X-Ray Scattering at Lanthanide M5 Resonances: Application to Magnetic Depth Profiling
ABSTRACT Quantitative analyses of x-ray scattering from thin films of Ho and Dy metal at the M_5 resonances result in values of the optical constants and the magnetic scattering lengths f_m, with f_m as large as 200 r_0. The observation of first- and second-order magnetic satellites allows to separate f_m into circular and linear dichroic contributions. This high magnetic sensitivity, in conjunction with the tunable x-ray probing depth across the resonance can be applied to monitor depth profiles of complex magnetic structures, as e.g. of helical antiferromagnetic domains in a Dy metal film.
arXiv:cond-mat/0509725v1 [cond-mat.other] 28 Sep 2005
X-Ray Scattering at Lanthanide M5Resonances:
Application to Magnetic Depth Profiling
H. Ott,(1,†)C. Sch¨ ußler-Langeheine,(1,2)E. Schierle,(1)A. Yu.
Grigoriev,(1,††)V. Leiner,(3), H. Zabel,(3)G. Kaindl,(1)and E. Weschke(1,∗)
(1)Institut f¨ ur Experimentalphysik, Freie Universit¨ at Berlin, D-14195 Berlin-Dahlem, Germany
(2)II. Physikalisches Institut, Universit¨ at zu K¨ oln, D-50937 K¨ oln, Germany and
(3)Institut f¨ ur Experimentalphysik/Festk¨ orperphysik,
Ruhr-Universit¨ at Bochum, D-44780 Bochum, Germany
(Dated: February 2, 2008)
Quantitative analyses of x-ray scattering from thin films of Ho and Dy metal at the M5 resonances
result in values of the optical constants and the magnetic scattering lengths fm, with fm as large
as 200r0. The observation of first- and second-order magnetic satellites allows to separate fm into
circular and linear dichroic contributions. This high magnetic sensitivity, in conjunction with the
tunable x-ray probing depth across the resonance can be applied to monitor depth profiles of complex
magnetic structures, as e.g. of helical antiferromagnetic domains in a Dy metal film.
PACS numbers: 61.10.Eq,75.70.Ak,75.25.+z
Magnetism in thin films, nanostructures, and other
complex materials is currently a field of considerable
interest, where diffraction and scattering methods can
provide detailed insight into spin structures and mag-
netic correlations. While magnetic neutron diffraction
had long been the method of choice, resonant mag-
netic x-ray diffraction using synchrotron radiation 
has emerged as a complementary technique.
the photon energy to an electronic core excitation leads
to an element-specific enhancement of magnetic scatter-
ing [2, 3, 4, 5, 6, 7] that is particularly strong at the L2,3
resonances of the 3d transition elements and the M4,5res-
onances of lanthanides and actinides. Quite early, Han-
non et al. predicted that at the M4,5resonances the mag-
netic contribution fmto the scattering length f should
be of the same order of magnitude as the contribution of
charge scattering, with values of fm up to 100r0 (r0 =
classical electron radius) . This agrees with the huge
enhancement of magnetic scattering by a factor of ≈ 107
at the M4resonance of uranium , leading to sizeable
intensities along purely magnetic crystal truncation rods
of antiferromagnets, and permitting the study of surface
magnetism of UO2. The magnetic sensitivity at reso-
nance is accompanied by strong x-ray absorption (XA),
a fact that usually renders a quantitative determination
of fm from magnetic superstructure peaks difficult .
When used properly, however, the strong XA can be ex-
ploited to vary the probing depth of magnetic x-ray scat-
In this Letter, we report on soft x-ray scattering from
lanthanide-metal films, providing a quantitative charac-
terization of magnetic scattering at the M5 resonances,
including a separation of fm into circular and linear
dichroic components and a determination of the resonant
index of refraction, n = 1 − δ + iβ. With quantitative
values for β in the resonance region, the x-ray probing
depth can be tuned in a controlled way, while retaining
high magnetic sensitivity. The probing depth can thus
be varied independently of the scattering vector, provid-
ing a tool for depth-resolved characterization of complex
magnetic structures, complementary to surface scatter-
ing along the crystal truncation rods. As an example, a
depth-resolved study of the growth of helical antiferro-
magnetic (AFM) domains across a magnetic phase tran-
sition in Dy metal is presented.
