Self-Doping Induced Orbital-Selective Mott Transition in Hg2Ru2O7

0.23 MB·

by  L. Craco

Self-Doping Induced Orbital-Selective Mott Transition in Hg Ru O
2 2 7
L. Craco,1,2 M.S. Laad,2 S. Leoni,1 and H. Rosner1
1Max-Planck-Institut fu¨r Chemische Physik fester Stoffe, 01187 Dresden, Germany
2Max-Planck-Institut fu¨r Physik komplexer Systeme, 01187 Dresden, Germany
(Dated: January 29, 2009)
Pyrochloreoxidesarefascinatingsystemswherestrong,multi-orbitalcorrelationsinconcertwith
geometrical frustration give rise to unanticipated physical properties. The detailed mechanism of
theinsulator-metal transitions (IMT) underpinningthese phenomenais, however, ill-understood in
general. Motivated thereby, we study the IMT in the pyrochlore Hg2Ru2O7 using LDA+DMFT.
Incontrast to thewell-known examples of Mott transitions in TMO, we show that, in thenegative
9
0 charge-transfer situation characteristic of Hg2Ru2O7, self-doping plays a crucial role in the emer-
0 gence of an orbital-selective IMT. We argue that this mechanism has broader relevance to other
2 correlated pyrochlore oxides.

n PACSnumbers: 71.28+d,71.30+h,72.10-d
a
J

9 I. INTRODUCTION showinganomalouslybroadPESlineshapes,withnohint
2 of FL quasiparticles, in the metallic phase. Given the

] The Mott-Hubbard insulator-metal transition (IMT) cubic pyrochlore structure for T > TMI, strong orbital
el is by now recognized to play a central role in our un- (from t2g orbital degeneracy) and spin fluctuations are
- derstanding of d- and f-band compounds.1 Understand- implied. How might strong scattering processes involv-
r ing these fluctuations produce the observed nFL metal?
t ing the complex interplay between strong, multi-orbital
s What drives the AFI as T is lowered? A correlatedelec-
(MO) electronic correlations, structural distortions, and
.
t strongly anisotropic, orbital-dependent hopping holds tronic structure study which can illuminate these issues
a
does not, to our best knowledge, exist. In this work we
m the key to a consistent theoretical description of their
study precisely these issues in part in Hg Ru O using
unique responses. Adding geometric frustration to the 2 2 7
- the LDA+DMFT method.8 We focus on the mechanism
d above results in a truly formidable problem. In geo-
n metricallyfrustratedsystems,theexponentiallylargede- of the T-driven IM transition, and leave the issue of the
o low-dimensional AF with a spin gap for future consider-
generacy of classical ordered states inhibits emergence
c ation.
of conventional order, permitting new, complex ordered
[
ground states to arise.2 In real systems, structural ef-

1 fects may partiallyremovethis huge degeneracy,making
v II. MODEL AND SOLUTION
the problem (counter-intuitively) somewhat simpler to
8
solve;3 however, in near-undistorted cases, near perfect
5
orbital degeneracy, and the consequent strong quantum Starting with the high-T cubic Fd¯3m structure found
6
4 orbital and spin fluctuations in a highly degenerate sys- byKleinet al.4 localdensityapproximation(LDA)band
. tem underpin their physical behavior. structure calculations were performed using a (scalar
1
The recently discovered pyrochlore system, and fully-relativistic) full-potential local-orbital scheme
0
9 Hg2Ru2O7,4 is a particularly interesting case in (FPLO)9andalinearmuffin-tinorbitals(LMTO)scheme
0 this context. As temperature (T) is reduced, the in the atomic sphere approximation.10 In Fig. 1 we
: anomalous (see below) non-Fermi liquid (nFL) metallic display our FPLO-LDA11 results for the one-particle
v
i statebecomesunstable,viaafirst-orderMotttransition, density-of-states (DOS). Clearly, the major contribution
X toanantiferromagneticMott-Hubbardinsulator(AFI).5 to the DOS comes from Ru(4d),O(1)(2p) orbitals, but
