K? studies confirm and quantify significant
intensity loss due to nondirect transitions. The band maps provide band dispersions and identify all the bands
in the ?XWWX? quadrant in momentum space. In particular, the results show that a hole pocket derived
from the X2↓downspin band exists in bulk Ni. This is in contrast to results of surfacesensitive ultraviolet
ARPES studies but consistent with other bulksensitive measurements. The Z1↓band is also shown to have
depthsensitive band dispersion and Fermi surface crossings. In addition, the magnetically active Z2↓down
spin band shows nearly flatband behavior. The Fermi surface and band dispersions determined by the present
ARPES measurements are in good agreement with local density approximation band structure calculations. SX
ARPES is thus a valuable probe of the intrinsic momentumresolved electronic structure of solids.
DOI: 10.1103/PhysRevB.74.045127PACS number?s?: 79.60.Bm, 73.20.At, 71.20.?b
I. INTRODUCTION
Angleresolved photoemission spectroscopy ?ARPES? is a
very important technique to study the energy and momen
tumresolved electronic structure of solids.1–4ARPES pro
vides direct experimental data on band dispersions to com
pare with and validate band structure calculations. In addi
tion, for systems showing deviations from band structure
calculations, it allows a measure of the renormalization of
band dispersions in terms of the real and imaginary parts of
the selfenergies, which can arise due to electronphonon,
electronelectron, and also electronmagnon interactions.3–7
While ARPES is conventionally carried out using low
energy photons ?h?=10–100 eV?, which is necessary for
working in the direct transition approximation, the validity
and importance of synchrotron soft xray ?SX? ?h?
=500–800 eV? ARPES has been demonstrated in very re
cent studies.8–12These studies actually mark the revival of a
field that was pioneered in the 1970s: ARPES carried out
using soft x rays from synchrotron as well as a monochro
matic Al K? laboratory source.13–17These original studies
established the importance of the direct transition model, as
well as the role of nondirect transitions at high incident pho
ton energy and high temperature, in interpreting the
momentum ?or angle? dependent photoemission spectra of
elemental metals such as gold, silver, tungsten, etc.
Recent advances in synchrotronbased ARPES allow a
relatively high resolution in energy and momentum, and high
throughput, at SX energies ?h?=300–800 eV?. Notable re
cent results include the high surface sensitivity in SXARPES
of Al?001?,8confirmation of the bulk Fermi surfaces in cop
per metal9and in layered ruthenates,10small deviations in the
Fermi surface of an electrondoped highTccuprate11com
pared to results of lowenergy ARPES, the intrinsic band
structure of doped diamond,12etc. A depthdependent change
of inplane band dispersions of Ni?100?, by spanning h?
=190–800 eV, was reported by us recently.18The experi
mental band structure of Ni metal, exhibiting itinerant ferro
magnetism derived from spinsplit dispersing bands, remains
a very good example to compare band structure calculations.
Much experimental18–29and theoretical30–43work has been
performed to correctly describe the band structure of Ni. Ex
perimentally, lowenergyARPES ?or angleresolved ultravio
let photoemission spectroscopy ?ARUPS?? studies have re
vealed the band structure19–29but have shown deviations
from local density approximation ?LDA? band structure cal
culations. Although LDA calculations successfully predict
several important groundstate properties of Ni, such as the
equilibrium lattice constant, bulk modulus, magnetic mo
ment, and spin wave stiffness,32the bandwidth and exchange
splitting observed by ARUPS experiments are 25% and 50%
narrower than those obtained from LDA calculations, respec
tively. A satellite structure at 6 eV binding energy observed
in the valence band is not reproduced by the LDA calcula
tions. These deviations are thought to originate in electron
correlations distinctive for the Ni 3d band. The GW approxi
mation ?GWA?,38in which longrange or offsite screening is
included from first principles, results in a bandwidth consis
tent with the ARUPS results. A recent calculation in the
GWA combinedwithdynamical
?DMFT?,42in which the onsite selfenergy is considered by
DMFT and the offsite selfenergy by the GWA, gave a va
lence band almost consistent with the ARUPS results, i.e.,
the existence of a 6 eV satellite and much improved ex
change splitting as well as bandwidth. These studies have
clarified characteristics of the Ni 3d states which consist of
localized and itinerant characteristics: the narrow bandwidth
and presence of the twohole bound state 6 eV satellite indi
meanfieldtheory
PHYSICAL REVIEW B 74, 045127 ?2006?