The helical AFM structures in Ho and Dy metal are
well suited for resonant magnetic soft x-ray studies, since
the magnetic periods match the x-ray wavelengths at
the respective M5 resonance. In Ho metal this helical
AFM structure persists in films down to 10 monolay-
ers (ML) , a thickness range where absorption ef-
fects are reduced, simplifying a quantitative determina-
tion of fm. Soft x-ray studies were carried out in an
ultra-high-vacuum (UHV) (Θ/2Θ) diffractometer on in-
situ grown lanthanide-metal films on W(110)  and on
Y/Ho/Y trilayer samples prepared ex situ by molecular-
beam epitaxy (MBE) on a-plane sapphire . For all
samples, the c axis was perpendicular to the film sur-
face. M5resonance data were taken at beamline U49/1
of the Berliner Elektronenspeicherring f¨ ur Synchrotron-
strahlung (BESSY) with linearly polarized x rays (π po-
larization). Resonant Dy L3 data (at ≈ 8 keV) were
recorded at beamline ID 10 A of the European Syn-
chrotron Radiation Facility (ESRF) in Grenoble.
The resonant enhancement of magnetic x-ray scatter-
ing at the M5 resonance and the concomitant strong
absorption are illustrated in Fig. 1(a), which displays
specular reflectivity curves from 110 ML Ho on W(110)
at 40 K, well below the bulk N´ eel temperature (TN =
131.2 K). Far below resonance (hν = 900 eV), the re-
flectivity is dominated by intensity oscillations (Kiessig
fringes) caused by interference of x rays scattered from
the surface with those scattered from the Ho/W inter-
face . At hν = 1340 eV, 14 eV below the M5 reso-
0,05 0,10 0,15 0,20 0,25 0,30
1320 133013401350 1360
1260 12701280 12901300
??? ( ?103)
??? ( ?103)
FIG. 1: (a) Specularly reflected intensities (Is on a log-scale)
from 110 ML Ho/W(110) versus momentum transfer q⊥(data
for different photon energies are vertically offset). The solid
lines represent fits with a superposition of magnetic (dotted)
and charge (dashed) contributions. Lower panels: optical pa-
rameters β (solid symbols) and δ (open symbols) of (b) Ho
and (c) Dy metal in the M5region. The dotted lines represent
the Kramers-Kronig transforms of the β values in (b), and β
obained from the scaled XA spectrum (solid line) in panel (c).
nance maximum, the diffraction peak caused by the mag-
netic superstructure, labeled (00τ), is already clearly vis-
ible. At maximum resonance (hν = 1354.2 eV), the sub-
stantial XA strongly alters the reflectivity curve: (00τ)
is broadened due to the reduced number of layers that
contribute to the magnetic signal , and the Kiessig
fringes are completely suppressed, since the x rays no
longer penetrate to the Ho/W interface.
As a first step towards a determination of fm, the
resonant optical constants were derived from reflectivity
curves by fit analyses using the Parratt formalism .
Far from resonance, tabulated values of β and δ  are
reliable and were used to fit the 900-eV data, yielding the
structural parameters of the film . The optical con-
stants at a given resonance energy were then obtained
from a fit of the respective reflectivity curve with β and
δ as the only adjustable parameters. The superimposed
magnetic peak was described by the structure factor of a
helix, taking a mean magnetic roughness and an angle-
dependent polarization factor into account . Refrac-
tion and absorption corrections to the shape of the mag-
netic peak were accounted for by a complex scattering
The resulting β and δ values are plotted in Fig. 1(b);
they are consistent with a Kramers-Kronig (KK) trans-
form of β that reproduces δ rather well. At maximum
resonance, β = (2.8±0.3)·10−3is obtained, a value that
fits well with recent results for Gd and Tb , and corre-
sponds to a photon attenuation length of 1/µ = λ/4πβ ≈
260˚ A, i.e., an effective probing depth of only ≈ 28˚ A at
the magnetic peak position (scattering angle Θ ≈ 12.5◦
with respect to the sample surface). Similar data were
obtained for Dy as shown in Fig. 1(c). Here, the solid line
represents β values obtained from the Dy M5XA spec-
trum, the KK transform of which consistently reproduces
the δ values obtained from the reflectivity curves.
For a quantitative determination of fm, a thin Y/Ho/Y
film was used that exhibits a larger τ compared to
Ho/W(110)  and hence a smaller charge-scattering
background at (00τ). Figure 2(a) displays the M5 XA
spectrum of Ho with its atomic 3d94f11final-state mul-
tiplet that separates into three subspectra with ∆J =
0,±1 [17, 18]. In the presence of magnetic order, the J
states split into MJsublevels, and the transitions are gov-
erned by the selection rule ∆MJ = 0,±1. In the heavy
lanthanides, the transition probabilities for a given ∆J
are dominated by a single ∆MJvalue, and the subspectra
can then be identified approximately by ∆MJ = 0,∓1,
respectively . These dipole transitions determine the
resonant scattering length [3, 7]
f = (e′·e)·f0−i(e′× e)·m·fc
m+(e′· m)(e · m)·fl
with f0 = a?F1
the energy-dependent dipole oscillator strengths with
∆MJ= 0,±1, and e and e′the polarization vectors of in-
cident and scattered x rays, respectively. a = (3/4πk) is
a wave-vector dependent factor and m is the unit vector
in direction of the local magnetic moment.