r External pressure (p) melts the AFI beyond a critical theO(2)(2p)orbitalsalsohavenoticeablespectralweight
a pc = 6.0 GPa, resulting in a low-T correlated FL at the Fermi level (EF). As seen in Fig. 1, the influence
behavior for T < T∗ = 13K. At ambient pressure, the of the spin-orbit coupling (SOC) in the cubic phase to
IMT transition is accompanied by lowering of lattice the t2g states near EF is negligible. Further, we ob-
symmetry from (high-T) cubic to (low-T) a lower, serve strong hybridization between Ru(4d) − O(1)(2p)
hitherto precisely unknown, type: depending upon its orbitals, and between O(2)(2p) − Hg(6s) orbitals, but
precise type, either AF or dimer order may be possible.6 weak mixing between these two sets. These important
The high-T >T∗ state in Hg Ru O is an anomalous findings will be exploited below to study the physics
2 2 7
nFL: the dc resistivity, ρ(T)≃T for T >TMI =108 K4 of Hg2Ru2O7using a multi-orbital Hubbard model in-
volving only the d-band sector. At one-particle level,
at ambient pressure, and deviates from the FL form for
T > T∗ beyond p . The uniform spin susceptibility is the corresponding model Hamiltonian reads, Hband =
c
Curie-Weiss like for T > TMI, indicating a strong local Pk,a,σǫkad†kaσdkaσ +Pi,a,b=1,2∆b(npi,b −ndi,a), where a
moment scattering regime. The nFL character is also labels the diagonalized combination of (e′ ,e′ ,a )12
g1 g2 1g
borne out from the recent photoemission (PES) data,7 the t orbitals, ∆ (b = 1,2) are the pd charge trans-
2g b
2
fer (CT) terms involving two Ru − O(1),(b = 1) and b=2 bandchannelhasappreciablysmallerDOSaround
Ru − O(2),(b = 2) channels. Clearly, neither an AFI E in the LDA results. In a DMFT-like approxima-
F
Mott-HubbardinsulatornoranFLmetalcanbeexpected tion, with negligible one-particle hybridization between
atthislevel,thisrequiringareliabletreatmentofstrong, theb=1,2bands,theintersiteMadelungtermwillpush
d-shell electronic correlations. This part reads, this small spectral weight away from E , to lower- and
F
higher energy (notice that the O-2p bands will be split
by U zhn i, where z is the co-ordinationnumber of the
pd d
Hint =UXndia↑ndia↓+U′ X ndiandia′−JH X Sia·Sia′ lattice, and hence quite large). This will already occur
i,a i,a,a′ i,a,a′ at the level of LDA+Hartree approximation. We then
expect that the correlated spectral function will be dom-
with a,a′ = e′ ,e′ ,a . Given the larger spatial ex-
g1 g2 1g inated by the d-bands over an appreciable range about
tent of 4d-orbital vis-a-vis their 3d counterpart, we also
E . Correlation effects in Hg Ru O via LDA+DMFT
include a Madelung term, H = U nd np F 2 2 7
M pdP<i,j>,a,b i,a j,b are studied below, subject to this caveat; we will show
in our calculations (see below). In Tl Mn O , the IMT
2 2 7 that this is indeed a good approximationa posteriori, in
(from a paramagnetic insulator (PI) to a ferromagnetic
the sense that our LDA+DMFT results with the above
metal (FMM)) is seemingly driven by the Tl(6s) states
caveatshow very good quantitative agreementwith one-
crossingE acrossT ,13 for instance. This canoccurvia
F c particlespectroscopyandkeythermodynamicandtrans-
aT-dependentCTfromtheTMd-statestotheO(2)−Tl
port data in Hg Ru O .
2 2 7
hybridizedstates. Inviewofthegenericrelevanceofself-
The full many-body Hamiltonian reads H = H +
dopinginTM4dpyrochlores,13,14thistermisanessential band
H +H . We solve this model within MO dynamical
int M
part. In the low-T phase, this will involve CT processes
mean field theory (MO-DMFT) developed and used for
involving the O(2p) −Hg(6s) channel (second term of a range of TMO with good success.8 We use the MO-
H ) across the IMT, as we describe below.