10980121/2006/74?4?/045127?9?
©2006 The American Physical Society 0451271
Page 2
cate the localized nature of 3d states, while the existence of
clear Fermi surface crossings implies itinerancy. The Fermi
surface of Ni has also been extensively studied as the Fermi
surface governs transport properties in materials via the
transport coefficient. Although LDA calculations predict two
minorityspin hole pockets around the X point with X5and
X2symmetries,32photoemission studies have reported only
the X5↓hole pocket.21,28De Haas–van Alphen studies44have
observed the X5↓hole pocket but are not conclusive about the
X2↓hole pocket. LDA+DMFT calculations41show that the
X2↓band lies below EF, and thus indicate absence of the X2↓
hole pocket. However, there exists an early spinpolarized
photoemission study showing that the X2↓state exists above
EF, indicating the existence of the X2↓hole pocket, consistent
with LDA calculations.45The anomalous behavior of the
magnetocrystalline anisotropy also indicated the existence of
the X2↓hole pocket,46and a very recent study of quantum
well states in Ag/Ni?111? has shown that the groundstate Ni
band structure is consistent with LDA calculations.47
In this work, we study the 3d band dispersions of Ni and
their EFcrossings by ARPES, using excitation energies from
h?=302 to 800 eV so as to probe the bulk electronic
structure.11,18The chief merit in the use of soft xrays as an
excitation source is the longer probing depth compared to
ARUPS, as given by what is called the universal curve.48
The gentle gradient of the universal curve at high kinetic
energies enables us to measure the threedimensional band
structure of Ni. In a recent study, we have shown the varia
tion in inplane band dispersions as a function of probing
depth. This resolved the confusion regarding the X2↓state
existing below EFin surfacesensitive ARPES, while the
bulk electronic structure showed the existence of the X2↓
state existing above EF, thus confirming the existence of the
X2↓hole pocket. Here we extend the study and present the
following. ?i? Comparative lowtemperature ?50 K? and
roomtemperature ?300 K? studies: The comparison confirms
and quantifies significant intensity loss due to nondirect tran
sitions, while the lowtemperature data are consistent with
the direct transition model. ?ii? Vertical and horizontal polar
ization inplane band maps which span k?over two succes
sive Brillouin zones: The band maps provide band disper
sions perpendicular to k?, and conclusively identify all the
bands in the quadrant ?XWWX? in momentum space
?Fig. 1?a??. ?iii? The Fermi surface of bulk Ni: We show it to
be consistent with LDA calculations.
II. EXPERIMENT
Experiments were performed at beamline 27SU of
SPring8 using linearly polarized light.49Total energy reso
lution was 50–160 meV. The beamline has a figure8 undu
lator, enabling an easy switch of the polarization vector from
horizontal to vertical polarization.50The Ni?100? surface was
prepared by Ar+sputtering and annealing. The surface was
checked by core level photoemission spectra measured with
h?=780 eV and contamination due to oxygen and carbon
was less than 1%. The surface crystallinity was confirmed to
be a sharp ?1?1? lowenergy electron diffraction pattern. In
this study, we used two photon energy ranges from 780
to 595 eV and from 435 to 302 eV. The inelastic mean free
paths for 780–595 and 435–302 eV are 12.1–10.0 and
8.1–6.5 Å, respectively.48Band dispersions along k?are ob
served by measuring the angular dependence from the nor
mal emission with the experimental setup shown in Fig. 1?b?.
