Strong coupling of Sm and Fe magnetism in SmFeAsO as revealed by magnetic x-ray scattering

Abstract

The magnetic structures adopted by the Fe and Sm sublattices in SmFeAsO have been investigated using element-specific x-ray resonant and nonresonant magnetic scattering techniques. Between 110 and 5 K, the Sm and Fe moments are aligned along the c and a directions, respectively, according to the same magnetic representation 5 and the same propagation vector (1 0 1 2). Below 5 K, the magnetic order of both sublattices changes to a different magnetic structure, and the Sm moments reorder in a magnetic unit cell equal to the chemical unit cell. Modeling of the temperature dependence for the Sm sublattice, as well as a change in the magnetic structure below 5 K, provides clear evidence of a surprisingly strong coupling between the two sublattices, and indicates the need to include anisotropic exchange interactions in models of SmFeAsO and related compounds.

Full text

PHYSICAL REVIEW B 84, 054419 (2011)
Strong coupling of Sm and Fe magnetism in SmFeAsO as revealed by magnetic x-ray scattering
S. Nandi,1,*Y. Su,2Y. Xiao,1S. Price,1X. F. Wang,3X. H. Chen,3J. Herrero-Mart´
ın,4C. Mazzoli,4H. C. Walker,4
L. Paolasini,4S. Francoual,5D. K. Shukla,5J. Strempfer,5T. Chatterji,6C. M. N. Kumar,1R. Mittal,7H. M. Rønnow,8
Ch. R¨
uegg,9,10 D. F. McMorrow,10 and Th. Br¨
uckel1,2
1J¨
ulich Centre for Neutron Science JCNS and Peter Gr¨
unberg Institut PGI, JARA-FIT,
Forschungszentrum J¨
ulich GmbH, D-52425 J¨
ulich, Germany
2J¨
ulich Centre for Neutron Science JCNS-FRM II, Forschungszentrum J¨
ulich GmbH, Outstation at FRM II,
Lichtenbergstraße 1, D-85747 Garching, Germany
3Hefei National Laboratory for Physical Science at Microscale and Department of Physics,
University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
4European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex 9, France
5Deutsches Elektronen-Synchrotron DESY, D-22607 Hamburg, Germany
6Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France
7Solid State Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India
8Laboratory for Quantum Magnetism, Ecole Polytechnique F´
ed´
erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
9Laboratory for Neutron Scattering, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
10London Centre for Nanotechnology and Department of Physics and Astronomy, University College London,
London WC1E 6BT, United Kingdom
(Received 3 July 2011; published 5 August 2011)
The magnetic structures adopted by the Fe and Sm sublattices in SmFeAsO have been investigated using
element-specific x-ray resonant and nonresonant magnetic scattering techniques. Between 110 and 5 K, the
Sm and Fe moments are aligned along the cand adirections, respectively, according to the same magnetic
representation 5and the same propagation vector (1 0 1
2). Below 5 K, the magnetic order of both sublattices
changes to a different magnetic structure, and the Sm moments reorder in a magnetic unit cell equal to the chemical
unit cell. Modeling of the temperature dependence for the Sm sublattice, as well as a change in the magnetic
structure below 5 K, provides clear evidence of a surprisingly strong coupling between the two sublattices, and
indicates the need to include anisotropic exchange interactions in models of SmFeAsO and related compounds.
