Mn L$_{2,3}$ edge resonant x-ray scattering in manganites: Influence of the magnetic state

Abstract

We present an analysis of the dependence of the resonant orbital order and magnetic scattering spectra on the spin configuration. We consider an arbitrary spin direction with respect to the local crystal field axis, thus lowering significantly the local symmetry. To evaluate the atomic scattering in this case, we generalized the Hannon-Trammel formula and implemented it inside the framework of atomic multiplet calculations in a crystal field. For an illustration, we calculate the magnetic and orbital scattering in the CE phase of \lsmo in the cases when the spins are aligned with the crystal lattice vector ${\vec a}$ (or equivalently ${\vec b}$) and when they are rotated in the $ab$-plane by 45$^{\circ}$ with respect to this axis. Magnetic spectra differ for the two cases. For the orbital scattering, we show that for the former configuration there is a non negligible $\sigma \to \sigma'$ ($\pi \to \pi'$) scattering component, which vanishes in the 45$^\circ$ case, while the $\sigma \to \pi'$ ($\pi \to \sigma'$) components are similar in the two cases. From the consideration of two 90$^\circ$ spin canted structures, we conclude there is a significant dependence of the orbital scattering spectra on the spin arrangement. Recent experiments detected a sudden decrease of the orbital scattering intensity upon increasing the temperature above the N\' eel temperature in \lsmo. We discuss this behavior considering the effect of different types of misorientations of the spins on the orbital scattering spectrum. Comment: 8 figures. In the revised version, we added a note, a reference, and a few minor changes in Figure 1 and the text. Accepted in Physical Review B

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arXiv:cond-mat/0505699v3 [cond-mat.str-el] 5 Sep 2005
Mn L2,3edge resonant x-ray scattering in manganites: Influence
of the magnetic state
N. Stoji´ c,1N. Binggeli,1,2and M. Altarelli1,3
1Abdus Salam International Centre for Theoretical Physics, Trieste 34014, Italy
2INFM Democritos National Simulation Center, Trieste I-34014, Italy and
3Sincrotrone Trieste, Area Science Park, 34012 Basovizza, Trieste, Italy
(Dated: February 2, 2008)
Abstract
We present an analysis of the dependence of the resonant-orbital order and magnetic scattering
spectra on the spin configuration. We consider an arbitrary spin direction with respect to the local
crystal field axis, thus lowering significantly the local symmetry. To evaluate the atomic scattering
in this case, we generalized the Hannon-Trammel formula and implemented it inside the framework
of atomic multiplet calculations in a crystal field. For an illustration, we calculate the magnetic and
orbital scattering in the CE phase of La0.5Sr1.5MnO4 in the cases when the spins are aligned with
the crystal lattice vector ? a (or equivalently?b) and when they are rotated in the ab-plane by 45◦with
respect to this axis. Magnetic spectra differ for the two cases. For the orbital scattering, we show
that for the former configuration there is a non negligible σ → σ′(π → π′) scattering component,
which vanishes in the 45◦case, while the σ → π′(π → σ′) components are similar in the two
cases. From the consideration of two 90◦spin canted structures, we conclude there is a significant
dependence of the orbital scattering spectra on the spin arrangement. Recent experiments detected
a sudden decrease of the orbital scattering intensity upon increasing the temperature above the
N´ eel temperature in La0.5Sr1.5MnO4. We discuss this behavior considering the effect of different
types of misorientations of the spins on the orbital scattering spectrum.
PACS numbers: 61.10.-i,75.10.-b,75.25.+z,71.27.+a