An important point to be noted is that the photon wave vec
tor is no longer negligible for the high photon energy used in
the experiments. However, since our experimental geometry
is near grazing incidence, the momentum transfer of the pho
ton results in a constant shift of parallel component of the
momentum k?, while k?is negligibly shifted. The shifts of k?
and k?are identified from accurate determination of the
highsymmetry points ? and X. We have confirmed this from
the measured spectra which show constant shifts in k? by
0.22??−X?, while the k?shifts only by 0.22??−X?, for
780 eV. For lower energies, the shift in k?is reduced system
atically and for the equivalent cut along ?−X with a photon
energy of 435 eV, the shift is 0.12??−X?, while the k?shift
could not be identified.
FIG. 1. ?Color online? ?a? The volume Brillouin zone of fcc Ni.
The region probed in the present study is marked by thick line. ?b?
The experimental setup in the soft xray ARPES with vertical po
larization. ?c? The k positions probed in the angular dependences
using h?=780–595 and 435–302 eV are marked as filled circles
and dashed lines, as estimated by Eq. ?1?.
KAMAKURA et al.
PHYSICAL REVIEW B 74, 045127 ?2006?
0451272
Page 3
III. RESULTS AND DISCUSSION
In order to establish that ARPES using soft xray energies
can reliably observe band dispersions, we have measured ?i?
the photon energy dependence of ARPES spectra ?Fig. 2? in
successive Brillouin zones as determined by the variation in
k??Fig. 1?c?? and ?ii? the ARPES spectra with a fixed high
energy ?780 eV, Fig. 3? at 50 and 300 K, to check and ensure
that the direct transition model is still valid at low tempera
ture, although the contribution of nondirect transitions is
known to be significant at 300 K. Band dispersion along k?
is obtained from an ARPES spectrum, depending on photon
energy, as given by the equations
?k?=?2m?h? − w − ??sin ?e,
?k?=?2m??h? − w − ??cos2?e+ V0?.
The k positions calculated by extending Eq. ?1? to the soft
xray energy range are shown in Fig. 1?c?.51Figure 1?c? in
dicates that the spectra at k?=0 using the photon energies
?1?
from 780 to 435 eV and from 595 to 302 eV are expected to
probe the k?dispersion from ? to X. The spectra along high
symmetry lines measured by these photon energies with ver
tical polarization are shown in Figs. 2?a?–2?d?. The spectra in
Fig. 2 show a clear smooth change in peak positions depend
ing on the photon energy. These photon energy dependences
result from the Ni band dispersion along k?. The spectrum
labeled 2 in Fig. 2?a? shows a peak at 0.51 eV, correspond
ing to the ?12point. This peak shifts with decreasing h? and
is identified as the ?1band. The energy position of ?12is
consistent with ARUPS results. In the spectra labeled 2?–5?
in Fig. 2?b?, the Z1band dispersion is observed ?Fig. 1?c??.
The energy position ??0.55 eV? of W1in the spectrum 5? is
also consistent with ARUPS results. These consistencies
show that ARPES using soft xray energies can adequately
and reliably measure band dispersions and Eq. ?1? is still
valid for probing kresolved electronic structure. The photon
energy dependences in the spectra using 435–302 eV, which
are marked 14–18 in Fig. 2?c? for the dispersion along the ?
line and 14?–18? in Fig. 2?d? including that along the Z line
in the Brillouin zone, are almost identical with the equivalent
spectra ?labeled 2, 4, 5, 10, and 13, and 2?, 4?, 5?, 10?, and
13?, respectively? in Figs. 2?a? and 2?b?. These observed pe
riodicities further demonstrate that the spectra at k?=0 using
the photonenergies from
435 to 302 eV surely measure the k?band dispersion from ?
to X. According to the dipole selection rules, the ?1symme
try band should be mainly observed along k?by this experi
mental setup ?Fig. 1?b?? using vertical polarization, which
corresponds to ppolarized light. Therefore, the observed
photon energy dependence is also consistent with the dipole
selection rules.
Figures 3?a? and 3?b? show the temperature dependences
of the ARPES spectra measured by h?=780 eV with vertical
and horizontal polarizations, respectively. The spectra, which
are normalized by the photocurrent of the incident light,
show a good match in intensities over the background energy
ranges. The peaks in the spectra at 300 K show broader
780 to 595 eV andfrom
FIG. 2. ?Color online? The photon energy dependence of the soft
xray ARPES using h?=800–595 and 435–302 eV. The numbers
labeling spectra in ?a?–?d? indicate the probed k positions, as shown
in Fig. 1?c?.
