Quasi-two-dimensional non-collinear magnetism in the Mott insulator Sr$_2$F$_2$Fe$_2$OS$_2$

4.3 MB·English

by  Liang L. Zhao

Quasi-two-dimensional non-collinear magnetism in the Mott insulator Sr F Fe OS
2 2 2 2
Liang L. Zhao1, Shan Wu2, Jiakui K. Wang1, J. P. Hodges3, C. Broholm2,4, and E. Morosan1
1Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA
2Institute for Quantum Matter and Department of Physics and Astronomy,
The Johns Hopkins University, Baltimore, MD 21218, USA
3Neutron Sciences Directorate, Instrument and Source Design Division,
Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
4Neutron Sciences Directorate, Quantum Condensed Matter Division,
Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
(Dated: January 23, 2013)
The magnetism of Sr F Fe OS was examined through neutron powder diffraction and thermo-
2 2 2 2
dynamicandtransportmeasurements. Quasi-two-dimensionalmagneticorderdevelopsbelowT =
N
3 106(2)Kwithanin-planecorrelationlengthexceeding310˚Aandanout-of-planecorrelationlength
1 ofjust17(3)˚A.Thedataareconsistentwithatwo-kstructurewithk =(1/2,0,1/2)andk =(0,
1 2
0
1/2, 1/2) and an ordered moment of 3.3(1) µ oriented along the in-plane components of k. This
2 B
structure is composed of orthogonal AFM chains intersecting at super-exchange mediating O sites.

n DensityFunctionalTheory(DFT)alsopointstothisstructureandanarrowerFe3dbandthanfor
a the iron pnictides from which electronic correlations produce a Mott insulator.
J

2 PACSnumbers: 75.25.-j,75.30.-m,71.20.-b
2

] Quasi-two-dimensional magnetic materials near the lencespacerlayers,severalotherrelatedcompoundswere
l
e metal-insulator transition have been the focus of in- synthesized, including A2T2OX2 with A = SrF, BaF
- tense research since the discovery of high T supercon- (“22212”)12 or Na (“2212”),15 and T = Mn, Fe and X
r c
t ductivity in layered copper oxides. The discovery of = S, Se.12 For a view into electronic correlations in this
s
superconductivity in the chemically distinct iron pnic- family of materials, we examine the magnetic structure
.
t
a tides has brought attention to the potential for novel of Sr2F2Fe2OS2 finding it distinct from anything seen in
m electronic phases in layered iron-based compounds at the copper oxides or the iron pnictides.
the local-to-itinerant moment boundary. Here we show
- Polycrystalline Sr F Fe OS was synthesized by solid
d that Sr F Fe OS is a Mott insulator with quasi-two- 2 2 2 2
2 2 2 2 state reaction, using SrF , SrO, Fe and S powders as
n dimensional non-collinear magnetic order. The unusual 2
o starting materials. The mixture was pelletized and an-
magnetic structure features two wave-vectors k = (1/2,
c 1 nealed in vacuum at temperatures between 800 ◦C and
0, 1/2) and k = (0, 1/2, 1/2) associated with perpen-
[ 2 850 ◦C. Neutron powder diffraction data were collected
dicular AFM spin chains that share super-exchange me-
for temperatures between 12 K and 300 K on the time-
1 diating oxygen sites.
v of-flight POWGEN powder diffractometer at the Spalla-
6 Sr2F2Fe2OS2 isstructurallyrelatedtoLa2O3Fe2X2 (X tion Neutron Source (SNS) at Oak Ridge National Lab-
5 = S, Se, “2322”) which was first reported by Mayer et oratory. In order to focus on the chemical and mag-
0 al.1 Thisisaalayered,tetragonalstructureconsistingof netic structures respectively, the data were acquired us-
5 stacked [La2O2]2+ and [Fe2OX2]2− sheets, composed of ing two different instrumental configurations with wave-
.
