Orthorhombic 3dOrthorhombic 3d11 PerovskitesPerovskites

SrSrVVOO33 CaCaVVOO33

LaLaTiTiOO33 YYTiTiOO33

MetalMetal

m*/m=2.7m*/m=2.7

MetalMetal

m*/m=3.6m*/m=3.6

InsulatorInsulator

Gap=0.2eVGap=0.2eV

GG--type AFtype AF

TTNN=140K=140K

M=0.45M=0.45μμBB

Isotropic Isotropic spinspin--wave wave spectrumspectrum

InsulatorInsulator

Gap=1.0eVGap=1.0eV

FF

TTCC=30K=30K

M=0.8M=0.8μμBB

Isotropic Isotropic spinspin--wave wave spectrumspectrumHere:Here: HighHigh--temperature paramagnetic phasestemperature paramagnetic phases

NMTO NMTO downfoldingdownfolding toto tt2g2g WannierWannier functionsfunctions

SrSr 4d5s4d5s

V 3d V 3d eeggtt2g2g

O 2pO 2p

Mostly Experiments:Mostly Experiments:

Computational MethodComputational Method

LDALDA

+ + DMFTDMFT

m*/m=2.2 m*/m=3.5

1.00.2

LDALDA++DMFTDMFT (U=5.0 (U=5.0 eVeV, J, JHH~~0.66 0.66 eVeV, , kkBBTT=0.1) =0.1) and comparison with and comparison with experimentsexperiments

2.7 3.6

SrSrVVOO33 CaCaVVOO33

LaLaTiTiOO33 YYTiTiOO33

Is the electron localization just caused by the reduction of Is the electron localization just caused by the reduction of W W ??

LDALDA++DDMMFFTT U=U=3.5,3.5, 4.0,4.0, 4.5,4.5, 4.75,4.75, 5.0,5.0, 6.06.0 eVeV

Uc= 4.8

7.12=

−W

JUc

LaLaTiTiOO33 YYTiTiOO33

1.2=W

Uc= 3.7

2.12=

−W

JUc0.2=W

WJUc 2−

No, decreases!No, decreases!

LDA densityLDA density--ofof--states matrix in the states matrix in the tt2g2g WannierWannier representationrepresentation

W=2.8 W=2.8 eVeV W=2.4 W=2.4 eVeV

W=2.1 W=2.1 eVeV W=2.0 W=2.0 eVeV

ΔΔ==.08 .08 eVeV

DiagonalizeDiagonalize the onthe on--site term of site term of HHLDALDA to get the crystalto get the crystal--field levels and their field levels and their eigeneigen--orbitalsorbitals::

.14.06 .14.06 eVeV .20.13 .20.13 eVeV

0.300.30

0.250.25

0.270.27

0.230.23

nm,m

n=

Nm≠n(E)

-1 -10

Low Low contour contour brings out brings out covalencycovalencyeffects:effects:

DiagonalizeDiagonalize the LDA+DMFT density matrix for the Mott insulators to get orbithe LDA+DMFT density matrix for the Mott insulators to get orbital occupations:tal occupations:

0.880.88 0.980.98

The most occupied orbitalThe most occupied orbital turns out to be the essentially same as the one with the lowestturns out to be the essentially same as the one with the lowest energy energy (i.e. crystal(i.e. crystal--field level), but the DMFT increases its field level), but the DMFT increases its occupancyoccupancy from the LDA value of about 0.5 from the LDA value of about 0.5 to about 1, that is, the Coulomb correlations strongly suppress to about 1, that is, the Coulomb correlations strongly suppress orbital fluctuations:orbital fluctuations:

Orbital and Magnetic OrdersOrbital and Magnetic OrdersSuperexchange: JAF ~ 4t2/U

tx=ty=99 meV

t z=10

5 m

eV

tx=ty=48 meV

t z=38

meV

What causes the progressive reduction of What causes the progressive reduction of tt2g2g bandwidth and splitting of the levels?bandwidth and splitting of the levels?

Bandwidth: Bandwidth: CationCation--oxygenoxygen covalencycovalency. Level splitting: . Level splitting: CationCation--transition iontransition ion covalencycovalency

Wannier functions

What causes the progressive reduction of What causes the progressive reduction of tt2g2g bandwidth and splitting of the levels?bandwidth and splitting of the levels?

Bandwidth: Bandwidth: CationCation--oxygenoxygen covalencycovalency. Level splitting: . Level splitting: CationCation--transition iontransition ion covalencycovalency

YY 4d(xy)4d(xy)YY 4d(3z4d(3z11111122--1)1)LaLa 5d(3z5d(3z111111

22--1)1)

YTiO3

LaLa 5d5d projected bandsprojected bands

LaTiO3

YY 4d4d projected bandsprojected bands

YYTiTiOO3 3 bandstructurebandstructure withwith and and withoutwithout the the JahnJahn--Teller distortion:Teller distortion:

The JThe J--T distortion hardly influences the T distortion hardly influences the pseudogappseudogap!!

Most recent work:Most recent work:

The three last calculations reach the essentially the same The three last calculations reach the essentially the same conclusion concerning the orbital order in LaTiO3conclusion concerning the orbital order in LaTiO3