Spin-dependence of Ce $4f$ hybridization in magnetically ordered
  systems: A spin-resolved photoemission study of Ce/Fe(110)
Spin-dependence of Ce 4f hybridization in magnetically ordered
systems: A spin-resolved photoemission study of Ce/Fe(110)
Yu. S. Dedkov,1,∗ M. Fonin,2 Yu. Kucherenko,3
S. L. Molodtsov,1 U. Rüdiger,2 and C. Laubschat1
1Institut für Festkörperphysik, Technische Universität Dresden, 01062 Dresden, Germany
2Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
3Institute for Metal Physics, National Academy of Sciences of Ukraine, 03142 Kiev, Ukraine
(Dated: October 30, 2018)
Abstract
Spin- and angle-resolved resonant (Ce 4d → 4f) photoemission spectra of a monolayer Ce on
Fe(110) reveal spin-dependent changes of the Fermi-level peak intensities. That indicate a spin-
dependence of 4f hybridization and, thus, of 4f occupancy and local moment. The phenomenon
is described in the framework of the periodic Anderson model by 4f electron hopping into the
exchange split Fe 3d derived bands that form a spin-gap at the Fermi energy around the Γ point
of the surface Brillouin zone.
PACS numbers: 71.20.Eh, 75.30.Mb, 75.70.-i, 79.60.-i
∗ Corresponding author. E-mail: dedkov@physik.phy.tu-dresden.de
http://arxiv.org/abs/0704.1254v1
As a function of chemical composition, the electronic properties of Ce 4f states in in-
termetallic compounds vary from localized 4f 1 character over heavy-fermion behavior and
mixed valence to the boarder of itinerant behavior [1]. This fascinating variety of characters
is already reflected in Ce metal, where in the course of the famous isostructural γ → α
transition a magnetic phase transforms into a nonmagnetic one depending on temperature
and/or pressure accompanied by a volume collapse of 15% [2]. While in the promotion model
this phenomenon was ascribed to a transition from a trivalent 4f 1(5d6s)3 to a tetravalent
4f 0(5d6s)4 configuration [3], later studies related the effect to a Mott-transition from local-
ized to itinerant character of the 4f state [4] or to a Kondo collapse [5].
The promotion model is clearly ruled out by photoemission (PE) that reveals only weak
intensity changes of the total 4f derived emission upon the γ → α transition [6]. Instead of a
single 4f 0 PE final state at about 2 eV binding energy (BE) as expected from a localized 4f 1
ground state a second 4f -derived feature is observed at the Fermi energy, EF , that increases
in intensity upon the γ → α transition [6]. An itinerant description based on the local
density approximation (LDA) fails to explain this double-peak structure [7], it is, however,
well reproduced in the framework of the single-impurity Anderson model (SIAM) considering
electron hopping between localized 4f 1 and valence-band (VB) states [8]. A momentum
dependence of the 4f signal as recently observed by angle-resolved PE experiments [9, 10, 11]
could be explained considering the translational symmetry of the solid within a simple
approach to the periodic Anderson model (PAM) [10, 11, 12].
From both SIAM and PAM the Fermi-peak intensity may be taken as a direct measure for
the hopping probability. The latter should increase with the VB density of states at EF , and
in fact huge Fermi-level peaks are typically observed in PE spectra of Ce transition-metal
compounds reflecting α-like behavior of the Ce 4f states due to hybridization with transition-
metal d-bands [13]. A spin-dependence of 4f hopping may be expected for magnetically
ordered systems where the exchange splitting of the VB leads to strong variations of the
density of states at EF for differently oriented VB spins. Respective spin-dependent γ → α
transitions have not be observed so far, the effect, however, could be of high importance for
the understanding of magnetic anomalies in these systems since the local magnetic properties
of the Ce atoms may strongly vary as a function of 4f spin orientation.
In this contribution we report for the first time on a spin-dependent γ → α−like transition
observed by a spin- and angle-resolved resonant PE from an ordered Ce adlayer on Fe(110).
