Temperature-dependent and anisotropic optical response of layered Pr$_{0.5}$Ca$_{1.5}$MnO$_{4}$ probed by spectroscopic ellipsometry

0.62 MB·English

by  M. A. Majidi

Temperature-dependent and anisotropic optical response of layered Pr Ca MnO
0.5 1.5 4
probed by spectroscopic ellipsometry
M. A. Majidi1,6, E. Thoeng1,2, P.K. Gogoi 1,2, F. Wendt 3, S. H. Wang 1,2, I. Santoso 1,2, T.C. Asmara 1,2,
I.P. Handayani 4,5, P. H. M. van Loosdrecht4, A. A. Nugroho 4,5, M. Ru¨bhausen1,3, and A. Rusydi1,2,3,5∗
1 NUSNNI-NanoCore, Department of Physics, Faculty of Science,
National University of Singapore, Singapore 117542, Singapore,
2 Singapore Synchrotron Light Source, National University of Singapore, Singapore 117603, Singapore
3 Institut fu¨r Angewandte Physik, Universita¨t Hamburg, Jungiusstrae 11, D-20355 Hamburg, Germany.
Center for Free Electron Laser Science (CFEL), Notkestraße 85, D- 22607 Hamburg, Germany,
4 Zernike Institute for Advanced Materials, University of Groningen,
Nijenborgh 4, 9747 AG Groningen, The Netherlands
5 Physics of Magnetism and Photonics, FMIPA,
5
Institut Teknologi Bandung, Bandung 40132, Indonesia and
1
0 6 Departemen Fisika, FMIPA, Universitas Indonesia, Depok 16424, Indonesia
2 (Dated: January 14, 2015)

n We study the temperature dependence as well as anisotropy of optical conductivity (σ ) in the
1
a pseudocubic single crystal Pr Ca MnO using spectrocopic ellipsometry. Three transition tem-
0.5 1.5 4
J peratures are observed and can be linked to charge-orbital (T ∼ 320 K), two-dimensional-
CO/OO
3 antiferromagnetic (2D-AFM) (∼ 200 K), and three-dimensional AFM (TN ∼ 125 K) orderings.
1 BelowT ,σ showsachargeorderingpeak(∼0.8eV)withasignificantblueshiftasthetem-
CO/OO 1
peraturedecreases. CalculationsbasedonamodelthatincorporatesastaticJahn-Tellerdistortion

] andassumestheexistenceofalocalchargeimbalancebetweentwodifferentsublatticessupportthis
l
e assignmentandexplaintheblueshift. Thisviewisfurthersupportedbythepartialspectralweight
- analysis showing the onset of optical anisotropy at T in the charge-ordering region (0.5−2.5
r CO/OO
t eV). Interestingly, in the charge-transfer region (2.5−4 eV), the spectral weight shows anomalies
s around the T that we attribute to the role of oxygen-p orbitals in stabilizing the CE-type
. 2D−AFM
t magneticordering. Ourresultshowstheimportanceofspin,charge,andlatticedegreesoffreedom
a
in this layered manganite.
m
- PACSnumbers: 78.20.Bh
d
n
o I. INTRODUCTION and 3D-AFM phases occur at T ∼ 210 K and
2D−AFM
c
T ∼130K,respectively.4 AneutronstudyofChiet al.4
[ N
showsastrongspin-latticecouplingwhereCO/OOcom-
Manganites have attracted intensive research over the
1 petes with the AFM superexchange interaction. Studies
past decades due to a wide variety of emerging com-
v
plex phenomena.1,2 They exhibit a rich phase diagram on the optical response related to CE-type phase have
9
also been reported for Pr Ca MnO 8 and other lay-
7 arising from a strong coupling between charge, or- 0.5 1.5 4
9 bital, spin, and lattice degrees of freedom.1,2 Among ered manganites,9,10 in which the authors address the
2 them, Pr-Ca-Mn-O compounds are of particular in- temperature dependence and the anisotropy in the opti-
0 terest. The three-dimensional (3D) pseudocubic per- calconductivitytakenfromthereflectancemeasurements
. up to 3 eV along and perpendicular to the zigzag FM
1 ovskite Pr1−xCaxMnO3 undergoes a transition from an
chain.
