Evidence of Orbital Ordering in Jahn-Teller Undistorted LaSr$_{2}$Mn$_{2}$O$_{7}$

Abstract

Resonant soft x-ray diffraction has been used to probe the temperature dependent orbital and magnetic structure of $\mathrm{LaSr_{2}Mn_{2}O_7}$. Previous crystallographic studies have shown that this material has almost no MnO$_{6}$ oxygen displacement due to Jahn-Teller distortions at low temperatures. Within the low-temperature A-type antiferromagnetic phase, we found strong intensity at the $({1/4},{1/4},0)$ orbital and $LaSr_{2}Mn_{2}O_7$ magnetic reflections. This shows that even in the near absence of Jahn-Teller distortion, this compound is strongly orbitally ordered. A fit to the Mn $L$-edge resonance spectra demonstrates the presence of orbital ordering of the Mn$^{3+}$ ions with virtually no Jahn-Teller crystal field in addition to possible Mn$^{3+}$ and Mn$^{2+}$~like valence fluctuations.

Full text

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arXiv:cond-mat/0412435v2 [cond-mat.str-el] 3 Jun 2006
LETTER TO THE EDITOR
Separating the causes of orbital ordering in
LaSr2Mn2O7using resonant soft x-ray diffraction
S. B. Wilkins1, N. Stoji´ c2, T. A. W. Beale3, N. Binggeli2,
P. D. Hatton3, P. Bencok1, S. Stanescu1, J. F. Mitchell4,
P. Abbamonte5, M. Altarelli2,6
1European Synchrotron Radiation Facility, Boˆ ıte Postal 220, F-38043 Grenoble
Cedex, France
2Abdus Salam International Centre for Theoretical Physics, Trieste 34014, Italy
3Department of Physics, University of Durham, Rochester Building, South
Road, Durham, DH1 3LE, UK
4Materials Science Division, Argonne National Laboratory, Argonne, Illinois
60439, USA
5National Synchrotron Light Source, Brookhaven National Laboratory, Upton,
NY 11973, USA
6European XFEL Project Team, Desy, Notkerstraße 85, 22607 Hamburg,
Germany
E-mail: wilkins@esrf.fr
Abstract.
temperature dependent orbital and magnetic structure of LaSr2Mn2O7. Previous
crystallographic studies have shown that this material has almost no MnO6oxygen
displacement due to Jahn-Teller distortions at low temperatures.
low-temperature A-type antiferromagnetic phase, we found strong intensity at
the (1
4,0) orbital and (0,0,1) magnetic reflections. This shows that even in
the near absence of Jahn-Teller distortion, this compound is strongly orbitally
ordered. A fit to the Mn L-edge resonance spectra demonstrates the presence of
orbital ordering of the Mn3+ions with virtually no Jahn-Teller crystal field in
addition to possible Mn3+and Mn2+like valence fluctuations.
Resonant soft x-ray diffraction has been used to probe the
Within the
4,1
PACS numbers: 61.10.-i,71.30.+h,75.25.+z,75.47.Lx
Ferromagnetism and charge ordering in the doped perovskite type manganese
oxides R1−xAxMnO3(R = rare earth, A = Sr,Ca) have attracted considerable interest
since the discovery of colossal magnetoresistance (CMR) [1]. Recently, much attention
has been paid to the importance of the charge, lattice, spin and orbital degrees of
freedom to explain the complex and anomalous structural, magnetic and transport
behavior observed in the manganites. The interplay between these degrees of freedom
can cause localisation of electrons on alternative manganese atoms to produce charge-
ordered lattices.The ferromagnetism and metallic conductivity observed at low
temperatures can be understood on the basis of the double-exchange mechanism
whereby eg electrons hop between Mn sites through hybridisation with oxygen 2p
orbitals and align the localised t2gspins by strong Hund’s coupling [2, 3, 4]. However
the understanding of the transport properties, such as CMR, and the complicated
magnetic phase diagrams of the manganites requires a further ingredient, that of the
orbital degree of freedom [5, 6].