Although hybridization is expected to be relatively weak in the outermost surface layer
due to the low coordination of the Ce atoms [14], the quasi two-dimensional structure of the
system allows for a proper determination of the position in k space probed in the experiment
as necessary for a quantitative description within PAM applied here. For Ce/Fe(110), our
local spin density approximation (LSDA) slab calculations reveal at the Γ point a strong
reduction of majority-spin states around EF that should lead to a respective weakening of
4f hybridization for this spin orientation. In fact, our spin- and angle-resolved PE spectra
show a lower Fermi-level peak intensity for the 4f majority- than minority-spin orientation.
Simulations of the PE spectra within PAM reproduce this effect as well as a spin-dependent
splitting of the ionization peak observed in the experimental data. Similar spin-dependencies
are expected to be of high importance for the understanding of magnetic anomalies in a
series of other RE systems, where hybridization phenomena were experimentally observed
and successfully described within SIAM or PAM [12, 15].
A Fe(110) substrate was prepared by thermal deposition of Fe films with a thickness
of 50 Å on W(110) and subsequent annealing at 450K. Low-energy electron diffraction
(LEED) yielded in sharp patterns with two-fold symmetry as expected for a structurally
ordered bcc Fe(110) surface [Fig. 1(a)]. Further deposition of 0.5 monolayer (close-packed
atomic arrangement) of Ce metal at 300K led to a sharp overstructure in the LEED pattern
[Fig. 1(b)] that could be reproduced by a kinematic LEED simulation [Fig. 1(d)] with the
structural model shown in Fig. 1(c). Ce atoms are placed on hollow-sites of the bcc Fe(110)
surface reproducing the arrangement of a (110) plane of fcc γ-Ce expanded by 11%. Spin-
and angle-resolved resonant PE experiments at the Ce 4d → 4f absorption threshold were
performed using a hemisherical PHOIBOS150 electron-energy analyzer (SPECS) equipped
with a 25 kV mini-Mott spin-detector and synchrotron radiation from beamline U125/1-
PGM of BESSY (Berlin). The energy and angle resolutions were set to 100meV and ±2◦,
respectively. The light incidence angle was 30◦ with respect to the sample surface, and the
photoelectrons were collected around the surface normal. Spin-resolved measurements were
performed in normal emission geometry at 130K in magnetic remanence after having applied
a magnetic field pulse of about 500Oe along the in-plane 〈11̄0〉 easy axis (perpendicular to
electric field vector of the light) of the Fe(110) film. The experimental setup asymmetry
was accounted for in the standard way by measuring spin-resolved spectra for two opposite
directions of applied magnetic field [16, 17]. The base pressure in the experimental chamber
was in the upper 10−11mbar range rising shortly to the upper 10−10 range during evaporation
and annealing.
Fig. 2 shows spin-resolved PE data of Ce/Fe(110) taken on- and off-resonance at 121 eV
and 112 eV photon energies, respectively. The off-resonance spectra are dominated by emis-
sions from Fe 3d-derived bands and are very similar to respective data of the pure Fe sub-
strate (not shown here). The spectra reflect clearly the exchange splitting of the Fe 3d bands
into a minority-spin component at EF (”spin down”: filled triangles) and a majority-spin
component shifted to higher BE (”spin up”: open triangles). While the spectra of the pure
substrate remain almost unchanged when going from 112 eV to 121 eV photon energy, the
on-resonance spectra of Ce/Fe(110) reveal an additional feature around 2.2 eV BE that is
ascribed to the resonantly enhanced 4f signal.
In order to extract the Ce 4f contributions from these spectra, the off-resonance data
were subtracted from the on-resonance spectra after proper normalization of the intensities
with respect to the photon flux and the slowly varying Fe 3d photoionization cross section.
The resulting spin-resolved 4f spectra are shown in the upper part of Fig. 3 together with
the corresponding spin polarization P (inset) defined as P = (I↑ − I↓)/(I↑ + I↓), where I↑
and I↓ denote the intensities of the majority- and minority-spin channels, respectively. The
spectra reveal the well-known double-peak structure of the Ce 4f emission consisting of a
main maximum at 2.2 eV corresponding to the ionization peak expected for an unhybridized
4f 1 ground state and the hybridization peak at EF . From the weak intensity of the latter
relative to the ionization-peak signal, a weak hybridization similar to the one in γ-Ce can
be concluded as it is expected for a Ce surface layer [18]. The most important observation
is, however, that the intensity of the hybridization peak is larger for the minority- than for
the majority-spin component (Fig. 3) indicating larger 4f -hybridization of the former. The
spin polarization of both, the ionization and the hybridization peaks, gives a negative sign
indicating that the preferred orientation of the Ce 4f spins is opposite to the magnetization
direction of the Fe layers. In addition to the double-peak structure another feature is visible
around 1 eV BE (Fig. 3), that is weaker in intensity and shifts to lower BE when going from
the minority- to the majority-spin component.