0 antiferromagnetic (AFM) insulator to a ferromagnetic
5 (FM) metal upon hole doping, and also exhibits colos- In this paper, we present our study of the temper-
1 sal magnetoresistance.3 On the other hand, in the 2D ature dependence and the anisotropy of the optical
:
v single-layered system Pr1−xCa1+xMnO4, the AFM insu- conductivity [σ1(ω,T)] and magnetic susceptibility
i lating phase is dominant in a wide doping range.4 [χ(T)] of Pr Ca MnO , in a temperature range
X 0.5 1.5 4
One of the most interesting phenomena that can be from above T down to below T . Note that
r CO/OO N
a observed in both systems with half doping is the for- different from experiments reported in Refs. 8–10, here
mation of charge-orbital ordering (CO/OO). Below the we have used spectroscopic ellypsometry covering an
CO/OO temperature (T ) charges form a checker- energy range of 0.5 to 4 eV and the measurements were
CO/OO
board pattern with alternating Mn3+/Mn4+ sites, while performed along the a and b crystalline axes. As the
the e orbitals are aligned in a zig-zag chain.4 Below the temperature decreases, we observe that a peak at 0.8 eV
g
Neel temperature (T ), the spins of Mn ions are coupled (referred to as a charge-ordering peak) monotonically
N
ferromagnetically along the zig-zag chain while they are increases in weight, however its position stays fixed for
coupled antiferromagnetically between the chains (CE- T >T andmovestohigherenergy(i.e.,blueshift)
CO/OO
typemagneticordering). Inthesingle-layeredmanganite as T < T . This trend was also observed in other
CO/OO
Pr Ca MnO , the CO/OO phase occurs above room manganites.8–11. Furthermore, through analysis of par-
0.5 1.5 4
temperature at T ∼ 325 K,5–7 while the 2D-AFM tialspectralweightsinthecharge-ordering(0.5−2.5eV)
CO/OO
2
and the charge-transfer (2.5−4 eV) regions, we observe
significantchangesofthespectralweightsinbothenergy
regions when temperature crosses T , T ,
CO/OO 2D−AFM
and T , indicating changes in the electronic structure of
N
the system occurring prior to each transition. From the
anisotropy of the spectral weight changes occurring at
those three transition temperatures, we suggest that the
charge, orbital, and spin correlations affect the electron
effective Mn-O hopping integrals through the deviation
of orientation of O-p orbitals with respect to a and b
axes. Although the detailed microscopic mechanism
of this interplay has not been fully understood, the
idea of a connection between such correlations and the
change in electron effective Mn-O hopping integrals is
consistent with our earlier studies12,13 that explains the
temperature dependence of σ of La Ca MnO up
1 0.7 0.3 3
to 22 eV. This outlines the importance of measuring
the optical conductivity over a wide energy range or
using such an unambiguous method as spectroscopic
ellipsometry.