DOI: 10.1103/PhysRevB.84.054419 PACS number(s): 74.70.Xa, 75.25.−j, 75.50.Ee
I. INTRODUCTION
Following the discovery of superconductivity in
LaFeAsO1−xFx, with Tc=26 K,1an increase of the supercon-
ducting transition temperature to above 50 K has been achieved
by replacing La with rare-earth (R) elements.2–6The highest
transition temperature is observed in SmFeAsO1−xFx(Tc∼
55 K). Interestingly, several studies on powder samples indi-
cate that Sm magnetic order coexists with superconductivity
over a range of fluorine doping.7–9Muon-spin relaxation mea-
surements on RFeAsO (R=La, Ce, Pr, and Sm) compounds
found considerable interaction between the rare-earth and Fe
magnetism below the ordering of Fe moments (T∼140 K)
only in CeFeAsO.10 This leads to the conclusion that the R-Fe
interaction may not be crucial for the observed enhanced su-
perconductivity in RFeAsO1−xFx. Recent neutron-scattering
measurements on NdFeAsO also found an interaction between
the two magnetic sublattices, however at T∼15 K, much
below the ordering temperature of the Fe moments.11 In the
case of EuFe2As2,12,13 the only known rare-earth containing
member of the AFe2As2(A=alkaline earth, rare earth) fam-
ily, no interaction has been found so far. Therefore, elucidating
the interaction between the two sublattices and determining its
nature is an important endeavor in understanding magnetism
and superconductivity in the RFeAsO family.
Due to the strong neutron absorption of Sm, the magnetic
structure determination in SmFeAsO via neutron diffraction
is considerably more challenging than that of other members
of the new superconductors. The only attempt was made on a
powder sample.14 Here we report on the first element-specific
x-ray resonant magnetic scattering (XRMS) and nonresonant
x-ray magnetic scattering (NRXMS) studies of SmFeAsO to
explore the details of the magnetic structure of the parent
compound and to determine the interaction between the two
magnetic sublattices. Our resonant scattering experiments
show that there is a strong interplay between Fe and Sm
magnetism. Magnetic order of Sm exists at temperatures as
high as 110 K and can be explained by the coupling between
Sm and Fe magnetism.
II. EXPERIMENTAL DETAILS
Single crystals of SmFeAsO were grown using NaAs flux
as described earlier.15 For the scattering measurements, an
as-grown platelike single crystal of approximate dimensions
2×2×0.1mm
3with a surface perpendicular to the caxis
was selected. The XRMS and NRXMS experiments were
performed on the ID20 beamline16 at the ESRF (European
Synchrotron Radiation Facility) in Grenoble, France at the Sm
L2,L3and Fe Kabsorption edges and at the Fe Kedge
at beamline P09 at the PETRA III synchrotron at DESY.
The incident radiation was linearly polarized parallel to the
horizontal scattering plane (πpolarization) and perpendicular
to the vertical scattering plane (σpolarization) for the ID20 and
P09 beamlines, respectively. The spatial cross section of the
beam was 0.5 (horizontal) ×0.5 (vertical) mm2for the ID20
while it was 0.2 (horizontal) ×0.1 (vertical) mm2for P09.
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S. NANDI et al. PHYSICAL REVIEW B 84, 054419 (2011)
Au (2 2 0) was used at the Sm L2edge, and Cu (2 2 0) was used
for both the Sm L3and Fe Kabsorption edges as a polarization
and energy analyzer to suppress the charge and fluorescence
background relative to the magnetic scattering signal. The
sample was mounted at the end of the cold finger of a standard
orange cryostat (at ID20), a vertical field cryomagnet (at
ID20) and a displex refrigerator (at P09) with the ac plane
coincident with the scattering plane. Measurements at ID20
were performed at temperatures between 1.6 K and 15 K,
while the lowest achievable temperature at P09 was 5 K.
III. EXPERIMENTAL RESULTS
A. Macroscopic characterizations
Figure 1shows the heat capacity of a SmFeAsO single
crystal, measured using a Quantum Design physical property
measurement system (PPMS). Specific-heat data show phase
transitions at 143.5±2 K and 4.8±0.2 K, respectively.
Figure 2(a) shows the magnetic susceptibility of a SmFeAsO
single crystal, measured using a Quantum Design (SQUID)
magnetometer. Magnetic susceptibility shows a clear phase
transition at 5 K. There is a clear anomaly χab >χ
cover
the whole temperature range. Figure 2(b) shows the M-H
curves at several temperatures for magnetic fields parallel to
both the cand ab planes, measured using a Quantum Design
vibrating sample magnetometer (VSM). Zero-field intercept of
the M-Hcurves for both field directions places an upper limit
of ferromagnetic contribution less than 1.7×10−6μB/f.u. for
all the temperatures measured.