For Ho, circular (fc
Eq. 1 are readily distinguished, since the corresponding
diffraction peaks at (00τ) and (002τ) are well separated
in momentum space (inset in Fig. 2(b)). The resonant
(00τ) peak at 2Θ ≈ 25◦is due to fc
factor linear in m. Characterized by a sinusoidal modu-
lation, the magnetic structure of Ho contains no higher
harmonics, and the (002τ) peak at 2Θ ≈ 50◦is thus solely
a resonance effect due to fl
m. With a polarization fac-
tor quadratic in m, fl
mgives rise to a resonant peak at
(002τ), since m2oscillates with half the magnetic period.
The linear dichroic term fl
mgenerally probes elements
that preserve time-reversal symmetry ; therefore it
can be used to study the ordering of quadrupole moments
in non-spherical charge densities. In the present case of
AFM Ho metal, however, a distinction of quadrupolar
and spin linear dichroism is of no significance, since the
strong spin-orbit interaction of the atomic-like 4f states
couples the arrangement of the quadrupole moments to
Here, the F1
m) and linear (fl
m) dichroic terms in
mwith a polarization
13451350 1355 1360
|fm| , |fm| (100r0)
0 20 40
FIG. 2: (a) M5 XA spectrum of 31 ML Ho/W(110) recorded
via sample drain current. The subspectra represent calculated
∆J = 0,±1 transitions . (b) Magnetic scattering lengths
scale) from a 16-ML Ho MBE film, taken at the two given
photon energies (in eV).
m| and |fl
m|. The inset shows reflectivity curves (on a linear
the spin structure . The (00τ) and (002τ) can be en-
tirely described by fc
m, respectively, according to
the ∆MJ = 0,±1 transitions from the MJ sublevels of
the helical AFM ground state of Ho.
From the respective integrated intensities, |fc
m| were calculated, taking polarization factors 
and absorption corrections into account (β values from
Fig. 1(b)). The resulting |fc
Fig. 2(b), revealing a clear correspondence to the sub-
spectra in Fig. 2(a): |fc
m| peaks at the maxima of the
∆J = ±1 subspectra, whereas |fl
imum of the ∆J = 0 subspectrum. Thus, the 3d94f11
multiplet of Ho allows to identify the circular and lin-
ear dichroic contributions to the scattering length; such
a separation is not equally straightforward in case of the
actinides . We obtain |fc
at the respective resonance maxima, i.e. values that are
somewhat larger, but of the same order of magnitude as
An application that exploits both the tunable x-ray
probing depth and the high magnetic sensitivity across
the resonance is the study of depth-dependent inhomo-
geneous magnetic structures, even in case of chemically
homogeneous materials. We demonstrate the potential
of the method for the growth of helical AFM domains
at the ferromagnetic (FM)/helical-AFM first-order phase
transition of Dy metal . As shown in Fig. 3(a) for a
180-ML film of Dy on W(110), this transition exhibits
substantial hysteresis. Here, the integrated intensity of
(002-τ) is displayed [1, 2], recorded at the L3resonance
of Dy (hν = 7780 eV), where all layers of the film con-
tribute about equally to the magnetic signal; the x-ray
probing depth of ≈ 9 µm is much larger than the film
m| and |fl
m| are plotted in
m| peaks at the max-
m| = 200r0and |fl
m| = 160r0
thickness of ≈ 500˚ A. Due to the weaker magnetic sen-
sitivity at L3 as compared to M5, a polarization anal-
ysis was required to separate (002-τ) from the charge-
scattering background [1, 2]. When cooling to the FM
phase (open symbols), (002-τ) disappears at ≈ 70 K; it
reappears when heating, but with a delay of ≈ 20 K
(solid symbols). Notably, the (002-τ) intensity does not
recover abruptly, but remains below the cooling-down
curve up to ≈ 140 K, indicating a temperature-dependent
growth of helical AFM domains. This is further charac-
terized by the widths of the magnetic diffraction peaks
displayed in Fig. 3(c), both in the direction perpendic-
ular (Wq⊥) and parallel (Wq?) to the film plane. Wq⊥
was determined both for (002-τ) at the L3(squares) and
for (00τ) at the M5(circles) resonance. The smaller Wq?