II. EXPERIMENTS
Single crystals of Pr Ca MnO were grown using a
0.5 1.5 4
floating zone technique. X-ray diffraction measurements
FIG. 1: (Color online) (a) The temperature depen-
were performed to ensure high quality samples and to
dence of zero-field-cooled magnetic susceptibility (χ) of
determine the lattice structure. The magnetic suscepti-
Pr Ca MnO singlecrystalalongdifferentcrystallineaxes
0.5 1.5 4
bilityχ(T)wasmeasuredusingSQUID-MPMSQuantum
inappliedmagneticfieldof0.1T.Theinsetshowsthetemper-
Design. The measurement of optical properties was ature dependence of the derivative of χ indicating the mag-
performedwithanextendedSentechSE850ellipsometer. netic and charge-ordering temperatures. (b) and (c) Con-
The single crystals Pr Ca MnO were mounted in a tour plots of optical conductivity as a function of temper-
0.5 1.5 4
continuous-He flow cold-finger cryostat operated below ature and photon energy, measured along a and b axis, re-
a base pressure of 3 x 10−8 mbar.14 Ellipsometry is spectively. Thickblackandredlinesconnectthepositionsof
a self-normalizing technique that measures changes of charge-ordering and charge-transfer peaks, respectively, be-
tween adjacent temperatures. Dashed black lines indicate
amplitude and phase of photons being reflected from
three transition temperatures identified from the magneti-
the sample. It provides more accurate and unambiguous
zation measurements. (d)-(f) Anisotropic optical conduc-
resultsofcomplexdielectricfunctionwithoutperforming
tivity for T > T , T > T > T , and
Kramers-Kronig transformation.11 For spectroscopic el- CO/OO CO/OO 2D−AFM
T >T >T ,alonga(solidlines)andb(dashedlines)
2D−AFM N
lipsometry measurements, the crystals were cleaved. All
axes.
measurements were done on two different single crystals
with the same composition to ensure the reproducibility.
b axis, respectively. They reveal an anisotropic profile
of σ (ω) as the temperature is varied. Note, that the
II. EXPERIMENTAL RESULTS AND 1
thickblacklineconnectingthecharge-orderingypeak(∼
DISCUSSION
0.8eV)betweenadjacenttemperaturesclearlytracesthe
Fig. 1(a) shows the temperature dependence and blue shift that starts as the temperature passes T
CO/OO
anisotropy of χ(T) of Pr Ca MnO along different for both measurements along a and b axes. This blue
0.5 1.5 4
crystalline axes. The charge-ordering temperature is shift signifies a direct connection between the electronic
clearly observed around 320 K. A broad maximum structure revealed in σ1(ω) and the formation of charge
around 200 K is the signature of short-range two- order parameter as outlined later in our calculations.
dimensionalAFMcorrelations. Thelong-rangeAFMor- In order to get a better insight in the anisotropic be-
deringisobservedat125Kandthemagneticsusceptibil- havior, in Fig. 1 (d)-(f) we plot σ (ω) at selected tem-
1
itybecomesstronglyanisotropicbelowtheN´eeltempera- peratures along both a and b axes. Above T , the
CO/OO
ture. Aninterestingobservationhereistheenhancement anisotropy persists although not so pronounced, indicat-
ofanisotropyofχforH||aandH||buponcooling, which ing that the difference of lattice contants a and b still
is consistent with σ as discuss below. causes a minor anisotropy. The anisotropic behavior for
1
Figures 1(b) and (c) give the contour plot of σ as a T >T >T and T >T >T looks
1 CO/OO 2D−AFM 2D−AFM N
function of photon energy and temperature along a and almost the same in the charge-ordering region (< 2.5
3
show that the total integrated spectral weight does not
conserve the total number of charge within the measure-
mentenergyrange. Asσ isrestrictedbythef-sumrule:
1
(cid:82)∞σ (ω)dω = πn2, where n is the number of electrons
0 1 2m∗
and m∗ is the effective mass of electron, our result in-
dicates that the missing charge is to be compensated at
much higher energies above 4 eV.
Figures 2(d)-(f) illustrate our scenario of the process
that yields to the anomalous anisotropy of the partial
spectral weight integral for the charge-transfer region
as the temperature crosses T ∼ 200K. At T
2D−AFM
slightly above T [see Fig. 2(d)], the Mn spins
2D−AFM
are oriented randomly. Thermal and photon-induced ex-
citations distort the orientation of many O-p orbitals
from a and b axes, allowing electrons to hop along both
axes with roughly equal probability. Hence, the charge-
transfer conductivity is roughly equal for both axes. At
T ∼ T [see Fig. 2(e)], some of the oxygen or-
FIG. 2: (Color online) Temperature dependence of partial 2D−AFM
spectral weight for energy regions: (a) charge ordering (0.5- bitals align with a or b axis, so as to effectively mediate
2.5 eV), (b) charge transfer (2.5-4 eV), and (c) the total in- the double-exchange (DE) hoppings between the neigh-
tegrated spectral weight. Dashed lines indicate the identified boring Mn spins. The system gains energy by ordering
transition temperatures in concordance with previous analy- the Mn spins in the CE-type AF configuration, howeve,
sis. Right panels illustrate the process causing the anoma- some pairs of O-p orbitals increase their energies asso-
lous anisotropy for the charge-transfer region as T crosses ciated with σ-antibonding states that are occupied by
T ∼200K:(d)above,(e)at,and(f)belowT .