B. Observation of resonant and nonresonant magnetic
scattering and characterization of the transition
temperatures
To determine whether there is a structural phase transition,
as observed in powder SmFeAsO,17 (ξξ0)Tscans were
FIG. 1. (Color online) Temperature dependence of the specific
heat. TN1and TN2are the spontaneous magnetic ordering temperatures
of the Fe and Sm magnetic moments respectively. TSis the structural
phase transition temperature. Vertical lines are guides to the eye after
x-ray diffraction measurements.
FIG. 2. (Color online) (a) Temperature dependence of the mag-
netic susceptibility measured upon heating of the zero-field cooled
sample in a field of 1 T. (b) M-Hcurves for magnetic fields parallel
and perpendicular to the cdirection at several temperatures.
performed through the tetragonal (T)(226)
TBragg reflection
as a function of temperature. As shown in the inset of Fig. 3(a),
the (2 2 6)TBragg reflection splits into orthorhombic (O)
(4 0 6)Oand (0 4 6)OBragg reflections below TS=140 ±1K.
This splitting is consistent with the structural phase transition
from space group P4/nmm to C mme. The orthorhombic
distortion δ17,18 increases with decreasing temperature without
any noticeable change at the 5 K phase transition. We
note that the transition temperature TSis consistent with
the peak observed in specific-heat data. In the remainder
of the paper, we will use orthorhombic crystallographic
notation.
Below TN1=110 K, a magnetic signal was observed at
the reciprocal lattice points characterized by the propagation
vector (1 0 1
2) when the x-ray energy was tuned through the
Sm L2and Fe Kedges, indicating the onset of Sm and Fe
magnetic order, respectively. Figure 3(b) shows a very similar
temperature evolution of the nonresonant and the resonant
signal at the Fe Kedge for the (1 0 6.5) reflection, supporting
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STRONG COUPLING OF Sm AND Fe MAGNETISM IN ... PHYSICAL REVIEW B 84, 054419 (2011)
FIG. 3. (Color online) (a) Temperature dependence of the or-
thorhombic distortion. Inset shows (ξ0 0) scans through the (4 0
6) reflection. (b) Temperature dependence of the (1 0 6.5) reflection
measured in both resonant (at E=7.106 keV, which is 6 eV below
the Fe K-edge energy of 7.112 keV) and nonresonant (100 eV below
the Fe Kedge) conditions at P09 with a displex. Lower inset shows
temperature dependence of the (1 0 6.5) reflection measured using the
cryomagnet. All other measurements below 5 K were performed using
the orange cryostat. Upper inset shows rocking scans at the (3 0 7.5)
and (0 3 7.5) reflections at selected temperatures. (c) Temperature
dependencies of the (3 0 7.5) and (−2 0 6) reflections measured
in resonant condition (E=7.314 keV) at the Sm L2edge. Open
(closed) circles represent measurements with (without) attenuation
of the primary beam. Solid thin lines serve as guides to the eye while
thick lines (red) show fit as described in the text.
the magnetic origin of the resonant signal. The resonant signal
was measured at the maximum in the resonant scattering
(E=7.106 keV) at the Fe Kedge, while the nonresonant
signal was measured approximately 100 eV below the Fe K
edge. Temperature dependence of this reflection below 5 K
(lower inset) together with rocking scans shown in the upper
inset confirm that the iron magnetic order changes below 5 K.
