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Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Transition Metal Oxides Transition Metal Oxides Rock Salt and Rutile:Rock Salt and Rutile:Metal-Metal BondingMetal-Metal Bonding
Chemistry 754Chemistry 754Solid State Chemistry Solid State Chemistry
Lecture #25Lecture #25May 27, 2003May 27, 2003
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Rock Salt and Rutile: Rock Salt and Rutile: Structure & PropertiesStructure & Properties
• Octahedral Molecular Orbital DiagramOctahedral Molecular Orbital Diagram
• Rock Salt Rock Salt *(t*(t2g2g) and ) and *(e*(egg) Bands) Bands
• M-M InteractionsM-M Interactions• Properties 3d Transition Metal MonoxidesProperties 3d Transition Metal Monoxides• Magnetic SuperexchangeMagnetic Superexchange
• Rutile Rutile *(t*(t2g2g) Bands, t) Bands, t and t and t
• Properties MOProperties MO22 (M=Ti, V, Cr, Mo, W, Ru) (M=Ti, V, Cr, Mo, W, Ru)
• Double Exchange in CrODouble Exchange in CrO22
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Rock Salt Crystal StructureRock Salt Crystal Structure
OO
MM
x
y
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Generic Octahedral MO Generic Octahedral MO DiagramDiagram
a1g ()
t1u ()
eg ()t2g ()
t1g & t2u
a1g ()
t1u ()
t2g ()
eg ()
nd eg (dx2-y2, dz2)
(n+1)d t2g (dxy, dxz, dyz)
(n+1)s
(n+1)p
O 2p (6) - t2g, t1u
O 2p NB(6)-t1g, t2u
O 2p (6)a1g, t1u, eg
TransitioTransition Metaln Metal
OxygenOxygen
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Simplified Band StructureSimplified Band Structure
nd eg (dx2-y2, dz2)
(n+1)d t2g (dxy, dxz, dyz)
(n+1)s
(n+1)p
O 2p
O 2p (6)a1g, t1u, egTransitioTransitio
n Metaln Metal
OxygenOxygen
M-O
M-O
O 2p NB
M-O [3]
M-O [2]
[4] Bands of Bands of interestinterest
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
3d Transition Metal 3d Transition Metal MonoxidesMonoxides
Compound M- MDistance
ElectricalProperties
MagneticProperties
TiO (d2) 2.94 Å Metallic Pauli Paramagnetic
VO (d3) 2.89 Å Intermediate Intermediate
MnO (d5) 3.14 Å Semiconductor AFM TN = 122 K
FeO (d6) 3.03 Å Semiconductor AFM TN = 198 K
CoO (d7) 3.01 Å Semiconductor AFM TN = 293 K
NiO (d8) 2.95 Å Semiconductor AFM TN = 523 K
AFM = Antiferromagnetic
How can we understand this behavior? Metallic conductivity for a fairly ionic Ti2+-O2- bond?
Semiconducting behavior for partially filled bands?
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Orbital Overlap in the tOrbital Overlap in the t2g2g BandBand point
(kx=ky=kz=0)
M
M
M M
M
M
M
M M
M
point (kx=ky=/a, kz=0)
M-O M-O nonbondingnonbonding
M-M bondingM-M bonding
M-O M-O antibonding antibonding M-M M-M nonbondingnonbonding
Band Runs Uphill from
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Orbital Overlap in the eOrbital Overlap in the egg BandBand point
(kx=ky=kz=0)
point (kx=ky=/a, kz=0)
M-O M-O nonbondingnonbonding
Band Runs Uphill from
M
M
M M
M
M
M
M M
M
M-O M-O antibonding antibonding
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Band Structure CalculationsBand Structure CalculationsSrTiOSrTiO33 TiOTiO
The eThe egg * band is more narrow in TiO because the Ti-O distance is * band is more narrow in TiO because the Ti-O distance is considerably longer and the overlap is smaller.considerably longer and the overlap is smaller.
The tThe t2g2g * band is also slightly more narrow in TiO, except for near the * band is also slightly more narrow in TiO, except for near the --point, where Ti-Ti bonding lowers the energy and widens the band.point, where Ti-Ti bonding lowers the energy and widens the band.
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Magnetic StructureMagnetic StructureMnO, FeO, CoO and NiO are all MnO, FeO, CoO and NiO are all
antiferromagnets with the structure shown antiferromagnets with the structure shown below (for MnO). below (for MnO).
The electrons align themselves in an antiparallel fashion due to The electrons align themselves in an antiparallel fashion due to AFM superexchange interactions arising primarily from the ½ AFM superexchange interactions arising primarily from the ½
filled efilled egg orbitals. The magnetic ordering temperature increases orbitals. The magnetic ordering temperature increases from Mn from Mn Fe Fe Co Co Ni due to increasing covalency (see Ni due to increasing covalency (see
Magnetism lecture). The magnetic ordering has implications for Magnetism lecture). The magnetic ordering has implications for the electronic transport properties.the electronic transport properties.