FIG. 3. ?Color online? Temperature dependence of soft xray
ARPES measured by h?=780 eV with ?a? vertical and ?b? horizon
tal polarizations. The blue ?light gray? and red ?dark gray? curves
are measured at 50 and 300 K, respectively. The spectra are nor
malized by the photocurrent.
BULK BAND STRUCTURE AND FERMI SURFACE OF¼
PHYSICAL REVIEW B 74, 045127 ?2006?
0451273
Page 4
widths and lower intensities than those at 50 K. This tem
perature dependence is attributed to the influence of phonon
assisted nondirect transitions,15–17,52which cannot be ne
glected in the ARPES with high photon energy and at high
temperature. The photoemission intensity at finite tempera
ture I?E,T? is generally written as a sum of the direct tran
sition IDT?E? component which shows dispersing bands in
ARPES, and the nondirect transition INDT?E,T? component:
I?E,T? = W?T?IDT?E? + INDT?E,T?.
?2?
In the above, W?T?=exp?−1
factor, ?U2?T?? is the threedimensional meansquared vibra
tional displacement, and g is the reciprocal lattice vector in
volved in the direct transitions. Since the DebyeWaller fac
tordiminishes in highenergy
temperature, the intensity of the direct transition peak de
creases with increasing photon energy and temperature.
When the valence bands of Ni?100? are excited by h?
=780 eV in the measurement of ARPES for normal emis
sion, W?T? is estimated to be 0.42 at 300 K and 0.74 at 50 K,
using reported values of the meansquared vibrational
displacement.53This implies that the intensity of the direct
transition peak at 300 K is ?57% of that at 50 K. These
estimates are in good qualitative agreement with the reported
estimates of W?T? for a higher photon energy ?W?300 K?
=0.22 and W?77 K?=0.53, for h?=1486.6 eV?. The experi
mental data indeed show a significant reduction ?of about
?40–50 %? between 300 and 50 K for the ?2, ?2?, and ?5
bands. This is clear from the data obtained at the ? and X
points shown in Figs. 3?a? and 3?b?, while for intermediate
values of k?between ? and X, the reduction is lower. Thus,
although the direct transition component in the ARPES spec
tra with h?=780 eV is predicted to decrease by 26% even at
50 K, the spectra measured at 50 K in Figs. 3?a? and 3?b?
show clear peaks which confirm dispersive bands. Table I
shows the estimated DebyeWaller factors for lower energies
and it decreases systematically to a value of about 0.89 for
h?=302 eV, the lowest energy used in the present study.
Hence, SX ARPES at h?=300–800 eV and a low tempera
ture of 50 K is appropriate for studying band dispersions and
Fermi surfaces of solids. This energy range bridges the low
energy ARUPS and highenergy xray photoemission spec
troscopy with a laboratory source and is expected to provide
valuable results on momentumresolved electronic structure.
In a recent theoretical study based on the Holstein model, it
3?U2?T??g2? is the DebyeWaller
excitation and high
was shown that electronphonon scattering leads to changes
in ARPES spectra on increasing temperature.7This behavior
can be associated with weight transfer from direct to nondi
rect transitions, as observed in the present study.
Figures 4?a?–4?h? and 4?a??–4?h?? show a series of in
plane band maps with clear band dispersions measured using
h?=780–595 eV with vertical and horizontal polarizations,
respectively. The k positions in the Brillouin zone probed by
these photon energies are indicated in Fig. 1?c?. The variation
of k?in measurements of angular dependence ?i.e., along a
cut at a particular photon energy? can be substantial in
ARUPS but diminishes with increasing h? in our experimen
tal geometry ?Fig. 1?b??. This is another advantage of SX
ARPES. Figure 4?a? shows the observed band map along ?
−X, that is, the ? line, which is measured using h?