Figure 3(c) depicts the temperature evolution of the (3 0 7.5)
and (−2 0 6) reflections measured at the Sm L2edge at
resonance (E=7.314 keV). At TN2=5 K, the intensity of
the (3 0 7.5) reflection drops quickly to zero, and reappears
at the position of the charge (−2 0 6) reflection, signaling a
change in the magnetic order of Sm with the magnetic unit
cell equal to the chemical unit cell. Here we note that all
the measurements below 15 K require significant attenuation
(transmission ∼10% of the incident beam) of the beam to
reduce sample heating.
To confirm the resonant magnetic behavior of the peaks,
we performed energy scans at the Sm L2,L3, and Fe K
absorption edges as shown in Fig. 4.19,20 At 6 K, at the Sm L2
edge, we observed a dipole resonance peak ∼2 eV above the
absorption edge for both the (1 0 7.5) and (−2 0 6) reflections.
We note that for the (−2 0 6) reflection, charge and magnetic
peak coincide. Therefore, measurement of a magnetic signal
which is five to six orders of magnitude weaker than the
Thomson charge scattering requires significant reduction of
the charge background. The charge background can be reduced
significantly by a factor of cos22θanalyzer ×cos22θsample in
the π→σgeometry for reflections with a scattering angle
(2θsample) close to 90◦.21 The (−2 0 6) reflection with scattering
angles (2θsample)of∼86◦and ∼95◦at the Sm L2and Sm L3
edges, respectively, fulfills these conditions. The charge signal
is reduced by a factor of ∼7×10−6with the scattering angle
of the analyzer (2θanalyzer) close to 92◦for both the edges.
Thus, measurement of magnetic signal seems feasible for
the (−2 0 6) reflection in the π→σgeometry. Figure 4(b)
shows energy scans through the (−2 0 6) reflection at 2 K
and 6 K. Subtraction of the energy scan at 6 K from 2 K
shows a pronounced resonance feature at the same energy as
that observed for the charge-forbidden (1 0 7.5) reflection.
Similar energy scans were performed at the Sm L3edge and
are shown in Figs. 4(d) and 4(e). In addition to the dipole
feature observed at the L2edge, a quadrupole feature appears
approximately 6 eV below the Sm L3edge. We note that the
change in the energy spectra from the Sm L2to the L3edge is
consistent with the observed resonance in another intermetallic
compound containing Sm.22
Figure 4(c) shows the energy scan through the Fe Kedge.
Several features are observable in the energy spectrum: (a)
Resonant features at and above E=7.106 keV and (b) an
energy independent nonresonant signal for energies below the
resonant features. The nonresonant signal is about a factor
of 2.5 smaller than the resonant signal. The overall energy
spectrum is similar to that observed in previous XRMS mea-
surements in the σ→πscattering channel at the transition
metal Kedges for the BaFe2As2,23 Ce(Co0.07Fe0.97 )2,20 and
NiO24 compounds. It is noteworthy that the pre-edge sharp
resonant feature observed at E=7.106 keV for SmFeAsO
is also present in all of the above-mentioned compounds. It
appears at an energy corresponding to the pre-edge hump
observed in the respective absorption (fluorescence) spectrum.
The broad resonant feature above E=7.106 keV is also
present in all the above compounds, however, its relative
intensity compared to the sharp feature varies from one
compound to another.
Further confirmation that the dipole and quadrupole reso-
nances at the L2and L3edges are magnetic is obtained from
the same temperature dependence of the dipole and quadrupole
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S. NANDI et al. PHYSICAL REVIEW B 84, 054419 (2011)
FIG. 4. (Color online) (a), (b), (d), (e) Energy scans of the (1 0 7.5), (0 1 7.5), and (−2 0 6) reflections and of the absorption coefficient at
the Sm L2(left panel) and L3edges (right panel). The dashed lines depict the Sm L2and L3absorption edges as determined from the inflection
point of the absorption coefficient. The absorption coefficient was calculated and the intensity was corrected following the recipe described
in Refs. 19 and 20. (c) Energy scans of the absorption coefficient and of the (1 0 6.5) reflection below (T=55 K, filled circles) and above
(T=112 K, open squares) TN1, and the measured background at T=55 K away from the magnetic Bragg peak (open circles). The dashed line
depicts the Fe Kedge. (f) Comparison of the temperature dependences of the dipole and quadrupole resonances for the (−2 0 6) and (1 0 7.5)
reflections, respectively. For the (−2 0 6) reflection, integrated intensity was measured approximately 30 eV below (off-resonance, O-R) the
observed resonance (R, E=6.710 keV and 7.314 keV for the Sm L3and L2edges, respectively) to show the temperature dependence of the
pure charge signal. The intensities have not been corrected for absorption. In (a)–(e), vertical arrows indicate the energies at which temperature
dependences of the resonant signal were measured for Figs. 3(b) and 3(c) and Fig. 4(f). In (a)–(f), lines serve as guides to the eye.