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Letter to the Editor
2
Figure 1. The crystal structure of the bilayer manganite La2−2xSr1+2xMn2O7
with x = 0.5 at low temperature. (a) The arrangement of the previously proposed
“Mn3+” and “Mn4+” manganese ions are shown within the tetragonal unit cell. A
plan view of the Mn3+orbitals within the ab plane displaying orbital order of the
x2−z2,y2−z2type is given in (a). This is the dominant type of orbital ordering
found in Ref. [18] for a doping x = 0.42. Our results suggest a checkerboard
pattern closer to Mn2+/Mn3+rather than Mn3+/Mn4+, however the alternating
pattern remains the same. The arrangement of the magnetic spins of the Mn3+
ions in the low temperature antiferromagnetic structure is shown schematically in
(b).
The study of the orbital ordering phenomenon is, therefore, vital for the
understanding of the complex properties of the manganite systems. Direct observation
of orbital ordering in manganites has recently become possible using resonant soft x-ray
diffraction at the Mn L2,3absorption edges after theoretical predictions by Castleton
and Altarelli [7]. Mn L2,3resonant x-ray scattering experiments have been performed
in La0.5Sr1.5MnO4[8, 9] and in Pr0.6Ca0.4MnO3[10], however in both cases the orbital
degree of freedom is controlled by strong Jahn-Teller distortions. In this letter we
report experimental results on LaSr2Mn2O7. Previous crystallographic studies [11, 12]
have indicated that this system undergoes extremely small Jahn-Teller distortions at
low temperature. Despite this our results demonstrate the presence of long-range
orbital order, in addition to magnetic order. The fit to the orbital ordering spectrum
using multiplet calculations in a crystal field shows the presence of a vanishing Jahn-
Teller distortion in addition to possible Mn3+and Mn2+like valence fluctuations.
The samples were single crystals of the bilayer manganite LaSr2Mn2O7 which
were melt grown in flowing oxygen using a floating zone optical image furnace.
The system La2−2xSr1+2xMn2O7 is a layered perovskite in which MnO2 double
layers and (La,Sr)2O2 blocking layers are stacked alternatively (see Fig 1 from
Ref [12]). The reduced dimensionality causes the system to display a greatly enhanced
magnetoresistance [13] and a reduced ferromagnetic transition temperature. Charge
ordering has been reported in the temperature range from 100 to 200 K existing only
over a narrow compositional range 0.475 < x < 0.55[14, 15]. Below 170 K the x = 0.5
material, LaSr2Mn2O7, adopts an A-type antiferromagnetic ordering of the Mn spins
[11] (see Fig. 1) and crystallographic and high-energy x-ray diffraction studies have
shown the disappearance[11, 16] or reduction[17] of the Jahn-Teller distortion, such
that the MnO6octahedra are almost undistorted below ∼ 100 K.
Experiments were carried out using the in-vacuum diffractometer on beamline
ID08 at the European Synchrotron Radiation Facility. A single crystal of LaSr2Mn2O7
cut with the [110] direction normal to the sample surface was used for measurements

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Letter to the Editor
3
635
640
Incident Photon Energy [eV]
645650655
660
665
670
Intensity [arb. units]
a)
b)
Figure 2. (a) Scattered x-ray intensity as a function of incident photon energy
at constant wavevector QOO= (1
4,0) (circles). The black dashed line shows
the theoretical fit to the data. (b) Theoretical simulation (dashed black line) of
the energy spectra with an 8-fold increase in the Jahn-Teller distortion. The fit
to the experimental data is repeated for comparison (solid line).
4,1
635
640
Incident photon energy [eV]
645650655
660
665
670
Intensity [arb. units]
a)
b)
Figure 3.
a constant wavevector QAF= (0, 0,1)
fits (solid black lines) describing the superposition of (a) Mn3+/Mn4+and (b)
Mn3+/Mn2+type.
Scattered x-ray intensity as a function of incident photon energy at
(red line with circles) with theoretical
of the (1
ray beam at ID08 by gas absorption gives an absolute accuracy of 0.2 eV at 640 eV.
Measurements of the anti-ferromagnetic reflection (001), were performed on a cleaved
crystal with the [001] direction surface normal. The temperature dependancies of both
these reflections were obtained using beamline X1B at the National Synchrotron Light
Source. At both beamlines the experimental procedure was identical to our previous
studies[17, 8].
At ID08, the sample was cooled to ∼ 20 K using liquid helium and an intense and
narrow reflection was found at a wavevector of QOO= (1
of 643 eV. The solid circles in Fig. 2a show the scattered intensity as a function of
the incident photon energy at constant wavevector, through the manganese L3 and
L2edges. On first inspection, there appears to be two main features at the L3edge
and three at the L2edge. In contrast to previous measurements on La0.5Sr1.5MnO4[8]
and Pr0.6Ca0.4MnO3[10] the maximum scattered intensity is primarily observed at the
L2edge rather than at the L3edge. Measurements of the A-type antiferromagnetic
reflection in La2−2xSr1+2xMn2O7for x = 0.475 at QAF= (0,0,1) have been reported
4,1
4,0) orbital order reflection. Calibration of the energy of the incident x-
4,1
4,0) at an incident energy