=780 eV with vertical polarization. In Fig. 4?a?, ?12is ob
served at 0.51 eV, which is consistent with ARUPS results
?Fig. 4?i??.19–29The intense band dispersion observed from
?12is the minorityspin band of ?2. Although most ARUPS
studies have reported that this band is located below EFin
the whole ? line resulting in disappearance of the X2↓hole
pocket, the band map in Fig. 4?a? shows the ?2↓band cross
ing EFat 0.57??−X?. Therefore, Fig. 4?a? shows that the X2↓
hole pocket exists in the bulk of Ni. The intense dispersion in
the vicinity of the X point originates from the ?5↑band,
connecting to X5↑observed at 0.125 eV, which is also con
sistent withARUPS results which locate X5↑between 0.1 and
0.15 eV.19,28The highsymmetry points ?12and ?25?are de
generate states as observed by two bands merging at 1.21 eV
for ?25?in Fig. 4?a?? measured with horizontal polarization.
This energy position is also consistent with ARUPS results.
The ?5band, which disperses from ?25?to X5, is seen as a
weak band in Fig. 4?a??. The EFcrossing of the minority
spin band of ?5is also observed as a weak feature near the
crossing point of ?2↓. This crossing of ?5↓is also observed
near EFin Fig. 4?a?. The dispersion of the ?5majorityspin
band connecting ?25?to X5↑is not clear in the central region
of the band maps in Fig. 4?a? although the high intensity near
the X point is clear in Figs. 4?a? and 4?a??. The energy dis
tribution curves shown in Fig. 2?b? do a better job of identi
fying the ?5band, although the exchange splitting is not
clear.
With decreasing h?, the band maps of Figs. 4?a? and 4?a??
to 4?h? and 4?h?? show variations in band dispersions and
Fermi surface crossings. The variation seems higher in the
horizontal polarization band maps. The dependence of the EF
crossing points on photon energy forms the Fermi surface of
Ni. Since the features near EFare clearer in the band maps
with vertical polarization, the EFcrossing points are marked
with arrows in Figs. 4?a?–4?f?. The locus formed by the set of
these estimated crossing points plotted in Fig. 6 below, con
stitutes the Fermi surface of Ni. Note the observation of ad
ditonal weak features which disperse and cross EFbetween
k?=0 and 0.5 ?in units of ??−X?? in Figs. 4?e?–4?h?. Since
the correct crossing points of this band cannot be directly
estimated from the band maps in Figs. 4?e?–4?h? owing to
low intensities, we have marked k?points showing a broad
maximum in the intensity at EFas approximate EFcrossings
in Fig. 6. The dipole selection rules predict that, in the nor
TABLE I. The meansquared vibrational displacements ?U2?
and DebyeWaller factors W in the soft xray regime for Ni at 50
and 300 K.
h? ?eV?
50 K300 K
?U2? ?10−18cm2?
W
0.44
0.74
0.80
0.85
0.89
1.27
0.42
0.52
0.61
0.71
780
595
435
302
KAMAKURA et al.
PHYSICAL REVIEW B 74, 045127 ?2006?
0451274
Page 5
mal emission spectrum measured with horizontal polariza
tion, the ?12and ?25?states are observed only at the ? point,
and the ?5band is observed all along the ? line. Hence, the
band maps measured with horizontal polarization exhibit fea
tures different from those with vertical polarization. How
ever, the EFcrossing points observed with horizontal polar
ization are consistent with the band maps obtained with
vertical polarization.