resonances as shown in Fig. 4(f) for both the (−206)and
(1 0 7.5) reflections. Since the quadrupole signal is directly
related to the ordering of the 4fmoments, the similarity
of the temperature dependences of both resonances implies
that both the dipole and quadrupole resonances are purely
magnetic.
C. Magnetic structure in the temperature range
5KT110 K
We now turn to the determination of the magnetic moment
configuration for the Sm moments in the temperature range
TN2TTN1. For the crystallographic space group Cmme,
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STRONG COUPLING OF Sm AND Fe MAGNETISM IN ... PHYSICAL REVIEW B 84, 054419 (2011)
TABLE I. Basis vectors for the space group Cmme with k17 =
(0,1,0.5). The decomposition of the magnetic representation for the
Sm site (0,0.25,0.137) is Mag =11
1+11
2+01
3+11
4+11
5+
01
6+11
7+11
8. The atoms of the nonprimitive basis are defined
according to 1 (0,0.25,0.137), 2 (0,0.75,0.863). Lattice parameters
of the orthorhombic crystal at 100 K17:a=5.5732 ˚
A, b=5.5611
˚
A, c=8.4714 ˚
A.
Magnetic intensity
BV components (h0l
2)(0kl
2)
IR Atom mambmcπ→σπ→ππ→σπ→π
11 100Yes No No Yes
2−100
21 0 1 0 No Yes Yes No
2 010
41 0 0 1 Yes No Yes No
2 001
51 0 0 1 Yes No Yes No
200−1
71 0 1 0 No Yes Yes No
20−10
81 100Yes No No Yes
2 100
and a propagation vector of the form (1 0 1
2), six independent
magnetic representations (MRs) are possible.25 All the MRs
along with the calculated intensities for different polarization
geometries are listed in Table I. Among all the MRs,
8(F) and 1(AF) MRs allow magnetic moment along a,
2(F) and 7(AF) along b, and 4(F) and 5(AF) along
the cdirection, respectively. Here, F and AF denote ferro
and antiferromagnetic alignment between Sm(1) and Sm(2)
moments, respectively [see Fig. 5(b)]. For a second-order
phase transition, Landau theory predicts that only one of the
six above-mentioned MRs is realized at the phase transition.25
We note that the π→πscattering geometry is sensitive only
to the moment perpendicular to the scattering plane for the
dipole resonance.26 Since no magnetic signal was observed at
the (0 1 7.5) (sensitive to 1and 8) and (1 0 7.5) (sensitive to
2and 7) reflections in the π→πscattering channel at the
Sm L2edge [see Figs. 4(a)–4(d)], we can exclude the moment
in the aand bdirections and hence, the MRs 1,8,2, and
7. To differentiate between the MRs 4and 5(the moment
along the cdirection), the integrated intensities for a series of
(1 0 l
2) reflections were measured [see Fig. 5(a)] and compared
with the calculated intensity as outlined below. The intensity
for a particular reflection can be written as
I=SAL|Fm|2,(1)
where Sis the arbitrary scaling factor, A=sin(θ+α)
sin θcos αis the
absorption correction, and L=1
sin 2θis the Lorentz factor.