2D−AFM 2D−AFM electrons participating in the Mn-O charge transfer. To
The Mn sites are drawn with arrows depicting their spin di-
minimize this cost of energy, the majority of O σ-bonds
rections, while the remainders are the O sites.
form along the b axis, rather than a axis (since b > a),
makingtheprobabilityofelectronsmovingstraightalong
the b axis significantly higher than that along the a axis.
eV),buttheirdifferenceismorenoticeableinthecharge- Thus,atT thecharge-transferconductivityalong
2D−AFM
transferregion(2.5-4eV).Thisindicatesthatphotonsof thebaxisbecomesremarkablyhigherthanthatalongthe
charge-transfer energy excite the system in such a way a axis, and is the highest among the conductivity values
that affect the 2D-AFM ordering. We elaborate more on for a and b axes in the three considered temperatures.
this along with the discussion related to Fig. 2 below. Below T [see Fig. 2(f)], the Mn spins are or-
2D−AFM
Temperature dependent changes in σ (ω) for two dif- deredinCE-typeAFconfiguration. TostabilizethisMn
1
ferent energy regions separated by a crossing point at spinconfiguration,theO-porbitalsareorientedinsucha
2.5 eV for both a and b axes can be better shown by way to effectively mediate the DE hoppings between Mn
the analysis of the partial spectral weight integral (W) sites with the same spin orientations, and minimize the
which describes the effective number of electrons excited hoppingprobabilitybetweenMnsiteswithoppositespin
byphotonsofagivenenergy. Thepartialspectralweight orientations. Here, electrons can only hop along zigzag
integralisdefinedasW =(cid:82)ω2σ (ω)dω,whereω andω chains, where only 50% of O sites contribute to the con-
ω1 1 1 2
are lower and upper boundaries of the energy region. ductivity. Thus, the charge-transfer conductivity along
Fig. 2(a)showsthatthespectralweightsinthecharge- a or b axes at this temperature would be roughly equal
ordering region, measured along a and b axes practically and is the lowest among those in the three considered
overlap above T . As the temperature decreases temperatures.
CO/OO
below T , both curves increase abruptly but in an Ontheotherhand,wealsoobservetheanisotropicbe-
CO/OO
anisotropic fashion. Finally, below TN the two sets of haviorofspectralweightchangesbelowTN inthecharge-
data appear to display more anisotropic behaviors. transfer region. The detailed origin of this behavior is
unclear in the present study, however, we argue that the
Inthecharge-transferregion[seeFig. 2(b)],bothspec-
increase of the spectral weight below T may suggest a
tral weights decrease monotonically from high tempera- N
stronger Mn-O hybridization for both axes facilitating
ture,behavepeculiarlyaroundT ,anddecreasefur-
CO/OO thestabilizationofthe3D-AFMlong-rangeorder. Thus,
ther below T . Interestingly, the b axis data show
CO/OO the formation of 2D- and 3D-AFM states requires the
remarkable enhancement over the a axis data around
interplay of spin, charge, orbital, and lattice degrees of
T . We propose a scenario explaining this rather
2D−AFM freedom.