band iteratedperturbationtheory(IPT)asanimpurity solver
in the DMFT selfconsistent procedure. Though not
60
ell) tRouta 4ld HHgg 55dd SnoO CSOC nmuamnyeraicdavlalynteaxgaecst: i(tliiksevQalMidCfo,rNTR=G,0,Dw-DheMreRQGM),Citchaans-
c t
V / 40 e2g Hg 6s not be used. NRG/DDMRG are extremely prohibitive
es / e g ftourratlhirnepeuotrsbaittalLDmAodleelvs,ele.veAnswshitohwonutineleecatrrlioenricwostrrku,1c5-
stat20 DMFT(MO-IPT)genericallygivesverygoodsemiquanti-
S ( tative agreement with PES/X-ray absorption (XAS) ex-
O
D periments for TMOs.15,16 For Hg2Ru2O7, DMFT(MO-
m) 0 O(1) 2p O(2) 2p IPT) has to be extended to treat the second CT chan-
o nel described above. Given the complexity of the
at 8
V / problem, we choose the following strategy to solve H
s / e 6 awbitohvien: DFoMrFthTe(MhiOgh-I-PTTp)havseer,siwone (uis)edsolevaerlHiebra,nfdor+tHecihnt-
e 4
at nical details see Ref. 15. (ii) As indicated by ex-
st
S ( 2 periment on the related Tl2Ru2O7 system,14 we study
O the effect of Ru(4d)−O(2)(2p)−Hg(6s) CT processes
D 0
-8 -6 -4 -2 0 2 4-8 -6 -4 -2 0 2 4 by incorporating this CT channel selfconsistently into
Energy (eV) Energy (eV)
the LDA+DMFT(MO-IPT) procedure: given the small
Ru(4d)−O(2)(2p) hybridization, the O(2)(2p)−Hg(6s)
FIG. 1: (Color online) LDA band structure for cubic
channel acts like a scattering (non-hybridizing) channel
Hg2Ru2O7. O(1) (O(2)) denotes Oxygen ions nearest to Ru
for the Ru−t bands in the impurity model of MO-
(Hg). 2g
DMFT. This enables us to treat this extra channel by
combining the MO-IPT solution for (i) with the exact
The d above should be understood as appropriate,
aσ DMFT solution of a Falicov-Kimball model (FKM) for
RuO cell-centered, combinations of the Ru-4d and O-
6 (ii),17 in a selfconsistent way.
2p orbitals, computed within LDA. Similarly, the b = 2
channel is to be understood as a band of hybridized O-
2p and Hg-6s orbital states. Because of the negligible
III. LDA+DMFT RESULTS AND DISCUSSION
one-particle mixing (hybridization) between the b = 1,2
channels,we approximatethe full problemof three Ru-d
bandscoupledtotheb=2bandchannelbyreplacingthe We now describe our LDA+DMFT results. We start
latterbya“reservoir”,whoseonlyfunctionistosimulate withthe(cubic)pyrochlorestructureathigh-T,withthe
the self-doping process arising from the negative charge correspondingLDADOSastheinputfortheMO-DMFT
transfer situation that obtains in Hg Ru O . Of course, calculation with total 4d occupation, n = 3. Further,
2 2 7 t
this is an approximation. It is, however,a goodone: the we work in the (LMTO)18 representation in which the
3
one-particle density matrix is diagonal in the t orbital tionseeninthea orbitalDOSgivesrisetounquenched
2g 1g
index, so that G(0)(k,ω) = δ G(0)(k,ω). We choose localmomemtsco-existingwith“itinerant”(butincoher-
U =5.5 eV, J =αβ1.0 eV, andαUβ′ ≃αα(U −2J )=3.5 eV ent as derivedabove)e′g carriersnaturally gives a Curie-
H H
Weiss form of the spin susceptibility, which is also ob-
for the Ru−4d shell, along with U ≃1.5 eV, as repre-
pd
served right up to the IMT. We have also estimated the
sentative values for Hg Ru O . We believe that U, J
2 2 7 H
γ-co-efficient of the metallic specific heat from the real
do not vary much for 4d-TMO pyrochlores,and, in fact,
U =5.0 eV was found for the CT insulator Cs AgF .19 partofΣα(ω)(notshown)asγ/γLDA =4.25: thisseems
2 4
to be in the range estimated in Ref 4. Actually, the
noticeable T dependence of γ above T 4 is additional
MI
0.8
evidenceofdisorderedlocalmomentsinthe“bad”metal,
0.0 and further supports our picture.