Here, αis the angle that the scattering vector Q(=kf−ki)
makes with the crystallographic cdirection perpendicular to
the surface of the sample, and θis half of the scattering angle.
αis positive (negative) for larger (smaller) angles for the
outgoing beam with respect to the sample surface. |Fm|is
the modulus of the magnetic structure factor. The magnetic
FIG. 5. (Color online) (a) ldependence of the integrated intensity
at the Sm L2edge along with the fits for the (1 0 l
2) reflections.
Open symbols are the calculated intensities. Lines serve as guides
to the eye. (b) Proposed magnetic structure in the temperature range
5KT110 K.
structure factor Fmfor the (hkl) reflections can be written as
Fm=
j
fje2πi(hxj+kyj+lzj).(2)
The summation is over all the magnetic atoms in the unit
cell. fjis the resonant (nonresonant) magnetic scattering
amplitude which is listed for different polarization geome-
tries by Hill and McMorrow for XRMS26 and by Blume
and Gibbs for NRXMS.27 In particular, fjdepends on the
polarization geometry as well as the moment direction. xj,yj
and zjare the atomic position of the jth atom within the
unit cell. The angular dependence of the magnetic structure
factor originates from the magnetic scattering amplitude fj.
For dipole resonance and for the π→σgeometry, fj∝
ki·μ,26,28 where kiand μare the wave vectors of the
incoming photons and the magnetic moment, respectively.
For the dipole resonance, and for the reflections of the type
(1 0 l
2), |Fm|2is proportional to sin2(2πzl)sin
2(θ+α) and
cos2(2πzl)sin
2(θ+α)forthe4and 5MRs, respectively.
z=0.137 is the atomic position of Sm moments within the
unit cell.17 While the sin2(2πzl)/cos2(2πzl) term comes from
the relative orientation of the magnetic moment within the
magnetic unit cell, the term sin2(θ+α) comes from the dot
product between kiand μ[(90◦−θ−α) is the angle between
kiand μ]. We note that there is only one free parameter for
the dipole intensity [see Eq. (1)], namely the arbitrary scaling
factor S. Figure 5(a) shows a fit to the observed intensities for
the two above-mentioned MRs. Since the model calculation
with the magnetic moment in the 5MR closely agrees with the
observed intensity, we conclude that the magnetic Sm moments
are arranged according to the MR 5.
For the determination of the MR for the Fe moments,
the nonresonant signal was measured at 15 K. Similar
representation analysis provides six possible MRs for the
magnetic order of Fe. All the MRs along with the calculated
intensities for different polarization geometries are listed in
Table II. Among all the MRs, 5and 6MRs allow magnetic
moment along a,3and 4along b, and 1and 2along the
cdirection, respectively. Among the two MRs for a particular
moment direction, the first one represents F alignment of the
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S. NANDI et al. PHYSICAL REVIEW B 84, 054419 (2011)
TABLE II. Basis vectors for the space group Cmme with k17 =
(0,1,0.5). The decomposition of the magnetic representation for
the Fe site (0.75,0,0.5) is Mag =11
1+11
2+11
3+11
4+11
5+
11
6+01
7+01
8. The atoms of the nonprimitive basis are defined
according to 1 (0.75,0,0.5), 2 (0.75,0.5,0.5).