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Letter to the Editor
4
by Wilkins et al.[17] at a temperature of 83 K. In Fig. 3(a,b) we show the scattered
intensity measured at 20 K in LaSr2Mn2O7 as a function of energy at constant
wavevector. In this case, at the L2 edge little scattering was observed but at the
L3edge very strong intensity was found which is comprised of two main features. Our
experimental data in Figs. 2 and 3 indicate that LaSr2Mn2O7
orbitally and magnetically ordered at low temperature.
not particularly surface-sensitive[17]. The inverse width in reciprocal space of the
reflections gives an indication of the penetration depth. This indicates we are probing
thousands of˚ Angstroms into the crystal.
In order to identify the origin of the resonant x-ray scattering signal, we have
performed multiplet calculations in a crystal field.
symmetry, two crystal field parameters are to be acquired from the fitting procedure:
cubic (X400) and tetragonal (X220). In the absence of the experimental evidence, we
assume that the spins are aligned in the [110] direction, which lowers the symmetry to
that of the Cipoint group. Choosing this direction as quantization axis, the resonant
scattering amplitude at the orbital ordering wave vector (1
the following combination of the atomic scattering tensors [19]:
is simultaneously
Soft X-ray diffraction is
On the Mn3+site with D4h
4,1
4,0), is proportional to
fOO
res∝ Fe
0;1− Fe
0;−1+ Fe
1;0− Fe
−1;0,(1)
with Fe
m;m′ defined as:
Fe
m;m′ =
?
n
?0|J1†
E0− En+ ¯ hω + iΓ/2,
m|n??n|J1
m′|0?
(2)
where m and m′denote polarization states and J1
in spherical coordinates. |0? represents the ground state with energy E0 and |n?
intermediate states with energy En. The photon energy is ¯ hω and Γ stands for the
broadening due to the core-hole lifetime. Similarly, for the magnetic scattering with
the wave vector (0,0,1) , the scattering amplitude can be expressed as:
mare the dipole operators defined
fMO
res ∝ Fe
1;1− Fe
−1;−1.(3)
The Slater integrals of the d-d and p-d direct and exchange interactions were scaled
down to 75% of their atomic value. The p-shell spin-orbit parameter was increased by
9% from the Hartree-Fock value to correspond to the experimental value [20]. We used
Γ =0.5 eV for the Lorentzian broadening due to the core-hole lifetime. In addition,
to take into account also the experimental energy resolution, the scattering intensity,
I(¯ hω) ∝ |fres|2, was convoluted with a Gaussian of width 0.1 eV.
The best fit to the orbital ordering is shown in Fig. 2a. The corresponding
crystal field parameters are X400= 3 eV and X220= 0.4 eV, (or 10Dq = 0.91 eV
and Ds= −0.048 eV). The fit did not significantly change for variations of the cubic
field X400in the interval 3−4 eV and for the tetragonal (Jahn-Teller) field X220in the
interval 0.1−0.6 eV. The fit displays a fair general agreement with the experimental
spectrum. The obtained L3/L2 ratio is satisfactory and we reproduce most of the
structure from the experimental spectrum. However, the first peak in the L3edge is
not reproduced [21] and broadened high-energy features at both edges are missing in
the fit. These wide shoulders may be related to band-structure effects, which are not
incorporated in our model. In Fig. 2b we illustrate the effect of an 8-fold increase of
the Jahn-Teller field. As shown before, [22], the L3/L2ratio is becoming larger with
the increase in the tetragonal component of the crystal field. In our calculations a
small Jahn-Teller tetragonal crystal field is necessary to lift the degeneracy of the eg