a
1g
−0.5 Im e ’
0.6 −1.0 σΣ(ω g minestuallator 3.0
)
PES (130K)
ω) −0.6 −0.3 0.0 0.3 0.6−1.5 ω) 2.0
ρ( σ0.4 ω (eV) units) ρ(total1.0
rb. 0.0−4.0 −2.0 ω0 (.0eV) 2.0 4.0
a
0.2 (
y
sit
n
e
nt
I
0.0
−6.0 −4.0 −2.0 0.0 2.0 4.0
ω(eV)
0.0
FIG. 2: (Color online) t2g-resolved LDA+DMFTdensitiesof −6.0 −4.0 ω (eV−)2.0 0.0
statesforHg2Ru2O7inthehigh-T nFLphase,forU =5.5eV
and JH = 1 eV. Notice the orbital selective nature of the
metal, as well as the nFL character in the orbital resolved
self-energies (see inset). FIG. 3: (Color online) Theoretical PES spectra
(LDA+DMFT DOS convoluted with instrumental res-
olution) in the nFL metallic and insulating phases of
Hg2Ru2O7. In the LDA+DMFT calculation, the total t2g
A. Metallic Phase electron density changes from < nt >= 3.0 (metallic) to
< nt >= 2.6 (insulating). The theoretical result shows very
goodagreementwithexperimentalPESresultinthemetallic
In Fig. 2, we show the correlated many-particle spec- phase, taken from Ref. 7 up to 2 eV binding energy. The
tral function for the metallic phase of Hg Ru O . The inset shows the total spectral function.
2 2 7
dynamicalspectralweighttransfer(SWT) overlargeen-
ergy scales, characteristic of strong, local correlations is Using the LDA+DMFT result, we also compare
explicitly manifest. More interestingly, the metal has an (Fig. 3) our computed PES lineshape, with very recent
orbital selective (OS) character: the a DOS is almost work from the RIKEN-SPring 8 group.7 Given our re-
1g
“Mott” localized, even as the e′ DOS develops a pre- striction to the t −Ru(4d) bands in the MO-DMFT
g 2g
cursor of a low-energy pseudogap, characteristic of an (Hg(d),O(2p) bands will start contributing at higher
incoherent metal behavior. This is further corroborated binding energies, as seen from LDA), good quantitative
by examining the orbitaldependent self-energies (Σ(ω)), agreement with experiment is evident up to −2.0 eV,
see inset in Fig. 2. Clearly, the e′ (imaginary part of) lending strong support to our theoretical work. Addi-
g
Σ(ω) shows quasi-linear frequency dependence near the tionally, we predict that an intense peak will be seen
Fermienergy(|ω−E |<0.3eV),whileImΣ (ω)shows around 0.4−0.5 eV in X-ray absorption (XAS) studies,
F a1g
quadratic behavior. This describes a nFL metal, with a as in Tl Ru O .21
2 2 7
linear-in-T quasiparticle damping rate. Within DMFT, Infact,theLDA+DMFTspectralfunctionsshowthat,
this is also the transport relaxation rate,20 since vertex atlowenergythefullMOproblemismappedontoanef-
corrections drop out in the computation of the conduc- fective FKM-like model15, since the bad-metal is of the
tivities in this limit. The dc resistivity is then given by orbital-selective type. There, the problem in the local
ρdc(T) ≃ (m∗/ne2)ImΣe′g(ω = T) ≃ AT, in accord with limit corresponds to itinerant (but incoherent) e′g car-
the linear-in-T resistivity observedexperimentally inthe riers scattering off (Mott) localized a electronic states.
1g
“high-T”metallicphase. Moreover,theselectivelocaliza- Theresultingproblemispreciselythe“X-rayedge”prob-
4
lem in DMFT.22 We now understand the structure of Fig. 2. Hence, the IMT is an OS Mott transition. Im-
the self-energies, and the nFL behavior, as an interest- portantly, however, notice that the self-doping process
ing manifestation of the Anderson OC caused by this leading to fractional d-orbital occupation is a crucial in-
X-ray-edge mapping. Building upon this understanding, gredient. Thus,incontrasttootherOScases,15 theIMT
using DMFT, we predict that, for T >T : (a) the op- inHg Ru O is drivenby the self-doping inthe negative
MI 2 2 7
tical conductivity will show a low-energy pseudogapped CT situation, ∆ = (ǫ −ǫ )=(-2.8eV+1.3eV)=-1.5eV.