anomalousbehaviorinthenextparagraph. Withfurther
decrease in temperature, the two sets of data are seen to
IV. MODEL AND CALCULATION RESULTS
overlap down to T , before they separate again with a
N
sudden drastic rise of the a axis data. In Fig. 2(c), we Toaddressthegeneralprofileofthe0-4eVopticalcon-
4
ductivity and the blue shift of the charge-ordering peak, a Hubbard parameter U for | e (cid:105) orbital. Upon
1(2) g 1(2)
wediscussthedynamicsoftheelectronsofthee orbitals taking U and U to be infinity, the double occupancy is
g 1 2
and the collective spins of the t electrons of the man- preventedineachoftheorbitals1and2,thusmakingthe
2g
ganese atoms, while the other elements are not consid- totaleffectivenumberofstatesaccessibletoelectronsper
ered. Since the optical response comes mainly from the unit supercell A-B equal to 4, instead of 8. To simplify
MnO plane, we model the system as a two-dimensional thecalculations,wetreattheJahn-Tellerandtheon-site
2
square lattice divided into sub-lattices A and B to ac- inter-orbital Hubbard U terms within the Hartree-Fock
commodate the formation of charge ordering. Each sub- approximation. Using the aforementioned basis set we
lattice atom has two e orbitals, and each orbital has propose the following effective Hamiltonian:
g
two possible spin orientations, hence we choose eight ba-
sis orbitals to construct the Hilbert space, which we or- 1 (cid:88) (cid:88)
H = η†[H (k)] η − JSs.ss . (1)
der in the following way: |MnA eg 1,↑(cid:105), |MnB eg 1,↑(cid:105), N k 0 eff k i iα
|MnA e (cid:105), |MnB e (cid:105), |MnA e (cid:105), |MnB e (cid:105), k i,s,α
g 2,↑ g 2,↑ g 1,↓ g 1,↓
|MnA e (cid:105), and |MnB e (cid:105). Here, | e (cid:105) and | e (cid:105)
g 2,↓ g 2,↓ g 1 g 2 The first term in Eq. (1) is the effective kinetic part,
are the original e states having degenerate on-site en-
g whereofη† (η )isarow(column)vectorwhoseelements
ergies, E0 (set to 0 eV), in the absence of Jahn-Teller k k
are the creation (annihilation) operators associated with
distortion. The effect of the assumed static Jahn-Teller
the eight basis orbitals. [H (k)] is an 8×8 matrix in
distortion is incorporated in terms of the displacements 0 eff
momentumspacewhosestructureisarrangedinfour4×4
u and v corresponding to two vibration modes as also
blocks corresponding to their spin directions as
used in Ref. 10. Here, we parameterize the static equi-
libriumvaluesofuandv withU andV ,respectively.
JT JT (cid:20) (cid:21)
Further, we take into account the on-site Coulomb inter- [H (k)] = HHF(k)↑ O , (2)
actionsbetweenelectronsinthetwoorbitalswithaHub- 0 eff O HHF(k)↓
bardparameterU. Wealsoconsidertheon-siteCoulomb
interactions between electrons in the same orbital with where O is a zero matrix of size 4×4, and
E +(cid:104)nA(cid:105)U +(cid:104)nA(cid:105)U (cid:15) (k ,k ) V (cid:15) (k ,k ) 
0 1 JT 2 11 x y JT 12 x y
HHF(k)↑(↓) = (cid:15)11(VkJxT,ky) E0−(cid:104)n(cid:15)1B12(cid:105)(UkxJ,Tk+y)(cid:104)nB2(cid:105)U E0+(cid:104)n(cid:15)1A22(cid:105)(UkxJ,Tk+y)(cid:104)nA1(cid:105)U (cid:15)22(VkJxT,ky) . (3)
(cid:15) (k ,k ) V (cid:15) (k ,k ) E −(cid:104)nB(cid:105)U +(cid:104)nB(cid:105)U
12 x y JT 22 x y 0 2 JT 1
ThekdependenceofH (k) comesfromthein-plane change interactions between the local spin Ss of Mn of
HF ↑(↓) i
tight-binding energy dispersions sub-latticesatasupercelli,formedbythestrongHund’s
couplingamongthreet electronsgivingS=3/2,andthe
2g
(cid:15)αβ(kx,ky)=−2tαβ(cos2kx+cos2ky), (4) electronspinss occupyingorbitalα. Theseinteractions
αi
are treated within the dynamical mean-field theory15,16,
where t , with α,β ∈ {1,2}, are the effective hopping
αβ restricted to the paramagnetic phase.
integrals connecting orbital α at a site and orbital β at
We calculate σ (ω) for various temperatures using the
1
its nearest neighbor site, or vice versa.