1 edge-sharing La4O tetrahedra and face-sharing FeO2X4 length bands of 1.066 ˚A–2.132 ˚A (Fig. 1a) and 4.264
0 octahedra, respectively. The Fe2OX2 sublattice forms a ˚A –5.33 ˚A (Fig. 2). The room temperature diffraction
3 checkerboard spin lattice, with O and X mediated Fe- pattern (red points, Fig. 1a) was refined to a tetrago-
1
Fe super-exchange interactions. Insulating behavior and nal structure (Fig. 1b) using fullprof.16 The lattice
:
v long range antiferromagnetic (AFM) ordering at 105 K parameters a = 4.0362(5) ˚A and c = 17.9915(1) ˚A are
i (X = S) or 93 K (X = Se) was reported in these sys- consistent with the previously reported values.12 The re-
X
tems. Density Functional Theory (DFT) indicates these fined atomic positions and isotropic thermal factors are
ar compounds are Mott insulators.2 provided as supplemental material.17 Minute amounts of
Very recently, the isostructural compounds impurity phases (0.84% FeF2 and 0.39% FeF3) were also
La O Co Se ,3,4 R O Mn Se (R = La, Ce, Pr),5–7 detected.
2 3 2 2 2 3 2 2
R O Fe S (R = Ce, Pr)8 and R O Fe Se (R =
2 3 2 2 2 3 2 2 For temperature below T = 106(2) K, additional
La-Sm)7,9 were reported. All “2322” materials known so N
peaks (green tick marks, Fig. 2b and c) appear in the
far are insulators or semiconductors with AFM order.3
neutrondiffractionpattern. Thesecorrespondtoaprop-
While no band structure calculations were reported
agationvectork=(1/2, 0, 1/2)andwillbeseentoarise
for the Mn compounds,5–7 transport and magnetic
from magnetic scattering. Two unusual aspects of the
properties similar to those of La O Fe S indicate a
2 3 2 2 magnetic diffraction pattern will be shown to define the
Mott-localization picture may be applicable.
magnetic structure: (1) The observable magnetic peak
By replacing [La O ]2+ sheets with different 2+ va- with the shortest wave vector is at Q = 1.75 ˚A−1 and
2 2
2
(a)
s) (a) Magnetic Phase T = 300 K
unit 2 Sr2F2Fe2OS2
b. FeF2 (0.84%)
y (ar FeF3 (0.39%)
sit 1
n
e
nt 0
I
s) (b) (0.5, 0, 4.5) T = 100 K
(b) (c) O Fe b. unit 2 (0.5, 1, -0.5)
S y (ar (0.5, 1, 1.5) (-0.5, 1, 2.5)
J3 J1 J2 Intensit 10
(c)
s) T = 16 K ± 4 K
nit
u 2
b.
ar
y (
sit 1
n
e
Int 0
1.70 1.75 1.80 1.85 1.90 1.95 2.00
FIG.1: Sr F Fe OS (a)neutrondiffractionpatternforT =
2 2 2 2 Q (Å-1)
300 K (red - measured, black - calculated, green - difference
between the measured and calculated patterns, blue vertical
lines-calculatednuclearpeakpositions)and(b)theunitcell,
withtheredarrowsindicatingtheFespinsorientationinthe
AFM state, and (c) the ab plane view of the Fe OS layer. FIG. 2: Neutron diffraction patterns for T = (a) 300 K, (b)
2 2
100 K and (c) 12 K and 20 K (averaged), showing the devel-
opment of magnetic peaks below T = 106(2) K (green tick
N
marks). The magnetic peaks are refined with a Warren-like
is associated with indexes (0.5, 0, 4.5) and (0.5, 1, –
line shape (red lines, see text) that consistently accounts for
0.5). This points to a longitudinally modulated mag-
the magnetic diffraction data. The fitting background and
neticstructurewherethepolarizationfactorextinguishes
the difference between the measured and calculated patterns
peaksatwavevectorsthatdonothaveanadequatecom- areshowninblackdottedlinesandbrownsolidlines,respec-
ponent transverse to the in-plane direction of unit cell tively. The blue dotted line represents the best fit profile
doubling (here the a-direction); (2) The (0.5, 1, –0.5) assuming an isotropic magnetic correlation length, which is
magnetic Bragg peak stands out by a sharp leading edge however inconsistent with the experimental data.