In order to understand the ground-state magnetic properties of Ce/Fe(110), as a first
step fully relativistic spin-polarized band-structure calculations were performed by means
of the linear muffin-tin orbital (LMTO) method. A pure Fe surface and the Ce/Fe(110)
system were considered using the structural model shown in Fig. 1(c). The Fe substrate was
simulated by a five-layer slab of Fe atoms with (110) orientation of the surface. The results
were compared to data calculated for the isostructural non-f system La/Fe(110).
For the atoms in the middle layer of the Fe slab the calculations give a local electronic
structure close to that obtained for Fe bulk [19]. The calculated Fe 3d spin moment value lies
between 2.35µB and 2.40µB. At the surface it increases to 2.60µB. In all cases contributions
of s and p electrons to magnetic moment are negligible.
By the presence of a Ce overlayer the Fe 3d spin moments of the surface atoms are
reduced to 2.14µB and 2.50µB, respectively, depending on whether the Fe atoms are nearest
neighbors of Ce atoms or not. Replacing in the calculation Ce by La atoms give very similar
results indicating that the electronic structure of the Fe atoms is perturbed by interactions
with extended valence states (mainly 5d) of the overlayer.
The calculations yield for a La atom on the Fe(110) surface a local spin moment of
−0.24µB, determined mainly by the 5d electrons (−0.20µB). The negative sign stands for
an antiparallel orientation with respect to the Fe 3d spin moment. For the Ce atom the local
spin moment is equal to −1.12µB, with 5d and 4f contributions of −0.28µB and −0.82µB,
respectively. Thus, like in other Ce-Fe systems [20, 21, 22], the Ce 4f electrons reveal a
spin orientation opposite to Fe 3d majority spin in agreement with the PE experiment.
Since the 4f electrons have additionally a large positive orbital momentum of 2.80µB due
to their reduced atomic coordination at the surface the total moment equals to 1.70µB
and corresponds, thus, to ferromagnetic coupling with respect to the Fe 3d spins. At finite
temperatures magnetic disorder leads to the situation encountered in the experiment where
a part of the 4f spins are flipped into the opposite direction.
In order to describe the observed variation of 4f hybridization as a function of spin
orientation, we used the simplified periodic Anderson model that was recently successfully
applied to explain the angle-resolved PE spectra of CePd3 [10] and Ce/W(110) [11]. In
this approach the double occupation of the 4f states is ignored (on-site f − f Coulomb
interaction energy, Uff → ∞) and k vector conservation upon hybridization is assumed. In
this case a simplified (without Uff term) Anderson Hamiltonian can be written as follows
εσ(k)d+
εσf (k)f
kσ + f
where the VB states |kσ〉 have a dispersion εσ(k) and are described by creation (annihilation)
operators d+
kσ (dkσ). The operator f
kσ creates a f electron with momentum k, spin σ,
and energy εσf (k). We assume that a non-hybridized f band has no dispersion: ε
f (k) =
εσf allowing, however, a possible small difference in the energy positions of 4f levels with
different spin σ due to exchange interaction. The two electron subsystems (VB and 4f
states) are coupled via a hybridization V σ
(E) that leaves the electron spin unaffected, i. e.
spin-flips upon electron hopping are excluded. E denotes the BE with respect to EF . This
form of the Hamiltonian allows us to diagonalize it for each particular k point of the surface
Brillouin zone (BZ) and for each spin state σ.