Kubo formula as done in Ref. 13, with the parameter
The Pr Ca MnO system has one e electron per
0.5 1.5 4 g values of E = 0 eV, t = t = 0.5 eV, t = 0.25 eV,
0 11 22 12
unit supercell A-B, hence the electron filling satisfies
U = 1.2 eV, V = 2 eV, U = 4 eV, and J = 0.6 eV.
(cid:104)nA(cid:105) + (cid:104)nA(cid:105) + (cid:104)nB(cid:105) + (cid:104)nB(cid:105) = 1. Further, we impose JT JT
1 2 1 2 The results are shown in Fig. 3.
a set of constaints (cid:104)nA(cid:105) = 0, (cid:104)nB(cid:105) = 0, (cid:104)nA(cid:105) = 1+∆n,
1 2 2 2 As shown in Fig. 3, our calculations capture the
and (cid:104)nB(cid:105)= 1−∆n, with ∆n=(cid:104)nA(cid:105)−(cid:104)nB(cid:105) being a local
1 2 2 1 general profile of σ1(ω), most notably the appearance of
charge imbalance between two different sublattices. As
a charge-ordering peak at 0.8 eV and a charge-transfer
this local quantity repeats throughout the entire crys-
peak at 3.6 eV, and the blue shift of the charge-ordering
tal, its existence is a precondition to a charge ordering.
peak as the temperature decreases below T . Ac-
CO/OO
We assume ∆n to have a ”mean-field” temperature de-
cording to our model, the low-energy peak arises along
pendence of the form (1− T )1/2. Note, the model
TCO/OO with the formation of Jahn-Teller gap, while its blue
accommodates a charge ordering (CO), but not orbital shift results from the formation of local charge imbal-
ordering (OO). We use the symbol T in our calcu- ance. This blue shift and the charge ordering itself are
CO/OO
lations just so we can compare its role with that in the only possible in the presence of the on-site interorbital
experimental data. Hubbard U, in consistency with the picture described in
Finally, the second term in Eq. (1) represents the ex- Ref. 17. Within our model, the charge-transfer peak at
5
consequence of the neglect of the role of O orbitals. The
middle and bottom panels of Fig. 3 show the anisotropy
along a and b axes, which our model does not capture.
V. CONCLUSION
In conclusion, we have observed the temperature
dependence and the anisotropy of σ (ω) and χ of
1
Pr Ca MnO measured along different crystalline
0.5 1.5 4
axes. The anisotropic behavior of partial spectral
weight of charge-ordering region of σ (ω) as a function
1
of temperature is similar to that of χ, indicating the
strong connection between the optical response and
the charge and spin correlations. The observation of a
blue shift of the charge-ordering peak of σ (ω) below
1
T signifies its connection with the formation of
CO/OO
a charge-order parameter, which is in agreement with
our calculations. Analysis of the prominent anisotropic
change of partial spectral weight around T
2D−AFM
suggests an interplay between spin, charge, and orbital
correlations through the change of the electron effective
FIG. 3: (Color online) Temperature dependence of optical
Mn-O hopping integrals along the a and b axes.
conductivity. The top panel shows the calculation results,
while the middle and bottom panels show the experimental
results obtained along a and b axis, respectively.
ACKNOWLEDGEMENT
3.6 eV corresponds to transitions from singly to doubly We acknowledge Tjia May On for the discussions and
occupied states in Mn sites. Since this peak appears his valuable comments. This work is supported by Sin-
morepronouncedintheexperimentaldata,theremaybe gapore National Research Foundation under its Com-
other contributions to this peak involving O bands that petitive Research Funding (NRF-CRP 8-2011-06 and
we negtect. Our calculatons also capture the increasing NRF2008NRF-CRP002024), MOE-AcRF-Tier-2, NUS-
trend in the intensity of the charge-ordering peak as YIA, FRC, BMBF under 50KS7GUD as well as DFG
the temperature decreases, with a little discrepancy through Ru 773/5-1. We acknowledge the CSE-NUS
that an abrupt decrease occurs as the temperature is computing centre for providing facilities for our numeri-
lowered just slightly below T . This may also be a cal calculations.