which is not apparent at (0.5, 1, 1.5). This indicates
strong correlation length anisotropy with much longer
thein-planecomponentof kistheonlyirrepthatiscon-
correlations in the a-b plane than along c.
sistent with the data.
For a systematic analysis of possible magnetic struc-
As the refinement based on the model of isotropic cor-
tures we used representation analysis and Rietveld re-
relation length (blue dotted line, Fig. 2c) failed to ac-
finement as implemented in sarah18 and fullprof.16
countfortheexperimentaldata(χ2=7.496),thecorrela-
For the I/4mmm symmetry with a single propagation
tion length anisotropy was quantified by replacing in the
vector of k = (1/2, 0, 1/2), the iron sites are divided
Rietveldanalysisofmagneticdiffractionthesphericalav-
into two independent sets: those forming Fe-O-Fe chains
erageofδ3(Q−τ)bythesphericalaverageofthefollow-
alongthein-planea-componentof k=(1/2, 0, 1/2)and
ingnormalizedanisotropiccorrelationfunction(Warren-
those forming Fe-S -Fe chains along a (Fig. 1c). Using
2 like function20):
Kovalev notation,19 the representation Γ associated
mag
with such magnetic structures decomposes into two irre- 1 1 |Q−τ| ξ 1
S(Q)= exp(− ( ⊥)2) c
duciblerepresentations(irreps),Γ1 andΓ3 intheformof 2πσ2 2 σ π 1+(ξ |Q−τ| )2
Γ =Γ +2Γ , with all three basis vectors projected. ⊥ ⊥ c (cid:107)
mag 1 3
Given the observations above which are quantitatively The gaussian and lorentzian respectively describe long
bornoutbytheRietveldanalysis,Γ withmomentsalong range in-plane correlations and short range correlations
3
3
ol)f.u.2.0 (a) Sr2F2Fe2OS2 4 (b) (a) (b) M
m FC H=1T 3
-2(10emu/11..68 ZFC2+µ(/Fe)B00..0002 2+µm(/Fe)B 12 Γ X
M/H1.4 M-0.02-1 0H(T)1 0 H=0
0 100 200 300
T(K) (d)
(c) K)150 H=0
Ωρ (cm)110035 H=0 Ωρ (cm)111000135 C(J/molpf.u.15000 C(J/molK)m1230000 FSdriIm2GFe.2nF4sie:o2nO(aaSl)2f,eNasothunor-wemsin.aggnaetnicarDroOwSFaen3dd(bba)ndFearnmdi qsuurafsai-ctewoo-f
200 300 400 0.01 0.1
101 T(K) 0 t
3 4 5 0 50 100 150 tinct magnetic sites with an average moment of 2.35(5)
1/T(10-3K-1) T(K) (=4.7(1)/2) µ /Fe2+, the two-k structure implies an or-
B √
dered moment of 3.3(1) (= 4.7(1)/ 2) µ /Fe2+ on all
B
FIG. 3: (a) DC magnetization measured for H = 1 T. The sites. Of these, only the latter structure yields a mo-
ZFC and FC data are shown as solid and open symbols, re-
ment comparable to the spin-only localized moment of
spectively; inset: the hysteresis loop M(H) for T = 2 K. (b)
4 µ /Fe2+, and is consistent with the observation of a
TheT-dependentstaggeredmagnetizationobtainedbyfitting B
single site Fe2+ hyperfine split M¨ossbauer spectrum.12
diffractiondata. ThesolidlineshowstheOnsagersolutionof
The noncollinear spin structure can be described as
the 2D square lattice Ising model. (c) semi-log plot of resis-
tivity vs. 1/T (symbols), with a linear fit that gives E = longitudinally polarized antiferromagnetic order on per-
g
0.28 eV. The raw ρ(T) data are shown in the inset; (d) zero pendicular Fe-O-Fe chains that intersect at oxygen sites.