2 p2 d
form, characteristic of an incoherent (nFL) metal. Po- Along with the microscopic elucidation of the nFL be-
larised optical studies should indicate the OS-character havior,the agreement with PES in the nFL metal phase
of the nFL state, and, (b) given the local version of the up to ω ≃ −2.0 eV (Fig. 3) constitutes strong evidence
Shastry-Shraiman relation,23 the electronic Raman line- in favor of our mechanism for the IMT in Hg Ru O .
2 2 7
shape should show a continuum response, cut off by a Quantitative comparison with PES in the low-T phase
pseudogap feature at low energy. requires an extension of our approach to include short-
ranged (intersite) orbital and spin correlations charac-
teristic of pyrochlores. This requires a cluster-DMFT
B. Insulating Phase analysis, presently a forbidding prospect. Nevertheless,
observation of a Curie-Weiss spin susceptibility right up
to the IMT,6,24 along with the excellent agreement with
Now, we turn to a description of the insulating phase.
PES in the nFL, justifies the use of DMFT to describe
A naive search for the instability of the nFL to a Mott-
Hubbard insulating state, where U,U′ were increased to the IMT.
unphysical values, nevertheless turned out to be unsuc- WeemphasizethatthisisanewpicturefortheIMTin
cessful. This is a clear indication of involvement of ad- correlatedsystems. Incontrasttothe earlyTMO,which
ditional, electronic-cum-structural effects in driving the are Mott-Hubbard insulators (Udd > ∆ in the Zaanen-
IMT.The observedstructuralchangeacrossT 4,5 sup- Sawatzky-Allen scheme),25 the Ru(4d) − O(1)(2p) CT
MI
ports this reasoning. From the LDA orbital assignment, channel, along with the Madelung term, are important
it is clear that an additional structural change necessar- in Hg Ru O . In the DMFT context, the importance
2 2 7
ily involves partial occupation of the two-fold degener- of the CT energy in the late-TMO is recognized.26 Our
ate e′ orbitals. Starting from the nFL-metal derived work is the first of its kind showing its relevance for the
g
above, this can only occur via a T-dependent change IMT in a MO pyrochlore system. Further, it is likely
in the “self-doping” process.14 As in Tl Ru O , this T- to be more broadly generic to pyrochlore TMOs; recall
2 2 7
dependence could be provided by electronic coupling to that, in Tl Mn O , the PI-FMM13 transition is driven
2 2 7
theRu−Ostretchingphononmode,whichisexperimen- by the shift of the Tl(6s) band through EF across Tc.
tally observed to split below T .14 This would imply a This is readily rationalized in our picture, in terms of
MI
structural change setting in below T , whose precise the “switching on” the Mn(3d)−O(2)(2p)−Tl(6s) CT
MI
nature is hitherto unknown. channel across Tc in Tl2Mn2O7.13
Motivated by this observation, we argue that this re- ThecorrelationbetweentheCTprocessdetailedabove
sulting change in the Ru(4d)→ O(2)(2p) CT leads to a and the IMT is also visible in a whole family of 4d py-
partial4doccupation,inducesorbitalorder,andlifts the rochlores, A Ru O , with A = Pb, Bi, Y.21 The low-
2 2 7
e′g degeneracyviaastructuraldistortion. WithinDMFT, T magnetic ordering in the Mott-Hubbard insulating
this will reduce the orbital-dependent hoppings, driving phase(s) may, however, be quite different, being sensi-
large SWT from low- to high energy, and stabilize the tively dependent on the nature of the structural change
second,Mott-Hubbardinsulating,solutionofthe DMFT across the IMT, as well as on spin state. For example,
equations. This is indeed seen in the LDA+DMFT cal- the spin S = 1 system, Tl Ru O , shows a very similar
2 2 7
culation, as we show below. Motttransition;however,the low-T phaseis foundto be
Basedonthisreasoning,weexploretheMott-Hubbard a Haldane spin chain.27 In Hg Ru O , the half-integer