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Letter to the Editor
5
levels, however the tetragonal field included is extremely small. Its value is one order
of magnitude smaller than that obtained, e.g., for La0.5Sr1.5MnO4[22], so that, except
for the lifting of orbital degeneracy, the Mn3+ion is essentially in a cubic field. This
shows we are within a regime where the scattering is dominated by orbital ordering
of the egelectrons.
We were not able to obtain a good fit to the magnetic scattering with Mn3+
ions alone, as it gave a single peak at each edge. Since the QAF= (0,0,1) sees a
superposition of all manganese ions within the ab plane, we included an additional
type of Mn ion in our model. Figure 3a shows the magnetic spectrum obtained by
superposing the contributions of Mn3+and Mn4+with equal weights. The Mn4+ion
induces a peak at higher energy (at both edges) relative to the Mn3+ion, as expected
for ions with larger oxidation number[23]. This gives rise to a spectrum with two peaks
at each edge, but shifted to a higher energy relative to the experimental spectrum.
Moreover, the ratio between the two main features at both the L3 and L2 edges is
inverted. In order to reproduce the feature at low energy, with a ratio consistent with
experiment, we need to consider a Mn ion with lower oxidation number. In panel b)
of Fig. 3 we show the spectrum obtained with a 1:1 ratio of Mn2+and Mn3+. In these
calculations, the Mn3+crystal field parameters were taken to be exactly the same as
for the orbital spectrum in Fig. 2a, and the Mn2+and Mn4+spectra were calculated in
a purely cubic crystal field (X400= 3.0 eV). In Fig. 3, we positioned the Mn2+(Mn4+)
edge, relative to the Mn3+edge, using the theoretical chemical shifts obtained from
our atomic multiplet calculations, i.e. ∼ -2 eV and 4 eV, respectively. Experimental
L-edge absorption results on Mn2+, Mn3+, and Mn4+reference compounds show
comparable chemical shifts (between -1 and -2 eV for Mn2+and between 2 and 3 eV
for Mn4+[24, 25, 26]).
Surprisingly, much better agreement with the experimental data in Fig. 3(a,b)
is obtained by the calculation for the Mn2+/Mn3+case than for the Mn3+/Mn4+
case. This may simply reflect the basic limitations of the atomic multiplet calculations
(which, for one thing, only allow integer values for the valence) to describe an extended
system with non-negligible interatomic hopping; on the other hand, it is noteworthy
that an average valence between 2+ and 3+ has recently been suggested by Hartree-
Fock calculations [27, 28], and experimental data which indicate that the additional
holes reside more on the oxygen ligands [29, 30]. Such a change in the manganese
valency from 3+/4+ to 2+/3+ would not alter the orbital occupancy of the Mn3+
ion. Both Mn2+and Mn4+are not Jahn-Teller active.
Figure 4 shows the temperature dependence of the orbital and magnetic
reflections. The (1
4,0) reflection is observed below TOO which is coincident with
TJT. The Jahn-Teller distortions maximise at TN (∼170 K) and decrease below this
temperature due to the occurance of antiferromagnetic interactions. Note that the
Jahn-Teller distortions are very weak below 100 K where the orbital and magnetic
reflections are very strong. We note that below 100 K the Jahn-Teller distortions
increase slightly, which coincides with a change in gradient of the intensity of the
orbital and magnetic reflections.
In conclusion, we have reported the results of resonant soft x-ray scattering
studies of the orbital and antiferromagnetic ordering in LaSr2Mn2O7. The data of
Fig. 2 and 3 immediately show that LaSr2Mn2O7 is simultaneously both orbitally
and antiferromagnetically ordered at low temperatures, despite the fact that the
Jahn-Teller distortions in this system are measured to be very small.
further supported by the theoretical fits, which display a good agreement with the
4,1
This is

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Letter to the Editor
6
255075
100
125
Temperature [K]
150175
200
225250275
0
Integrated Intensity [arb. units]
Magnetic Order
Orbital Order
Jahn-Teller Distortion
Figure 4. Temperature dependence of the integrated intensity of the (1
orbital order reflection and the (001) magnetic order reflection. The temperature
depedence of the (3
4,5) Jahn-Teller distortion peak, a measure of the
amplitude of the Jahn-Teller distortion, is taken from Ref [12].
4,1
4,0)
4,−1
experimental data for very small values of tetragonal crystal field. From these we
can conclude that it is possible to obtain a strongly orbitally ordered phase within
an A-type antiferromagnetic configuration in the absence of significant Jahn-Teller
distortions. In such case, the energetics of the orbitally ordered configuration is
favored by the magnetic interactions, originating from the superexchange mechanism,
as described by Goodenough, [31]. The fit to the magnetic scattering data suggests a
fluctuating valence situation, with Mn ions with valence charge between +3 and +2.
This work was supported by the Synchrotron Radiation Related Theory Network,
SRRTN, of the EU. N.S. gratefully acknowledges the assistance of Paolo Carra in
learning how to use the Cowan and “Racah” codes. We thank F. M. F. de Groot for
helpful discussions. We are grateful for support from EPSRC for a studentship for
T.A.W.B. and for a travel grant to NSLS.
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