Chemistry 754 - Solid State Chemistry Transition Metal Oxides Rock Salt and Rutile: Metal-Metal...

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


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


Rock Salt Crystal StructureRock Salt Crystal Structure

OO

MM

x

y


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


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


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?


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


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


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.


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


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


Rutile Crystal StructureRutile Crystal Structure

z

x

y


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


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


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=


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


+ 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


Band Structure CalculationsBand Structure Calculations

SrTiOSrTiO33 TiOTiO22


TiOTiO22 VOVO22 CrOCrO22

Calculated Band Structure Calculated Band Structure (Tetragonal, Z=2)(Tetragonal, Z=2)


TiOTiO22 VOVO22 CrOCrO22

Density of States (Tetragonal Density of States (Tetragonal Structure)Structure)


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


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


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


MoOMoO22 Monoclinic Monoclinic

(Z=4)(Z=4)

CrOCrO22 Tetragonal Tetragonal

(Z=2)(Z=2)

Mo-Mo

Mo-O


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


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.

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