fieldheatcapacity. Aftersubtractingthephononcontribution As for the “2322” compounds, the intra-layer exchange
(dashedline),themagneticheatcapacityC (T)isplottedvs. interactions between the nearest and next nearest neigh-
m
t=|T−TN|/TN (inset),showinglogarithmicdivergencenear boring Fe sites involve three distinct exchange paths
TN for both T <TN (solid) and T >TN (open). (green arrows, Fig. 1c): J1 links spins within chains
via the 180◦ Fe-O-Fe super-exchange interaction and is
expected to be dominant. J links perpendicular chains
2
along c. The polarization factor associated with the Γ through the 90◦ Fe-O-Fe and the approximately 90◦ Fe-
3
structure was implemented within the spherical average. S-Fe super-exchange interactions. J corresponds to the
3
The corresponding fit shown in Fig. 2 provides an ex- Fe-S-Fe super-exchange with a bond angle of 100.22◦,
cellent account of the magnetic diffraction data (χ2 = which links parallel spin chains. The observed magnetic
1.033). The in-plane peak width σ = 0.0036 ˚A−1 is structure is favored by AFM J and FM J interactions.
⊥ 1 3
near the resolution width extracted from the nearby nu- Isotropic J interactions are frustrated due to the 90◦
2
clear peak: σ = 0.0023 ˚A−1, indicating the in-plane angle between nearest neighbor spins.
res
correlation length exceeds 310 ˚A. By contrast, the cor- The proposed magnetic structure differs from those
relation length along c, ξ⊥ = 17(3)˚A, is indistinguish- inferred for the structurally analogous “2322” systems
ablefromthelatticeparameterc,sothelowtemperature La O T Se (T = Mn, Fe, Co), for which the T = Mn
2 3 2 2
magnetic order can rightfully be characterized as quasi- compound shows a G-type AFM structure with all spins
two-dimensional. These results are consistent with the parallel to the c axis,5 the T = Fe compound exhibits a
initial phenomenological observations. bi-collinear AFM structure with all spins parallel to the
A well-known ambiguity presents itself in interpreting aaxis,10 whileforT=Coanon-collinearplaquetteAFM
the results. The Fe-O-Fe and Fe-S -Fe chains associ- structure with 90◦ angles between the spin orientations
2
atedwithk =(1/2,0,1/2)haveidentical,realmagnetic ofneighboringCoisobserved.11 Noneofthesestructures
1
structurefactorsforallowedmagneticBraggpeaksinthe is consistent with the magnetic diffraction pattern for
collinear Γ spin structure. The magnetic diffraction in- Sr F Fe OS (Fig. 2c). The unusual diversity of mag-
3 2 2 2 2
tensity from a single wave vector domain thus depends neticstructuresindicatesfrustrationinthemagnetismof
only on the sum of the ordered moment on the two sites. the checkerboard Fe OX spin lattice.
2 2
By calibrating the magnetic diffraction intensity against The lamellar magnetism revealed by the neutron
thenucleardiffractionintensityintheconventionalfash- data is also reflected in the thermodynamic properties.
ion, the magnitude of the total moment comes out to The DC magnetization M(T), measured in a Quantum
be 4.7(1) µ . It is not possible, on the basis of diffrac- Design Magnetic Property Measurement System (QD
B
tion alone, to distinguish the collinear structure from a MPMS) for H = 1 T, shows a peak at T = 106(2)
N
non-collinear two-k structure where perpendicular Fe-O- K (Fig. 3a), as expected for long range AFM order-
Fe chains are modulated antiferromagnetically (Fig. 1c). ing. While the N´eel temperature is consistent with a
However, while the collinear structure defines two dis- previous report,12 the anomaly reported here is much
4
TABLE I: Relative energies ∆E (meV per unit cell) of six spin configurations and exchange constants J (meV/bond) for
i
different values of U .