Magnetic intensity
BV components (h0l
2)(0kl
2)
IR Atom mambmcπ→σπ→ππ→σπ→π
11001YesNoNoNo
2 001
21 0 0 1 No No Yes No
200−1
31 010 No Yes No No
2 010
41 0 1 0 No No Yes No
20−10
51100YesNoNoNo
2 100
61 1 0 0 No No No Yes
2−100
magnetic moments along band AF alignment along a, while
the second one represents exactly the opposite alignment in
the respective directions. 2,3,4, and 6MRs can be
excluded from the fact that finite intensity was observed for the
(1 0 6.5) reflection in the π→σgeometry (see Table II). Zero
intensities for the (0 3 7.5) reflection in the π→σgeometry
[see inset of Fig. 3(b)] and of the (1 0 6.5) reflection in the
π→πchannel are also consistent with the absence of 4and
3MRs, respectively. Finite intensity of the (1 0 6.5) reflection
in the π→σchannel implies that the moments are within the
a–cscattering plane, i.e., 1and 5are the possible MRs. We
measured the off-specular reflections (3 0 7.5) and (3 07.5)
to determine the moment direction. The angular dependence
of the nonresonant magnetic scattering cross section for the
π→σgeometry, fj=−2sin
2θkf·S(assuming a spin-only
magnetic moment of iron),27 is different for these two reflec-
tions providing strong sensitivity to the moment direction. kf
and Sare the wave vectors of the outgoing photons and the spin
magnetic moment, respectively. The ratio can be written as
Ih0l
2
Ih0l
2=sin(θ−α) cos2(θ−α)
sin(θ+α) cos2(θ+α).(3)
The calculated ratio I(307.5)/I (307.5) amounts to 5.2 and
0.35 for moments along the aand cdirections, respectively.
The experimentally determined ratio 6.5±0.9 confirms
that the moments are in the adirection, i.e., the MR is 5.
We note that this is the same MR as that of Sm, which is
expected if there is significant coupling between the two
magnetic sublattices. Arrangements of the magnetic moments
according to the MR 5is shown in Fig. 5(b).
D. Temperature dependence of the magnetic intensity in the
temperature range 5 KT110.0K
Although the ordering temperatures are the same for
both the Fe and Sm sublattices, the order parameters are
qualitatively different, as can be seen from Figs. 3(b) and
3(c). Particularly, the order parameter for the Sm moment is
quite unusual. Very similar temperature dependence of the
Ce sublattice magnetization in CeFeAsO has been obtained
indirectly using muon-spin relaxation measurements.10 With
reference to other systems, this unusual behavior can be ex-
plained with a ground-state doublet crystal-field level, split by
an exchange field.29,30 The Kramer’s Sm3+ions in SmFeAsO
are at the positions of local point symmetry C2vand, therefore,
must have a doublet ground state. At low temperatures, only
the ground-state doublet is appreciably populated, because
the energy difference between the ground-state and the next
crystal electric-field levels, in general, is large and of the order
of 17 meV in the case of CeFeAsO.31 Taking into account only
the ground-state doublet and a splitting (T), we can write
mSm
z(T)=gjμB
2tanh (T)
2kBT,(4)
where (T)=gJμBBeff
z(T) is the splitting of the ground-state
doublet by the effective field produced by the Fe sublattice.
gJ=2
7is the Land´
egfactor of the free Sm3+, and μBis the
Bohr magneton. The effective field should be proportional to
the ordered magnetic moment of Fe, and can be written as
Beff
z(T)=B01−T
TNβ
.(5)
Since the observed intensity is proportional to the square of
the ordered magnetic moment (I=Am
2), TN(=110 ±1K)
and β(=0.112 ±0.008) can be extracted from a fit to the
integrated intensity for the (1 0 6.5) reflection in Fig. 3(b).A
fit to the temperature dependence of the (3 0 7.5) reflection in
Fig. 3(c) over the whole temperature range gives B0=(56.4±
1.9) T and the corresponding (T=0) =(0.93 ±0.03) meV.