was measured only at the M5resonance, where sufficient
momentum resolution could be achieved.
ing, Wq⊥remains essentially constant down to ≈ 70 K;
Wq⊥≈ 1.2×10−2˚ A−1corresponds to 180 ML of Dy, i.e.,
the helical AFM structure extends through the whole
film. Below ≈ 70 K, Wq⊥increases abruptly with the
decay of the helical AFM order and – with increasing
temperature – exhibits the same hysteresis as the inten-
sity of (002-τ). In contrast, Wq?is essentially constant in
the studied temperature range, showing that the helical
AFM domains develop in a laterally homogeneous way
in the direction perpendicular to the film plane.
For a depth-resolved characterization of domain
growth, (00τ) was studied at the Dy M5 resonance.
6080 100 120 140 160 180
FM/helical-AFM phase transition in 180-ML Dy/W(110)
upon cooling down (open symbols) and warming up (filled
symbols); lines serve as guides to the eye. (a) Integrated in-
tensities of (002-τ) at the L3 resonance (7780 eV). (b) Anal-
ogous data from (00τ) recorded at the M5 resonance.
Widths of magnetic peaks in the direction parallel (Wq?) and
perpendicular (Wq⊥) to the film plane recorded at 7780 eV
(squares) and at 1305 eV (circles).
Magnetic diffractiondata characterizing the
50 75 100 125 150175
Layer Index n
FIG. 4: Temperature-dependent growth of helical AFM do-
mains in 180-ML Dy/W(110) in the direction perpendicular
to the film plane. For details, see text.
Fig. 3(b) displays the integrated intensities obtained at
hν = 1293 eV where the effective x-ray probing depth
is only ≈ 35˚ A. Here, the delayed formation of the he-
lical AFM phase upon heating is more pronounced than
at 7780 eV excluding a nucleation of the helical domain
in the topmost surface layer. Instead, the domain nucle-
ates close to the surface as discussed below. A further
detail of the reflectivity curves recorded at highest sur-
face sensitivity (data not shown here) is the occurrence
of a magnetic signal at smaller scattering angles in ad-
dition to (00τ). This is the signature of a surface AFM
structure with a larger mean modulation period in the
surface layers of the film that develops when cooling be-
low ≈ 125 K and that disappears upon heating above
this temperature. Such a structure had previously been
reported for a 10-ML thick Ho film , and results from
the tendency of helical AFM lanthanide films to favor
FM order in the surface region .
The complete depth profile, shown in Fig. 4, was de-
rived from data recorded with various x-ray probing
depths across the Dy M5 resonance. The β values de-
termined for the same film (Fig. 1(c)) allowed an analy-
sis, where the magnetic scattering amplitude of an indi-
vidual layer n at depth dnis reduced by e−µdn/sinθ.
The consistent analysis of temperature-dependent inten-
sities leads to the following scenario: Upon cooling, the
whole film orders helical AFM below TN ≈ 179 K. Be-
low ≈ 125 K, the surface AFM structure develops as de-
scribed above, consistent with the minute increase of Wq⊥
by ≈ 1% in this temperature region. Below ≈ 70 K, the
film turns FM, except for the topmost ≈ 19 layers that
retain the surface AFM structure (cross-hatched area).
Upon heating, the helical AFM domain nucleates below
this surface region and grows with increasing T towards
the two interfaces. When reaching ≈ 140 K, it has devel-
oped across the whole film.
We point out that the present approach of exploiting
the tunable x-ray probing depth across a resonance is
not restricted to magnetic signals, and is also applicable
to systems containing 3d transition elements, where at
the L2,3resonances similarly strong absorption has been
observed . Such depth-dependent diffraction studies
will be particularly interesting with focused x-ray beams
providing additionally lateral resolution .
Expert support by the staff members of BESSY and
the ESRF is gratefully acknowledged, particularly the
commitment of G. Gr¨ ubel. We acknowledge helpful dis-
cussions with M. W. Haverkort. The work was finan-
cially supported by the BMBF, projects 05KS1KEE/8
and 03ZA6BC2, the Sfb-290 (TPA06) of the DFG,
and the Landesministerium NRW f¨ ur Wissenschaft und
[∗] Corresponding author:
[†] present address: II. Physikalisches Institut, Universit¨ at
zu K¨ oln, D-50937 K¨ oln, Germany
[††] present address: Department of Materials Science and
Engineering, University of Wisconsin, Madison, WI
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