U (eV) FM AFM1 AFM2 AFM3 AFM4 AFM5 J J J
1 2 3
1.5 0 -191 121 -64 -319 -247 27.4 11.1 -12.3
3.0 0 -277 -27 -79 -330 -278 23.3 17.1 -7.2
4.5 0 -248 -36 -73 -262 -228 18.0 15.2 -5.5
sharper, indicating, as is generally the case in frustrated as observed in LaMnPO F .21
1−x x
magnets, that sample quality can affect the transition. To connect our experimental observations with the
Heat capacity data (Fig. 3d), measured on a QD Phys- electronic structure of Sr F Fe OS , DFT calculations
2 2 2 2
ical Property Measurement System (PPMS) also shows were performed using the full-potential linearized aug-
a sharp anomaly. By subtracting the estimated phonon mentedplanewave(FP-LAPW)methodimplementedin
contribution from a polynomial fit of the Cp(T) data at thewien2kpackage.22 Thegeneralizedgradientapprox-
temperatures away from TN (dashed line, Fig. 3d), the imation(GGA)wasusedfortheexchangecorrelationpo-
singular magnetic specific heat Cm was extracted and tential, and different effective onsite Coulomb repulsion
plotted vs. t = |T −TN|/TN in the inset of Fig. 3d. values U from 1.5 to 4.5 eV were considered. An Fe 3d
The observed logarithmic divergence of Cm is expected band between –2 eV and 1.5 eV is revealed in the non-
for a two dimensional Ising system. Fig. 3b shows the magnetic density of states (DOS) spectrum (Fig. 4a).
temperature dependence of the sublattice magnetization The 3d band is narrower than that of LaOFeAs23 and
m(T) inferred from diffraction. Consistent with the spe- BaFe As ,24 adirectconsequenceofthelargerFesquare
2 2
cific heat, the data resemble the Onsager result for the lattice in Sr F Fe OS and the quasi-one-dimensional
2 2 2 2
square lattice Ising model (solid line).13 Ising criticality connectivity. Sincethebandwidthisproportionaltothe
is consistent with strongly anisotropic exchange interac- kinetic energy t, the narrow 3d band suggests enhanced
tions which also characterize the iron pnictides.14 electron correlations U/t, leading to the insulating be-
The zero-field-cooled (ZFC) and field-cooled (FC) havior and a relatively high N´eel temperature. The Sr-F
magnetization curves (full and open symbols, respec- layers (red and dark yellow lines, Fig. 4a) contribute
tively, in Fig. 3a) exhibit irreversibility below T and negligible DOS to the Fermi level, hence the inter-layer
N
this is also reflected by the magnetic hysteresis loop for electron hopping is strongly reduced, giving rise to the
T = 2 K (inset, Fig. 3a). This indicates glassy be- quasi-two-dimensional electronic structure. The low di-
havior, consistent with the short range inter-plane cor- mensionalityofSr F Fe OS isalsoreflectedintheFermi
2 2 2 2
relations. While commensurate AFM order on a square surface, which mainly consists of quasi-2D ribbons ex-
lattice comes in two time-reversed versions, the spins in tending along the Γ−Z direction (Fig. 4b).
eachoftheperpendicularsetsofchainscanbeseparately ThemagneticgroundstateandexchangeconstantsJ ,
1
reversed in the two-k structure, leading to a total of J and J are estimated from spin-polarized calculations
2 3
four different versions. Noting substantial in-plane cor- forthefollowingsixspinconfigurations(asshowninRef.