For the hybridization matrix element V σ
(E) we use calculated f -projected local expansion
coefficients cσf (E,k) of the Bloch functions around the rare-earth sites: V
(E) = ∆·cσf (E,k),
where ∆ is a constant, adjustable parameter. Expansion coefficients cσf (E,k) that charac-
terize the local f character of VB states were taken from the results of the band-structure
calculations of the La/Fe(110) system, in order to exclude the contribution of localized Ce
4f orbitals. For normal emission of the photoelectrons we have to consider VB states at
the Γ point of the surface BZ. The calculated values of
∣cσf (E,Γ)
are shown in the bottom
part of Fig. 2. The energy distributions of the VB states of local f character are quite
different for majority- and minority-spin electrons. Since these states are formed by linear
combination of wave functions of the neighboring atoms (mainly Fe 3d) penetrating into
the La atomic spheres, they reflect to some extent the energy and spin distribution of the
latter (see off-resonance spectra in Fig. 2). Their different amplitude and energy distribution
for majority- and minority-spin states causes strong differences in the respective hybridiza-
tion matrix elements and results in different shape of the 4f PE spectra for the two spin
directions.
The spectral functions of the Ce 4f emission were calculated using the parameters ε
−1.9 eV, ε
= −1.7 eV, and ∆ = 0.85 eV. These values deviate from those used in Ref. [11]
for Ce/W(110) only by slightly higher BE of the non-hybridized 4f level resulting from the
lower coordination of the Ce atoms. An energy-dependent life-time broadening of the form
ΓL = 0.030 eV+0.085E was considered. The calculated spectral functions were additionally
broadened with a Gaussian (ΓG = 100meV) to simulate finite instrumental resolution and
an integral background was added to take into account inelastic scattering.
The calculated spin-resolved Ce 4f PE spectra are presented in Fig. 3 (lower part). The
energy distribution of the PE intensity agrees well with that of the experimental spectra
(Fig. 3, upper part). The minority-spin spectrum reveals high intensity of the hybridization
peak due to large density of the minority-spin VB states close to EF . A shoulder near 1 eV
BE is formed by hybridization with VB peaks at 0.9 eV and 1.3 eV BE (Fig. 1). In accordance
with the experiment, in the calculated majority-spin spectrum the ionization peak is split
into three components (maxima at 0.9 eV, 2.1 eV, and shoulder at 3 eV BE) as a result of
hybridization with the VB states (at 1.4 eV and between 2 eV and 3 eV BE). No majority-
spin hybridization peak is obtained in the calculation due to the negligibly small density of
VB states for this spin direction at the Fermi level. This theoretical result deviate from the
experiment where a reduced but finite hybridization peak was observed. The latter may be
ascribed to the finite angle resolution of the experiment that samples also regions in the k
space where majority-spin bands cross EF . The calculated spin polarization (Fig. 3, inset in
the lower part) reproduces qualitatively the energy dependence of the measured polarization.
Particularly good agreement is obtained for the points where the spin polarization changes
its sign.
In summary, we have shown that the observed spin-dependence of the shape of the Ce 4f
emission in Ce/Fe(110) system may be explained by a spin-dependence of 4f -hybridization.
From this result 4f -occupancy as well as effective magnetic moment are generally expected to
vary with spin-orientation, an effect that may be of crucial importance for the understanding
of many-body effects and magnetic anomalies in RE systems.
This work was funded by the Deutsche Forschungsgemeinschaft, SFB 463, Projects TP
B4 and TP B16 as well as SFB513. We would like to acknowledge BESSY staff for technical
support during experiment.
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FIG. 1: (Color online) LEED images obtained from (a) Fe(110) and (b) Ce/Fe(110); assumed
surface crystallographic structure of the Ce/Fe(110) system (c) and simulation of the LEED-image
(d). The shaded rectangle in (c) visualizes the fcc Ce(110) plane expanded by 11%.
FIG. 2: (Color online) Spin-resolved PE spectra of Ce/Fe(110) system measured in on- and off-
resonance at the 4d → 4f absorption threshold. Open/filled triangles denote contributions of
majority/minority spin directions, respectively. Bottom part: Calculated local 4f character of the
VB states (|cσ
(E,Γ)|2) at the La site in the Γ point of the surface BZ for La/Fe(110) system for
majority- (solid line) and minority-spin (shaded area) direction.
FIG. 3: (Color online) Spin-resolved experimental (upper part) and calculated (lower part) Ce
4f emission for Ce/Fe(110). Majority- and minority-spin emissions are shown by open and solid
triangles, respectively. The insets show the corresponding spin polarization P .
	References