The band maps along X−W, i.e., the Z line, measured by
h?=595 eV with vertical and horizontal polarization, are
shown in Figs. 4?h? and 4?h??. These two band maps identify
three bands, symmetrically located about the Z line, but are
observed with different intensities for vertical and horizontal
polarizations. First, the band dispersion with high group ve
locity and extending to high energies is due to the Z3↑band
from W3↑to X5↑?Fig. 4?i??. The energy position of X5↑is
consistent with that measured from the ?5↑band dispersion
in Fig. 4?a?. The second band is the Z2↑band from W1?↑. This
is very clear in Fig. 4?h?? measured with horizontal polariza
tion, and again the Z2↑band is consistent with ARUPS re
sults. This band is magnetically active and from a careful
analysis using the maximum entropy method and inverse
photoemission spectroscopy, it was shown that the spin split
ting between the Z2↑and Z2↓bands vanishes at the Curie
temperature.26A Stonertype collapsing behavior of spin
split bands from lowenergy ARPES spectra is also well
known.27In Fig. 4?h?, the intensity of the Z2↑band is seen
only near W1?↑, while near the X point it is not clear because
X5↑from the Z3↑band has higher intensity in vertical polar
ization and overlaps it. The third band is the Z1band, which
disperses from W1at 0.647 eV to the X2point and is clear
only in the vertical polarization map. The energy position of
W1is consistent with theARUPS results ?0.65 eV?.Although
the peak intensity of Z1weakens near EFon the righthand
side of the X point, the dispersion is clearly seen on the
lefthand side of the X point. From the dispersion on the
lefthand side of the X point, the Z1band is found to cross EF
at about −0.21?X−W? and this Z1band crossing EFis thus
the minorityspin band.
The band maps obtained in the successive Brillouin zones
but for a smaller number of photon energies between h?
=435 and 302 eV ?Fig. 1?c?? with vertical and horizontal
polarizations are shown in Fig. 5. These band maps show
band dispersions similar to those observed using h?
=780–595 eV. The ?2↓band shown in Fig. 5?a? also crosses
EFas in Fig. 4?a?, but this crossing point is estimated to be
0.62??−X?, i.e., it is nearer to the X point than the crossing
point in Fig. 4?a?. In our earlier study, we reported the varia
tion in band dispersion of the ?2↓band in three successive
Brillouin zones with progressively shorter mean free paths
and interpreted the changes as due to a bulktosurface varia
tion of the band dispersions. The results indicate that the ?2↓
hole pocket is present in the bulk but is absent in the surface
electronic structure as the ?2↓band becomes flatter with in
creasing surface sensitivity. As a further check, we have
carefully investigated the vicinity of EFof the Z1↓band
shown in Fig. 5?e?. The Z1↓ band measured with h?
=302 eV approaches the Z3band more closely than that ob
served using h?=595 eV and nearly overlaps with the strong
FIG. 4. ?Color online? Inplane band maps measured using h?
=780 eV ?a? and ?a?? to h?=595 eV ?h? and ?h?? with vertical and
horizontal polarizations, respectively. As shown in Fig. 1?c?, ?a? and
?a?? show the band dispersions along the ? line, and ?h? and ?h??
show those along the Z line. ?i? The semiempirical band dispersions
along ? ??X? and Z ?XW? from Ref. 33. The solid and dashed
lines indicate the majority and minorityspin bands, respectively.
BULK BAND STRUCTURE AND FERMI SURFACE OF¼
PHYSICAL REVIEW B 74, 045127 ?2006?
0451275
Page 6
intensity from the Z3band. This also indicates that the EF
crossing point of the Z1band in Fig. 5?e? is significantly
closer to the X point than that observed using h?=595 eV
?Fig. 4?h??. The Z1↓band appears to cross EFat about
−0.12?X−W?. This behavior of the Z1↓band dispersion de
pending on the probing depth is consistent with the probing
depth dependence of the ?2↓band dispersion. Thus, both the
Z1↓and X2↓bands show variation in band dispersion with
incident photon energy indicating that the band structure ob
served with shorter probing depth approaches that observed
by ARUPS.
In Fig. 6, the Fermi surfaces estimated by soft xray
ARPES with the photon energy range between h?=780 and
595 eV are plotted along with the Fermi surface obtained by
LDA calculations and de Haas–van Alphen measurements.
The photon energy dependence of the normal emission spec
trum probes mainly the ?1band by vertical polarization and
the ?5band by horizontal polarization according to the di
pole selection rules. The angular dependence with decreasing
h? from h?=780 eV sweeps the k?dispersion from the nor
mal emission. Although the ARPES with h?=780 eV probes
the ?2↓band crossing EF, as a function of photon energy, the
EFcrossing points do not trace the X2↓hole pocket, but in
stead trace the d↓Fermi surface ?empty squares in Fig. 6?.