CO/OO
∗ Electronic address: [email protected] Nagaosa,andY.Tokura,Phys.Rev.B75,144407(2007).
1 M. B. Salamon and M. Jaime, Rev. Mod. Phys. 73, 583 9 T.Ishikawa,K.Ookura,andY.Tokura.Phys.Rev.B59,
(2001). 8367 (1999).
2 Y. Tokura, Rep. Prog. Phys. 69, 797 (2006). 10 Y.S.Lee,S.Onoda,T.Arima,Y.Tokunaga,J.P.He,Y.
3 Y. Tomioka, A. Asamitsu, H. Kuwahara, Y. Moritomo, Kaneko, N. Nagaosa, and Y. Tokura Phys. Rev. Lett. 97,
and Y. Tokura, Phys. Rev. B 53, R1689R1692 (1996). 077203 (2006).
4 S. Chi, F. Ye, P. Dai, J. A. Fernandez-Baca, Q. Huang, J. 11 J. Kunze, S. Naler, J. Ba¨ckstro¨m, M. Ru¨bhausen, and J.
W. Lynn, E. W. Plummer, R. Mathieu, Y. Kaneko, and F. Mitchell, Phys. Rev. B 67, 134417 (2003).
Y.Tokura,Proc.Natl.Acad.Sci.USA104,10796(2007). 12 A.Rusydi,R.Rauer,G.Neuber,M.Bastjan,I.Mahns,S.
5 X. Z. Yu, R. Mathieu, T. Arima, Y. Kaneko, J. P. He, M. Muller, P. Saichu, B. Schulz, S. G. Singer, A. I. Lichten-
Uchida, T. Asaka, T. Nagai, K. Kimoto, A. Asamitsu, Y. stein,D.Qi,X.Gao,X.Yu,A.T.S.Wee,G.Stryganyuk,
Matsui, and Y. Tokura, Phys. Rev. B 75, 174441 (2007). K.Do¨rr,G.A.Sawatzky,S.L.Cooper,andM.Ru¨bhausen,
6 M.Ibarra,R.Retoux,M.Hervieu,C.Autret,A.Maignan, Phys. Rev. B 78, 125110 (2008)
C. Martin, and B. Raveau, J. Solid State Chem. 170, 361 13 M. A. Majidi, H. Su, Y. P. Feng, M. Ru¨bhausen, and A.
(2003). Rusydi, Phys. Rev. B, 84, 075136 (2011).
7 R.Mathieu,J.P.He,X.Z.Yu,Y.Kaneko,M.Uchida,Y. 14 R. Rauer, G. Neuber, J. Kunze, J. Ba¨ckstro¨m, and M.
S.Lee,T.Arima,A.Asamitsu,andY.Tokura,Europhys. Ru¨bhausen, Rev. Sci. Instrum. 76, 23910 (2005).
Lett. 80, 37001 (2007). 15 A. Georges, G. Kotliar, W. Krauth and M. Rozenberg,
8 Y.S.Lee,T.Arima,S.Onoda,Y.Okimoto,Y.Tokunaga, Rev. Mod. Phys. 68, 13 (1996).
R.Mathieu,X.Z.Yu,J.P.He,Y.Kaneko,Y.Matsui,N. 16 N. Furukawa, J. Phys. Soc. Japan 63, 3214 (1994) and
6
Proc. Conference on Physics of Manganites (1998) (avail- Rev. Lett. 83, 5118 (1999).
able at http://xxx.lanl.gov/abs/cond-mat/9812066).
17 J. van den Brink, G. Khaliullin, and D. Khomskii, Phys.