relations above T indicated by the susceptibility max- 2): (1) FM, (2) checkerboard AFM (AFM1), (3) single
N
imum around 150 K (Fig. 3), consider now the stacking stripe+FM(AFM2),(4)doublestripe+FM(AFM3),(5)
of such spin planes along c. To establish long range or- (1/2, 1/2) state with antiparallel alignment across the
deralongc,Dzyaloshinskii-Moriya(DM)interactionsbe- O sites (AFM4), (6) stripe AFM (AFM5). For differ-
tween spins displaced by c/2 and exchange interactions ent values of the Coulomb repulsion U, the ground state
between spins displaced by c, which - depending on the energies are listed in Table I.
sign of the DM interaction - could even be frustrated, For U = 0, finite DOS exists at the Fermi level for all
must select just one out of these four copies. Consider- spin configurations, while a Mott gap opens for finite U.
ing the slow dynamics associated with transitioning be- Out of all the calculated spin configurations (Table I),
tween the four different Ising spin planes, it is plausible AFM4 is found to be the lowest energy state, with the
the process fails due to kinetics and/or disorder. ordered moment determined to be 3.49 µ /Fe2+. Al-
B
Like all other “2322” and “22212” compounds, though the specific orthogonal spin configuration is not
Sr F Fe OS is an insulator for which the temperature uniquely identifiable in the DFT results due to software
2 2 2 2
dependent resistivity ρ(T) (inset, Fig. 3c) can be de- limitations, the moment value is in very good agreement
scribed by ρ ∝ eEg/kBT, as shown in the Arrhenius plot withthevalueassociatedwiththetwo-kmagneticstruc-
(symbols,Fig. 3c). Alinearfitoflnρvs. 1/T (solidline, ture (Fig. 1c). In addition, the signs of the exchange
Fig. 3c)suggestsanactivationgapE =0.28eV,whichis coupling constants J and J (Table I) suggest an AFM-
g 1 2
considerablylargerthanthepreviouslyreportedvalueof type Fe-O-Fe superexchange coupling and an FM-type
0.10 eV but equal to E = 0.28 eV for Ba F Fe OSe .12 coupling along the Fe-S-Fe paths, which are consistent
g 2 2 2 2
At temperatures lower than 250 K, the resistivity starts with the two-k structure rather than the collinear struc-
todeviatefromtheactivationgapmodel,whichsuggests ture with k = (1/2, 0, 1/2). As suggested by the phase
1
the importance of hopping between localized gap states, diagram proposed in Ref. 2, the condition for AFM4
5
to be the ground state is J > J and J < 0, which to magnetic hysteresis and short-range interlayer corre-
1 2 3
also agrees well with the calculated exchange constants lations. The intersecting chain-like structure is the basis
of Sr F Fe OS . By calculating the energy difference fortheunusualnon-collinearmagnetisminSr F Fe OS
2 2 2 2 2 2 2 2
betweenparallelandantiparallelspinconfigurations,the and through effective electronic one-dimensionality per-
inter-layer interaction J is estimated to be three orders haps also its Mott insulating state. The variety of mag-
⊥
of magnitude weaker. netic structures suggests significant potential for tuning
In conclusion, we have provided evidence for a non- electronic correlations in the extended “2322” family of
collinear magnetic structure in the layered oxychalco- materials.
genide Sr F Fe OS . The Fe spin lattice consists of
2 2 2 2
orthogonally intersecting 1D AFM chains, with frus- Acknowledgements The authors thank Quan Yin,
tratednearneighborinteractions-astructurethattoour Gabriel Kotliar, Rong Yu, Qimiao Si and Jian-Xin Zhu
knowledge has not previously been observed in a square for useful discussions. The work at Rice University was
lattice Mott insulator. The phase transition is of the supportedbyAFOSR-MURI.TheworkatIQMwassup-
2DIsingvarietyandelectronictwo-dimensionality,inter- ported by the U.S. Department of Energy (DOE), Office
layer magnetic frustration, and four degenerate versions of Basic Energy Sciences, Division of Materials Sciences
of the two-k magnetic structure are contributing factors and Engineering under award DE-FG02-08ER46544.