2 2 7
insulating phase of Hg2Ru2O7by searching numerically spin S = 3/2 rules out the Haldane analogy. If the low-
for the instability of the first (metallic) solution found T magnetic structure corresponds to having Ru chains,
above to the second, insulating solution of the DMFT as in Tl Ru O , one would have an AF ground state
2 2 7
equations in the quantum paramagnetic phase. The with gapless spin excitations. Observation of the spin-
DMFT(MO-IPT) equations are solved with U,U′,Upd, gapin the uniform spin susceptibility in Hg2Ru2O7 may
and nt = 2.6. We vary nt in trial steps, and look for a therefore point to the relevance of the spin-orbit cou-
criticaln(c) whichstabilizesthePIsolutionoftheDMFT pling in the insulating phase: this will induce Ising-like
t
equations. As discussed above, and indeed seen in the anisotropy in an S =3/2 Heisenberg chain and generate
inset of Fig. 3, partial occupation of the 4d − e′ or- a gap to spin excitations.28 More experimental work is
g
bitalsleadstoremovalofthe orbitaldegeneracy,andthe also called for to pinpoint the specific factors affecting
corresponding modification of orbital orientation gives this issue. Giventhe structuraldistortionnecessarilyac-
rise to a reduced intersite one-electron overlap. Within companyingthe IMTcausedbylifting ofthee′ degener-
g
MO-DMFT, this triggers the Mott-Hubbard insulating acy in Hg Ru O , more detailed theoretical work awaits
2 2 7
state via large SWT on a scale of 5.0 eV, as seen in more precise characterization of the low-T structure of
5
Hg Ru O . We planto addressthe issue ofmagnetic or- as well as with the linear-in-T resistivity and mass en-
2 2 7
der and its associated excitation spectrum in the low-T hancement in the metallic phase. In stark contrast to
(insulating) phase of Hg Ru O in a future work. the better known examples1 of Mott transitions in 3d-
2 2 7
transition metal compounds, our results imply a new
mechanism for MIT in the 4d pyrochlore-based electron
IV. CONCLUSION systems (like Hg Ru O ). Namely, a negative charge-
2 2 7
transfer associated self-doping drives an orbital-selective
Inconclusion,we haveperformedLDA+DMFT calcu- MIT at low temperatures via the Mott-Hubbard route.
lations to demonstrate the role of multi-orbital electron- Our study should be more generally applicable to MO
electron interactions on the electronic structure of a re- pyrochloresystems,and,inparticular,toTl2Mn2O7,ex-
cently discovered pyrochlore system, Hg Ru O . This hibiting Mott-Hubbard transitions14,21,24,29 as functions
2 2 7
system exhibits a first-order temperature dependent of suitable “tuning parameters”.
IMT.Thehigh-Tmetallicphaseisshowntobeanorbital
selectivenon-Fermiliquid,signalledbyaquasi-linearfre-
quency dependence of the imaginary part of the corre- Acknowledgments
lated self-energy and the absence of quasi-particle peaks
in the orbital-selective spectral functions at very low We are indebted to A. Chainani for discussions, and,
frequencies. The LDA+DMFT spectral function shows especially, for sending us his unpublished PES results.
good quantitative agreement with recent photoemission LC and HR thank the Emmy-Noether Program of the
(PES)data,showinganomalouslybroadPESlineshapes, DFG for support.
1 M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 1.8712,2.1247 (O1,O2),andr=2.4971 (Ru)a.u.inorder
70, 1039 (1998). to minimize their overlap.
2 K.S.Raman,R.Moessner,andS.L.Sondhi,Phys.Rev.B 19 D.Kasinathan,K.Koepernik,U.Nitzsche,andH.Rosner,
72, 064413 (2005), and references therein. Phys. Rev.Lett. 99, 247210 (2007).
3 S. Di Matteo, G. Jackeli, C. Lacroix, and N.B. Perkins, 20 A. Georges, G. Kotliar, W. Krauth, and M.J. Rozenberg,
Phys. Rev.Lett. 93, 077208 (2004). Rev.Mod. Phys.68, 13 (1996).