We note that the value of B0characterizing the strength of
interaction between the two sublattices is comparable or even
higher than the value for Ce-Fe interaction in CeFeAsO.10,32
The value of =0.93 meV is comparable to the ground-
state splitting of Ce crystal electric field levels of 0.9 meV in
CeFeAsO, measured using inelastic neutron scattering.31
E. Magnetic structure below T5.0K
For the low-temperature phase (T5.0 K), the deter-
mination of the magnetic structure of the Sm subsystem
is considerably more difficult due to the overlap of the
magnetic intensity with the charge intensity. Magnetization
measurements with magnetic fields along the cdirection and
in the ab plane exclude ferromagnetic arrangement in the
respective direction (plane) [see Fig. 2(b)]. There remain
three antiferromagnetic representations along the a,b, and c
directions. The relative change in magnetization below 5 K is
much more pronounced for a magnetic field applied along the
cdirection than in the ab plane [see Fig. 2(a)]. Therefore,
we conclude that the Sm moments are aligned along the
cdirection below 5 K, which is in agreement with recent
neutron-scattering measurements.14
To determine the magnetic structure of the Fe moments
below T=5 K, a number of possible propagation vectors
054419-6

STRONG COUPLING OF Sm AND Fe MAGNETISM IN ... PHYSICAL REVIEW B 84, 054419 (2011)
FIG. 6. (Color online) (a) and (b) land hscans through the (1 0 6.5) reflection. 10% of the incident beam was used to reduce the sample
heating. For comparison, scans at T=4.5 K is plotted together with scans taken at T=2.0 K. We noticed that the sample heating is much
greater in the cryomagnet than in the orange cryostat. The remaining intensity at T=2 K is due to the residual sample heating in the cryomagnet.
suggested for the RFeAsO family,10 (100.5),(100),
(0.5 0 0.5), and (0 0 0.5), were checked by rocking scans
with a counting time (∼3min/data point) a factor of three
larger than other measurements at 2 K. Measurements were
performed in both the π→σand π→πchannels to exclude
possible reorientation of the magnetic moments from the ato b
direction. Additionally, long scans along the hand ldirections
for the (1 0 6.5) reflections were performed to exclude possible
incommensurate order in the respective directions (see Fig. 6).
However, no signal was observed for the above measurements.
The magnetic structure with the same propagation vector as
that of Sm implies a N´
eel-type in-plane structure, which is
impossible to check with hard x rays given the weakness of the
resonant (nonresonant) signal and the overlap of the magnetic
FIG. 7. (Color online) Rocking scans through the (1 0 7) reflection
in both the π→σand π→πchannels. Higher background in
the π→πchannel is mainly due to the less suppression of the
fluorescence background.
signal with the charge signal. In NdFeAsO, a change in the
coupling along the caxis (AFM to FM) has been observed
upon the spontaneous order of Nd.11 However, this is not the
case here, as confirmed by the absence of the scattering signal
at the (1 0 7) reflection as shown in Fig. 7. The absence
of the scattering signal in the positions mentioned above
indicates that the in-plane as well as out-of plane correlations
are modified upon the spontaneous ordering of Sm. This
observation is unique among the RFeAsO family and indicates
an intricate interplay between the two sublattices. Here we
note that the rare-earth sites project onto the centers of the
Fe plaquettes, and thus isotropic interactions between the two
vanish by symmetry. Hence, anisotropic exchange interactions
play a major role in determining the spin structure of the Fe
sublattice and should be studied theoretically to understand
the magnetism in the RFeAsO family.
IV. CONCLUSION
In summary, using XRMS and NRXMS we found that
between 110 K and 5 K, the Sm moments are aligned in the
cdirection while Fe moments are aligned in the adirection
according to the same MR 5and the propagation vector
(1 0 1
2). Modeling of the temperature dependence indicates
that the Sm moments are induced by the exchange field of
the Fe moments. Below 5 K, the magnetic order of both
sublattices changes to a different magnetic structure, indicating
an intricate interplay between the two magnetic sublattices.
Our finding of an intricate interplay between the magnetism
of Sm and Fe in the SmFeAsO compound sheds light on the
currently debated importance of the R-Fe interaction in the
family of iron-based superconductors.
ACKNOWLEDGMENTS
S.N. would like to acknowledge S. Adiga, M. Angst,
B. Schmitz, T. Trenit, and S. Das for technical help.
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S. NANDI et al. PHYSICAL REVIEW B 84, 054419 (2011)
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