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I.INTRODUCTION
The physics of perovskite-type manganites is one of the very exciting areas of the present-
day solid-state research, displaying abundance of interesting phenomena, of which the most
known is the huge resistivity change upon the application of magnetic fields, the so-called
colossal magnetoresistance effect1. Manganites have rich phase diagrams with several types
of magnetic, charge and orbitally ordered phases, often exhibiting mesoscale phase coexis-
tence. The physics of these systems is controlled by a complex interplay of magnetic, orbital,
charge and structural degrees of freedom. Orbital order is characterized by the spatial ar-
rangement of the outermost valence electrons. Although it was predicted and described
theoretically 50 years ago2, it has been recognized as a hidden degree of freedom, because
of difficulties related to its direct observation.
The resonant x-ray scattering (RXS) is a promising tool for the study of orbital order, and,
at the same time, convenient for the study of magnetic and charge ordering. In particular,
it can be applied to investigate the correlations between the orbital order parameter and
the magnetic and charge order parameters. The first RXS experiments with the goal of
detecting orbital ordering were done at the K-edge. At the manganese K-edge, one 1s
electron is excited into the empty 4p band after absorption of a photon of the resonant
energy. This intermediate state has a finite lifetime, after which the ion emits a photon and
relaxes back to the initial state. Today it is believed that the observed signal is not sensitive
to the onsite orbital ordering of the 3d orbitals, but to band-structure effects including
the effect of the Jahn-Teller crystal field on the 4p states together with the hybridization
of the 4p orbitals with the neighboring oxygen orbitals (also controlled by the Jahn-Teller
distortion) and with empty 3d orbitals of the neighboring Mn atoms3,4,5. Instead, the L2,3-
edge scattering measurements6,7,8,9,10,11, stimulated by the theoretical work of Castleton and
Altarelli12, are sensitive to both the onsite orbital ordering and the Jahn-Teller distortion.
At the Mn L2,3edges, the virtual dipole transition consists of an excitation of one 2p electron
into the 3d shell, thus directly probing the orbital ordering. The specific contributions of the
orbital ordering and Jahn-Teller distortions must then be disentangled in order to interpret
the results of such experiments. This is usually done by comparing the experimental spectra
to theoretical simulated spectra. Previous theoretical work10,11has indicated that the Jahn-
Teller distortion affects almost exclusively the L3edge. However, to monitor the effect of

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a change in the magnetic order on the orbital ordering in particular (or on the Jahn-Teller
distortion), one needs also to know the direct influence of the magnetic configuration on the
orbital spectra. So far, to our knowledge, this effect on the L edge orbital scattering has
not been addressed. Also, obviously, if the spin configuration has a significant influence on
the orbital scattering, it must be properly included in the analysis used to disentangle the
effects of the orbital ordering and Jahn-Teller distortion.
Recently, Wilkins et al.11reported measurements of the temperature dependence of the
orbital scattering at the Mn L2,3 edge in La0.5Sr1.5MnO4
which displayed a substantial
decrease in the orbital scattering intensity, as the temperature is raised, at the transition
from the antiferromagnetic to paramagnetic phase. Analogous behavior when crossing the
N´ eel temperature was previously reported in LaMnO313, at the Mn K edge, and in KCuF314,15
at the Cu K edge (but the origin may not be the same). More recently, Staub et al.9also
presented measurements of the temperature dependence of the orbital scattering at the
Mn L2,3edge in La0.5Sr1.5MnO4, which showed a smaller change at the N´ eel temperature.
Furthermore, based on a polarization analysis, they showed that the orbital signal below the
N´ eel temperature includes a non negligible contribution of magnetic scattering from twinned
minority ferromagnetic domains. However, it is still unclear whether this fully explains the
temperature dependence of the observed orbital signal9,11. In principle, the change in the
magnetic configuration at the N´ eel temperature in the majority domain could also affect the
spectrum.
In this work, we address the direct influence of the magnetic configuration on the orbital
scattering spectra for a fixed orbitally ordered configuration. As a prototype system, we focus
on La0.5Sr1.5MnO4. We find that the spin configuration has indeed an influence on the orbital
scattering, but mostly when the spins are noncollinear. For the magnetic scattering we find
that the spin configuration has a non-negligible influence on the spectrum, and this even
in the collinear CE structure. Previous studies generally considered spin oriented along the
highest local symmetry axis of the Mn3+crystallographic site. In order to allow an arbitrary
orientation of the spin with respect to the local crystal field axis, we generalized the Hannon-
Trammell formula16for atomic scattering, derived for spherical local site symmetry, by a
systematic expansion in invariants of decreasing symmetry down to Ci. We use these results
to derive the scattering formulae for different spin configurations, including the polarization
dependence. Finally, we consider various types of spin misalignments and misorientations to