4 W. Klein, R.K. Kremer, and M. Jansen, J. Mater. Chem. 21 J. Okamoto, T. Mizokawa, A. Fujimori, T. Takeda, R.
17, 1356 (2007). Kanno, F. Ishii, and T. Oguchi, Phys. Rev. B 69, 035115
5 A.Yamamoto,P.A.Sharma,Y.Okamoto,A.Nakao,H.A. (2004).
Katori, S.Niitaka,D.Hashizume,andH.Takagi,J.Phys. 22 P.W. Anderson,Phys. Rev.Lett. 18, 1049 (1967)
Soc. Jpn. 76, 043703 (2007). 23 B.S.ShastryandB.I.Shraiman,Phys.Rev.Lett.65,1068
6 N.Takeshita, C.Terakura,Y.Tokura,A.Yamamoto, and (1990).
Hidenori Takagi, J. Phys. Soc. Jpn. 76, 063707 (2007). 24 J.Okamoto,S.-I.Fujimori,T.Okane,A.Fujimori,M.Ab-
7 A. Chainani et al., privatecommunication. bate, S. Yoshii, and M. Sato, Phys. Rev. B 73, 035127
8 G.Kotliar,S.Y.Savrasov,K.Haule,V.S.Oudovenko,O. (2006).
Parcollet, andC.A.Marianetti,Rev.Mod.Phys.78,865, 25 J. Zaanen, G. A. Sawatzky, and J.W. Allen, Phys. Rev.
(2006); K. Held, Advancesin Physics 56, 829 (2007). Lett. 55, 418 (1985).
9 K. Koepernik and H. Eschrig, Phys. Rev. B 59, 1743 26 J. Kunes, V.I. Anisimov, S.L. Skornyakov, A.V. Lukoy-
(1999). anov, and D. Vollhardt, Phys. Rev. Lett. 99, 156404
10 O.K. Andersen,Phys. Rev.B 12, 3060 (1975). (2007).
11 Self-consistency was obtained on a 12x12x12 k mesh for 27 S.Lee,J.-G.Park,D.T.Adroja,D.Khomskii,S.Streltsov,
the full Brillouin zone. K.A.McEwen, H.Sakai,K.Yoshimura,V.I.Anisimov,D.
12 Within the LMTO framework, the diagonalized combina- Mori,R.Kanno,andR.Ibberson,NatureMaterials,5,471
tionofthet2g orbitalsreads: |e′g1i≃0.195(|dxzi−|dyzi)+ (2006).
0.888|dx2−y2i,|e′g2i ≃ 0.888|dz2i+0.112(2|dxyi+|dyzi+ 28 I.Affleck,in Fields, Strings and Critical Phenomena, pro-
|dzxi),|a1gi=0.577(|dyzi+|dzxi−|dxyi). ceedingsoftheLesHouchesSummerSchool,LesHouches,
13 A.P. Ramirez and M.A. Subramanian, Science 277, 546 France, 1988, edited by E. Br´ezin and J.Z. Justin, Les
(1997). Houches Summer School Proceedings Vol. 49 (Elsevier,
14 J.S.Lee,Y.S.Lee,K.W.Kim,T.W.Noh,J.Yu,T.Takeda, Amsterdam, 1989).
and R.Kanno, Phys.Rev.B 64, 165108 (2001). 29 J.S. Lee, S.J. Moon, T.W. Noh, T. Takeda, R. Kanno,
15 M.S.Laad,L.Craco,andE.Mu¨ller-Hartmann,Phys.Rev. S. Yoshii, and M. Sato, Phys. Rev. B 72, 035124 (2005);
B 73, 045109 (2006). A. Higashiya, S. Imada, A. Yamasaki, A. Irizawa, A.
16 O.MiuraandT.Fujiwara,Phys.Rev.B77,195124(2008). Sekiyama, S. Suga, Y. Taguchi, M. Iwama, K. Ohgushi,
17 Q. Si, G. Kotliar and A. Georges, Phys. Rev. B 46, 1261 and Y. Tokura, Phys. Rev. B 75, 155106 (2007); R.S.
(1992). Singh,V.R.R.Medicherla,K.Maiti,andE.V.Sampathku-
18 Self-consistency is reached by performing calculations on maran, Phys. Rev.B 77, 201102 (2008).
a12x12x12k-meshfortheBrillouinintegration.Theradii
oftheatomicsphereswerechosenasr=2.8781(Hg), r=