The band maps measured with h?=780 and 435 eV show the
two crossing points of ?2↓and ?5↓between ? and X. In the
Fermi surface calculated by the LDA, five bands cross EFat
nearly the same points along ?−X, while the X2↓hole pocket
disappears in the ARUPS results. In Fig. 6, the Fermi surface
observed by soft xray ARPES shows that the crossing point
of ?2↓is very close to that of ?5↓and the d↓Fermi surface
evolves from there, as shown in the Fermi surface obtained
by the LDA calculation. In addition, the tightbinding calcu
lation including spinorbit coupling has shown that the spin
orbit coupling separates the crossing points of ?5↓and ?2↓
and results in the crossing point of ?2↓located slightly on the
?point side of the ?5↓crossing.34This effect of the spin
orbit coupling predicted by one electron band calculation
including spinorbit coupling is observed in the present soft
xray ARPES along the ? line. ?Fig. 6? The d↓Fermi surface
in Fig. 6 is rather similar to that estimated by LDA and de
Haas–van Alphen measurements. The sp Fermi surfaces
?empty triangles and circles in Fig. 6? are traced by the EF
crossing between k?=0 and 0.5 ?in units of ??−X??. The ob
tained sp Fermi surface is also consistent with the LDA cal
culation and de Haas–van Alphen measurements.
Several studies have addressed the X2↓hole pocket in the
Ni Fermi surface.18,28,41,54The X2↓observed below EFin the
ARUPS is thought to be associated with a particularly nar
row exchange splitting of the egtype X2state ??0.1 eV?
FIG. 5. ?Color online? Band maps measured
using h?=435 eV ?a? and ?a?? to h?=302 eV ?e?
and ?e?? with vertical and horizontal polariza
tions, respectively, for the successive Brillouin
zones ?see also Fig. 1?c??.
KAMAKURA et al.
PHYSICAL REVIEW B 74, 045127 ?2006?
0451276
Page 7
compared to that of the t2gtype X5state ??0.4 eV?. In Ref.
35, which calculated the selfenergy corrections in the va
lence bands of Ni, it was shown that the nonspherical nature
of the spin density, i.e., the difference between the electron
occupations in egand t2gstates, results in the difference in
the exchange splitting between these states. A band structure
calculation based on a multiband Hubbard model has indi
cated that there is energy gain by increasing t2gholes in the
minority spin bands because of the large nearestneighbor
hopping between t2gorbitals.28,54In addition, there is first
neighbor hybridization between the egand t2gstates via the
large dd? integral and the t2gband corresponds the most
strongly antibonding bands, as indicated in Ref. 54. For these
reasons, a smaller occupation of the t2gtype X5↓bands and a
higher occupation of the top of the egtype X2↓bands have
been thought to be energetically favorable, which results in
the disappearance of the X2↓hole pocket in the ARUPS. The
soft xray ARPES results would then indicate that such elec
tron hopping ?depending on the orbital symmetry and the
hybridization between t2gand egstates?, which enforces the
occupation of the X2↓state, is not effective in the bulk but
only at the surface. X2↓is located above EFin the bulk band
structure of Ni observed by soft xray ARPES, as obtained
by LDA calculations. This result implies that the difference
in the exchange splitting between egand t2gstates is not so
large in the bulk of Ni as at the surface.
Alternatively, the change in the ?2↓and Z1↓band disper
sions as a function of incident photon energy and hence
probing depth can also be regarded as an indication of the
?2↓and Z1↓bands being wider in the bulk than at the surface.
