transition metal oxides rock salt and rutile: metal-metal bonding

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Chemistry 754 Chemistry 754 -- Solid State ChemistrySolid State Chemistry

Transition Metal Oxides Transition Metal Oxides Rock Salt and Rock Salt and RutileRutile::MetalMetal--Metal BondingMetal Bonding

Chemistry 754Chemistry 754Solid State Chemistry Solid State Chemistry

Lecture #25Lecture #25May 27, 2003May 27, 2003


Rock Salt and Rock Salt and RutileRutile: : Structure & PropertiesStructure & Properties

�� Octahedral Molecular Orbital DiagramOctahedral Molecular Orbital Diagram�� Rock Salt Rock Salt ππππππππ*(t*(t2g2g) and ) and σσσσσσσσ*(*(eegg) Bands) Bands�� MM--M InteractionsM Interactions�� Properties 3d Transition Metal MonoxidesProperties 3d Transition Metal Monoxides�� Magnetic Magnetic SuperexchangeSuperexchange�� Rutile Rutile ππππππππ*(t*(t2g2g) Bands, t) Bands, t and tand t⊥⊥⊥⊥⊥⊥⊥⊥

�� Properties MOProperties MO22 (M=Ti, V, Cr, Mo, W, (M=Ti, V, Cr, Mo, W, RuRu))�� Double Exchange in CrODouble Exchange in CrO22

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Rock Salt Crystal StructureRock Salt Crystal Structure

OO

MM

x

y


Generic Octahedral MO DiagramGeneric Octahedral MO Diagram

a1g (σσσσ)

t1u (σ σ σ σ + π)

eg (σσσσ)t2g (ππππ)

t1g & t2u

a1g (σ∗σ∗σ∗σ∗)

t1u (σ∗ σ∗ σ∗ σ∗ + π∗)

t2g (π∗π∗π∗π∗)

eg (σ∗σ∗σ∗σ∗)

nd eg (dx2-y2, dz2)

(n+1)d t2g (dxy, dxz, dyz)

(n+1)s

(n+1)p

O 2p π π π π (6) - t2g, t1uO 2p NB (6)-t1g, t2u

O 2p σ σ σ σ (6)a1g, t1u, eg

Transition Transition MetalMetal

OxygenOxygen

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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 π π π π (12)

O 2p σ σ σ σ (6)a1g, t1u, egTransition Transition

MetalMetal

OxygenOxygen

M-O σσσσ

M-O ππππO 2p NB

M-O π∗π∗π∗π∗ [3]

M-O σ∗σ∗σ∗σ∗ [2]

σ∗σ∗σ∗σ∗ [4] Bands of interestBands of interest


3d Transition Metal Monoxides3d Transition Metal Monoxides

Compound M-MDistance

ElectricalProperties

MagneticProperties

TiO (d2) 2.94 Å Metallic Pauli ParamagneticVO (d3) 2.89 Å Intermediate IntermediateMnO (d5) 3.14 Å Semiconductor AFM TN = 122 KFeO (d6) 3.03 Å Semiconductor AFM TN = 198 KCoO (d7) 3.01 Å Semiconductor AFM TN = 293 KNiO (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?

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Orbital Overlap in the tOrbital Overlap in the t2g2g BandBandΓΓΓΓ point (kx=ky=kz=0)

M

M

M M

M

M

M

M M

M

ΜΜΜΜ point (kx=ky=ππππ/a, kz=0)

MM--O O ππ nonbondingnonbonding MM--M bondingM bonding

MM--O O ππ antibondingantibonding MM--M nonbondingM nonbonding

Band Runs Uphill from

Γ Γ Γ Γ →→→→ ΜΜΜΜ


Orbital Overlap in the Orbital Overlap in the eegg BandBandΓΓΓΓ point (kx=ky=kz=0)

ΜΜΜΜ point (kx=ky=ππππ/a, kz=0)

MM--O O σσ nonbondingnonbonding Band Runs Uphill from

Γ Γ Γ Γ →→→→ ΜΜΜΜ

M

M

M M

M

M

M

M M

M

MM--O O σσ antibondingantibonding

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Band Structure CalculationsBand Structure Calculations

DOS (e/eV)10 20

k

Ener

gy (v

s. O

2s)

10

15

20

25

10

15

20

25

DOS (e/eV) 10 20X R M Γ R

kX R M Γ R

SrTiOSrTiO33 TiOTiO

The The eegg σσσσσσσσ* band is more narrow in * band is more narrow in TiO TiO because the Tibecause the Ti--O distance is considerably O distance is considerably longer and the overlap is smaller.longer and the overlap is smaller.