AFM
eg
t2g
==
eg
t2g
==MnO
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Mott-Hubbard InsulatorsMott-Hubbard Insulators
M-O-M Interaction is AFM (M-O-M Interaction is AFM () ) when both TM have 1/2 filled when both TM have 1/2 filled configurations (dconfigurations (d55-d-d55 or d or d33-d-d33))
FeFe OO FeFeThe AFM coupling of ions is shown The AFM coupling of ions is shown
for FeO. The ½ filled efor FeO. The ½ filled egg orbitals orbitals stabilize AFM coupling. Notice that stabilize AFM coupling. Notice that
there is no mechanism for the there is no mechanism for the minority spin electrons (shown in minority spin electrons (shown in red) to move from one Fe ion to red) to move from one Fe ion to
the next without undergoing a spin the next without undergoing a spin flip (the tflip (the t2g2g orbitals of the same orbitals of the same
spin are occupied). spin are occupied).
Consequently the AFM coupling of Consequently the AFM coupling of ions forces a localization of the tions forces a localization of the t2g2g electrons, even in the absence of a electrons, even in the absence of a ½ filled or completely filled band. ½ filled or completely filled band. This is essentially the opposite of This is essentially the opposite of
double-exchange. Such double-exchange. Such compounds are called Mott-compounds are called Mott-
Hubbard insulators.Hubbard insulators.
eg
t2g
eg
t2g
eg
t2g
eg
t2g
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Rutile Crystal StructureRutile Crystal Structure
z
x
y
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MOMO22 with the Rutile with the Rutile StructureStructure
Compound M- M Distance
Electrical Properties
Magnetic Properties
TiO2 (d0) 2.96 Å Semiconductor Diamagnetic
VO2 (d1) T>340K
VO2 (d1) T<340K
2.88 Å
2.65;3.12Å
Metallic
Semiconductor
Paramagnetic
Diamagnetic
CrO2 (d2) 3.14 Å Metallic Ferromagnetic
TC = 398 K
MoO2 (d2) 2.52;3.10Å Metallic Pauli Paramagnetic
RuO2 (d4) 3.14 Å Metallic Pauli Paramagnetic
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c/a Ratio in Rutile-Type c/a Ratio in Rutile-Type OxidesOxides
VOVO22 (T > 340K) (T > 340K)MetallicMetallicV-V Even V-V Even Spacing Spacing
VOVO22 (T < 340K) (T < 340K)MetallicMetallic
V-V AlternatingV-V Alternating
MoOMoO22 MetallicMetallicMo-Mo Mo-Mo
AlternatingAlternating
RuORuO22 MetallicMetallic
Ru-Ru Even Ru-Ru Even SpacingSpacing
CrOCrO22 MetallicMetallic
Cr-Cr Even Cr-Cr Even SpacingSpacing
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M-M Overlap in the tM-M Overlap in the t2g2g Band Band
M-M M-M bonding bonding
M
M
MM
M
M
M
M
M
M-M M-M antibondingantibonding
M-M M-M bonding bonding
point kx=0ky=0
kz=/a
M-M M-M antibondingantibonding
M
M
MM
M
M
M
M
M
M-M M-M bonding bonding M-M M-M antibondingantibonding
point kx=0ky=0kz=
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Combined M-O & M-M EffectsCombined M-O & M-M Effects•The M-O The M-O * and M-M bonding interactions both make a * and M-M bonding interactions both make a contribution to the tcontribution to the t2g2g band. band.
•The M-O The M-O * interactions are dominant, but the M-M * interactions are dominant, but the M-M interactions preturb the picture. The M-M interactions preturb the picture. The M-M & & interactions interactions are of minimal importance.are of minimal importance.
•As we fill up the tAs we fill up the t2g2g band we can roughly think of the band we can roughly think of the following picture in terms of M-M bonding strength.following picture in terms of M-M bonding strength.