In the obtained data, the group velocity of ?2↓at EFis esti
mated to be 1.11 and 0.82 eV Å using h?=780 and 435 eV,
respectively. This indicates that the ?2↓band shows greater
group velocity in the bulk than at the surface. The same
probing depth dependences are also identified in the Z1band
along X−W. These characteristics indicate that the electron
correlation of Ni is weaker in the bulk than at the surface,
leading to the hole pocket of X2↓in the bulk of Ni. A cluster
model calculation, which can effectively treat the shortrange
correlation for the electronic structure of Ni in terms of the
surface versus bulk, has also been reported.37In this cluster
model calculation, the relative intensity of the satellite struc
ture at the surface is much higher than that in the bulk, and
indicates that the correlation effects are stronger at the sur
face. The narrowing of the bandwidth on the surface as well
as absence of the X2↓hole pocket are well described by
LDA+DMFT.41This probing depth dependence of the X2↓
band is expected since correlation effects, which can be en
hanced near the surface, are more important for slower elec
trons and the velocity near the X2↓hole pocket is rather small
from lowenergy ARPES. While the X2↓state is located be
low EFin LDA+DMFT studies, the energy position of X2↓is
very sensitive to the value of J. The X2↓hole pocket appears
in the calculated Fermi surface if J is decreased from
1.2 to 1.1 eV, i.e., only by 0.1 eV. Since the present data
show wider bandwidth for the ?2↓and Z1↓bands in the bulk
of Ni and the value of J is generally reduced by the delocal
ization of the orbital, it is plausible that the X2↓hole pocket
in the bulk of Ni can also result from a slightly reduced J in
the bulk.
IV. CONCLUSION
In conclusion, the band structure of Ni has been studied
by soft xray ARPES. SX ARPES at low temperature ?50 K?
provides band dispersions consistent with the direct transi
tion model, while roomtemperature ?300 K? studies indicate
significant intensity loss due to nondirect transitions. In
ARPES with h?=780 eV, the ?2↓band is found to cross EF
between ? and X. This shows that the X2↓state in the bulk of
Ni is located above EFin contrast to the ARUPS results
giving the X2↓state below EF. The EFcrossing point of ?2↓
shifts toward the X point in ARPES with shorter probing
depth. A similar behavior is also observed in the Z1↓band
along X−W in ARPES with h?=595 and 302 eV. The ob
served behavior in the ?2↓and Z1↓bands shows that the bulk
band structure involving the X2↓hole pocket consistently ap
proaches the surface band structure observed by ARUPS,
which indicates the X2↓state to be below EF. The disappear
ance of the X2↓hole pocket at the surface is caused by the
peculiarly narrow exchange splitting in egstate compared to
that in t2gstates and the reduced bandwidth due to stronger
correlation. In addition, the magnetically active Z2↓down
spin band shows nearly flatband behavior. The Fermi surface
and band dispersions determined by the present ARPES mea
surements are in good agreement with local density approxi
mation band structure calculations. SX ARPES is thus a
valuable probe of the intrinsic momentumresolved elec
tronic structure of solids.
FIG. 6. ?Color online? The Fermi surfaces of Ni observed by
h?=780–595 eV. The closed red circles indicate the k positions
shown by the arrows in the band maps, corresponding to Fermi
surface crossings. The Fermi surfaces calculated by the LDA with
von Barth and Hedin potential are indicated by the solid lines. In
the calculated Fermi surface, a is the X5↓hole pocket, b is the X2↓
hole pocket, c is the major d↓hole Fermi surface, d and e are sp↑
and sp↓Fermi surfaces, respectively. The experimental results from
de Haas–van Alphen measurements are shown by the smallersize
symbols ?the circles, triangles, and squares? and dotted lines ?Refs.
32 and 34?.
BULK BAND STRUCTURE AND FERMI SURFACE OF¼
PHYSICAL REVIEW B 74, 045127 ?2006?
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Page 8
ACKNOWLEDGMENTS
The experiments were performed at the SPring8 with the
approval of the Japan Synchrotron Radiation Research Insti
tute ?Grants No. 2002A0589NS1np and No. 2003A0682
NS1np?. We thank H. Ohashi, Y. Tamenori, T. Ito, P. A.
Rayjada, and K. Horiba for help with this work and K. Tera
kura, J. Igarashi, A. Fujimori, T. Yokoya, A. Kotani, T. Jo, M.
Taguchi, and M. Usuda for valuable discussions.
*Present address: Institute of Materials Structure Science ?IMSS?,
High Energy Accelerator Research Organization ?KEK?, Oho 11,
Tsukuba, Ibaraki 3050801, Japan.
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