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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
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