M-M d1 TM Ion
EF
DOS
M-M d2 TM Ion
M-M
M-M d5 TM Ion
M-M d6 TM Ion
M-O
M-O * ~ M-M > M-M > M-M
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+ M-M
Tetragonal Structure (TiOTetragonal Structure (TiO22,CrO,CrO2,2,RuORuO22))
d ed egg
d td t2g2g
Oxygen Oxygen 2p2p
TransitioTransition Metaln Metal
M-O
M-O
O 2p NB
M-O [2]
M-O [4]
+ M-M
Z = 2 Z = 2 (M(M22OO44))
EEFF TiO TiO22
EEFF VO VO22
EEFF CrOCrO22
EEFF RuORuO22
DelocalizDelocalized ed
ElectronsElectrons
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Band Structure CalculationsBand Structure Calculations
SrTiOSrTiO33 TiOTiO22
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TiOTiO22 VOVO22 CrOCrO22
Calculated Band Structure Calculated Band Structure (Tetragonal, Z=2)(Tetragonal, Z=2)
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TiOTiO22 VOVO22 CrOCrO22
Density of States (Tetragonal Density of States (Tetragonal Structure)Structure)
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
M
M
M
M
a
M
M
M
M
a
M
M
M
M
a
M
M
M
M
a
M
M
M
M
a
M
M
M
M
a
TiOTiO22
Tetragonal Tetragonal Z=2Z=2
MoOMoO22
Monoclinic Z=4Monoclinic Z=4
point
point
BondingBonding
AntibondingAntibonding
M-M Short=BondingM-M Short=BondingM-M Long=BondingM-M Long=Bonding
M-M Short=ABM-M Short=ABM-M Long=ABM-M Long=AB
M-M Short=BondingM-M Short=BondingM-M Long=ABM-M Long=AB
M-M Short=ABM-M Short=ABM-M Long=BondingM-M Long=Bonding
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Pierls DistortionPierls Distortion
The dimerization which occurs in the rutile structure and The dimerization which occurs in the rutile structure and it’s effects on the band structure are similar to the Pierls it’s effects on the band structure are similar to the Pierls
distortion we discussed for a 1D chain of Hydrogen atoms, distortion we discussed for a 1D chain of Hydrogen atoms, except that it occurs on top of the M-O except that it occurs on top of the M-O * interactions.* interactions.
a
a
a
a
a
a
E
k0 /a
EF
E
k0 /a
EF
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
M-O
M-O
O 2p NB
M-M [2]
M-O [8]
M-O [8]
M-M [2]
d ed egg
d td t2g2g
Z = 4 Z = 4 (M(M44OO88))
EEFF VO VO22
EEFF MoO MoO22
Oxygen Oxygen 2p2p
Monoclinic Structure (VOMonoclinic Structure (VO22,MoO,MoO22))
Delocalized Delocalized ElectronsElectrons
M-O M-O AntibondingAntibonding
Localized Localized ElectronsElectrons
M-M M-M BondingBonding
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MoOMoO22 Monoclinic Monoclinic
(Z=4)(Z=4)
CrOCrO22 Tetragonal Tetragonal
(Z=2)(Z=2)
Mo-Mo
Mo-O
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CrOCrO22 and RuO and RuO22
Why are alternating long-short M-M contacts, indicative of Why are alternating long-short M-M contacts, indicative of Metal-Metal bonding not observed in CrOMetal-Metal bonding not observed in CrO22 and RuO and RuO22. The . The electron count suggests that the M-M electron count suggests that the M-M levels should be levels should be
full and the M-M full and the M-M ** levels empty? levels empty?
There is a competition between localized M-M bonding There is a competition between localized M-M bonding (prefers dimers) and delocalized electronic transport in the (prefers dimers) and delocalized electronic transport in the
M-O M-O ** band (prefers equal spacing). band (prefers equal spacing).
Favors M-M Favors M-M bonding and bonding and localized elocalized e-
Dominant in MoODominant in MoO22
Favors delocalized Favors delocalized transport in the M-O transport in the M-O
** band band
Dominant in Dominant in CrOCrO22 (poor overlap) (poor overlap)
RuORuO22 (electron count) (electron count)
VOVO22 IntermediateIntermediate
Chemistry 754 - Solid State ChemistryChemistry 754 - Solid State Chemistry
Double ExchangeDouble ExchangeCrOCrO22 is ferromagnetic. A property which leads to it’s use in magnetic is ferromagnetic. A property which leads to it’s use in magnetic
cassette tapes. What stabilizes the ferromagnetic state?cassette tapes. What stabilizes the ferromagnetic state?
Localized tLocalized t|||| electronselectrons
No M-M BondingNo M-M Bonding
M
M
MM
M
M
Delocalized tDelocalized t2g2g ** electrons electrons
Ferromagnetic: Delocalized Ferromagnetic: Delocalized transport of ttransport of t** electrons electrons
allowedallowed..
tt||||
tt**
tt||||
tt**
Antiferromagnetic: Antiferromagnetic: Delocalized transport Delocalized transport violates Hund’s Ruleviolates Hund’s Rule..
Localized tLocalized t|||| electrons polarize itinerant electrons polarize itinerant (delocalized) t(delocalized) t2g2g ** electrons. Magnetism and electrons. Magnetism and
conductivity are correlated.conductivity are correlated.