1 J. M. Mayer, L. E. Schneemeyer, T. Siegrist, J. V. K. Ohoyama, J. Am. Chem. Soc. 132, 18020 (2010).
Waszczak,andB.V.Dover,Angelic.Chem.Int.Ed.Engl. 12 H.Kabbour,E.Janod,B.Corraze,M.Danot,C.Lee,M.-
31, 1645 (1992). H. Whangbo, and L. Cario, J. Am. Chem. Soc. 130, 8261
2 J.-X.Zhu,R.Yu,H.Wang,L.L.Zhao,M.D.Jones,J.Dai, (2008).
E.Abrahams,E.Morosan,M.Fang,andQ.Si,Phys.Rev. 13 L. Onsager, Phys. Rev. 65, 117 (1944).
Lett. 104, 216405 (2010). 14 T. Yildirim, Phys. Rev. Lett. 101, 057010 (2008).
3 C.Wang,M.Q.Tan,C.M.Feng,Z.F.Ma,S.Jiang,Z.A. 15 J.B.He,D.M.Wang,H.L.Shi,H.X.Yang,J.Q.Li,and
Xu,G.H.Cao,K.Matsubayashi,andY.Uwatoko,J.Am. G. F. Chen, Phys. Rev. B 84, 205212 (2011).
Chem. Soc. 132, 7069 (2010). 16 J. Rodriguez-Carvajal, Physica B 192, 55 (1993).
4 Y. Fuwa, M. Wakeshima, and Y. Hinatsu, Solid State 17 See supplemental material at [url will be inserted by pub-
Comm. 150, 1698 (2010). lisher] for the refined atomic positions and isotropic ther-
5 N. Ni, E. Climent-Pascual, S. Jia, Q. Huang, and R. J. mal factors of Sr F Fe OS .
2 2 2 2
Cava, Phys. Rev. B 82, 214419 (2010). 18 A. S. Wills, Physica B 276-278, 680 (2000).
6 R. H. Liu, J. S. Zhang, P. Cheng, X. G. Luo, J. J. Ying, 19 O. V. Kovalev, Irreducible Representations of the Space
Y. J. Yan, M. Zhang, A. F. Wang, Z. J. Xiang, G. J. Ye, Groups (Gordon and Breach, New York, 1965).
et al., Phys. Rev. B 83, 174450 (2011). 20 B. E. Warren, Phys. Rev. 59, 693 (1941).
7 D.G.Free,N.D.Withers,P.J.Hickey,andJ.S.O.Evans, 21 J. W. Simonson, K. Post, C. Marques, G. Smith,
Chem. Mater. 23, 1625 (2011). O. Khatib, D. N. Basov, and M. C. Aronson, Phys. Rev.
8 D. O. Charkina, V. A. Plotnikov, A. V. Sadakov, O. E. B 84, 165129 (2011).
Omelyanovskii, and S. M. Kazakov, J. Alloys. and Comp. 22 P. K. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and
509, 7344 (2011). J. Luitz, WIEN2K package, http://www.wien2k.at.
9 N. Ni, S. Jia, Q. Huang, E. Climent-Pascual, and R. J. 23 D. J. Singh and M.-H. Du, Phys. Rev. Lett. 100, 237003
Cava, Phys. Rev. B 83, 224403 (2011). (2008).
10 D. G. Free and J. S. O. Evans, Phys. Rev. B 81, 214433 24 I. R. Shein and A. L. Ivanovskii, JETP Lett. 88, 107
(2010). (2008).
11 Y. Fuwa, T. Endo, M. Wakeshima, Y. Hinatsu, and