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understand the effect of spin disorder on the orbital spectrum of the paramagnetic phase. We
separately discuss the effect of the loss of spin order between the ab-planes at temperatures
just above TNand spin misalignments inside these planes at higher temperatures.
This work is organized as follows: in Section II we describe the system and the theoretical
method, while in Section III we present the scattering formula in the Cisymmetry, and its
applications towards the description of the orbital and magnetic scattering in four special
cases of spin arrangement. In Section IV, we present the corresponding orbital and magnetic
spectra for La0.5Sr1.5MnO4
and address the influence of the spin configuration, while in
Section V we discuss our results in connection with the issue of the orbital spectrum of the
paramagnetic phase. Section VI gives the conclusions of the work, while two appendices
describe some calculational details.
II. DESCRIPTION OF THE SYSTEM AND THEORETICAL APPROACH
In the present work, we focus our attention on the half doped manganites with
a low temperature CE antiferromagnetic structure.As an example, we consider the
La0.5Sr1.5MnO4
compound, which displays a variety of phases17,18. The charge and or-
bitally ordered phase sets on upon cooling at 230 K. The disproportionation of the Mn ions
into the formal valences Mn3+and Mn4+is usually assumed, while recent experiments19,20
indicate that the charge difference in manganite materials is much smaller than 1. In the
present atomic-based approach, we approximate the charge on the manganese ions by the
integral values of 3+ and 4+. The four (three) 3d electrons of the Mn3+(the Mn4+) are
under the strong influence of the crystal field. In the presence of the cubic ligand field,
the degenerate d orbitals split into triple degenerate t2g and doubly degenerate eg levels.
Cooperative Jahn-Teller distortions of the MnO6octahedra further reduce the symmetry of
the crystal field to D4hat the Mn3+site and thus lift the orbital degeneracy. t2glevel splits
into dxyand doubly-degenerate dxz,yzorbitals, and eginto orbitals of the d3z2−r2 and dx2−y2
type. Only one of the egorbitals is occupied on the Mn3+ions, leading to orbital ordering,
i.e. an alternate arrangement of orbitals oriented along the ? a and?b axes on neighboring
Mn3+A and B sites (see Fig. 1). The antiferromagnetic phase, characterized as the CE type
structure, exists under 115 K. In this phase, the spins are lying in the ab-plane21, displaying
ferromagnetic ordering along spin-chains in the ab-plane (see Fig. 1: A−− B−− A−and

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− "Mn "
4+
− "Mn "
3+
− O
− spin
ba
αA(B) − angle between the
spin and the local
αA(B)
B− B+
A−A+
B−B+
A−A+
Case I:
α = 45
o
Case II:
α = 0
o
α − angle between
the spin direction
and lattice vector b
c.f.
axis
crystal field −c.f.−
axis on site A(B)
FIG. 1: The MnO2plane of La0.5Sr1.5MnO4 representing charge, orbital and spin ordering for two
different cases of spin orientation in the CE structure. Case I: the spin and crystal axis?b enclose
an angle α = 45◦and Case II: α = 0◦.The dashed lines denote the ferromagnetic spin chains. For
reasons of clarity, the spins on the “Mn4+” ions are omitted. We assumed the x2−z2/y2−z2type
of orbital ordering11, in the crystal coordinate system with x, y, and z along the ? a,?b, and ? c axis,
respectively.
A+− B+− A+spin chains, “+” and “-” refer to the spin direction) and antiferromagnetic
ordering between the spin chains both in the ab-plane and along the c-axis.
Figure 1 presents two possible cases of spin orientation in the CE structure, which we will
consider in the present work. In Case I, the spins are parallel to the? a +?b axis, corresponding