The tThe t2g2g ππππππππ* band is also slightly more narrow in * band is also slightly more narrow in TiOTiO, except for near the , except for near the ΓΓ--point, point, where Tiwhere Ti--Ti bonding lowers the energy and widens the band.Ti bonding lowers the energy and widens the band.


Magnetic StructureMagnetic StructureMnOMnO,, FeOFeO,, CoOCoO and and NiO NiO are all are all antiferromagnets antiferromagnets

with the structure shown below (for with the structure shown below (for MnOMnO). ).

The electrons align themselves in anThe electrons align themselves in an antiparallelantiparallel fashion due to AFM fashion due to AFM superexchangesuperexchange interactions arising primarily from the ½ filled interactions arising primarily from the ½ filled eegg

orbitalsorbitals. The magnetic ordering temperature increases from . The magnetic ordering temperature increases from MnMn →→Fe Fe →→ Co Co →→ Ni due to increasing covalency (see Magnetism lecture). Ni due to increasing covalency (see Magnetism lecture). The magnetic ordering has implications for the electronic transpThe magnetic ordering has implications for the electronic transport ort

properties.properties.

AFM

eg

t2g

==

eg

t2g

==MnO

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MottMott--Hubbard InsulatorsHubbard Insulators

MM--OO--M Interaction is AFM (M Interaction is AFM (↑↓↑↓) ) when both TM have 1/2 filled when both TM have 1/2 filled configurations (dconfigurations (d55--dd55 or dor d33--dd33))

FeFe OO FeFeThe AFM coupling of ions is shown The AFM coupling of ions is shown for for FeOFeO. The ½ filled . The ½ filled eegg 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 the red) to move from one Fe ion to the next without undergoing a spin flip next without undergoing a spin flip

(the t(the t2g2g orbitals orbitals of the same spin are of the same spin are occupied). 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 ½ electrons, even in the absence of a ½ filled or completely filled band. This filled or completely filled band. This is essentially the opposite of doubleis essentially the opposite of double--

exchange. Such compounds are exchange. Such compounds are called Mottcalled Mott--Hubbard insulators.Hubbard insulators.

eg ↑↑↑↑

t2g ↑↑↑↑

eg ↓↓↓↓

t2g ↓↓↓↓

eg ↓↓↓↓

t2g ↓↓↓↓

eg ↑↑↑↑

t2g ↑↑↑↑


RutileRutile Crystal StructureCrystal Structure

z

x

y

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MOMO22 with the with the Rutile Rutile StructureStructureCompound 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 c/a Ratio in RutileRutile--Type OxidesType Oxides

VOVO22 (T > 340K)(T > 340K)MetallicMetallic

VV--V Even Spacing V Even Spacing VOVO22 (T < 340K)(T < 340K)

MetallicMetallicVV--V AlternatingV Alternating

MoOMoO22MetallicMetallic

MoMo--Mo AlternatingMo Alternating

RuORuO22MetallicMetallic

RuRu--RuRu Even SpacingEven Spacing

CrOCrO22MetallicMetallic

CrCr--Cr Even SpacingCr Even Spacing

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MM--M Overlap in the tM Overlap in the t2g2g BandBand

MM--M M σσ bondingbonding

M

M

MM

M

M

M

M

M

MM--M M ππ antibondingantibonding MM--M M δδ bondingbonding

ΖΖΖΖ point kx=0ky=0

kz=ππππ/a

MM--M M σσ antibondingantibonding

M

M

MM

M

M

M

M

M

MM--M M ππ bondingbonding MM--M M δδ antibondingantibonding

ΓΓΓΓ point kx=0ky=0kz=0000


Combined MCombined M--O & MO & M--M EffectsM Effects��The MThe M--O O ππ* and M* and M--M bonding interactions both make a M bonding interactions both make a contribution to the tcontribution to the t2g2g band. band. ��The MThe M--O O ππ* interactions are dominant, but the M* interactions are dominant, but the M--M M σσσσσσσσinteractions interactions preturb preturb the picture. The Mthe picture. The M--M M ππππππππ & & δδδδδδδδ 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 following band we can roughly think of the following picture in terms of Mpicture in terms of M--M bonding strength.M bonding strength.

M-M σ σ σ σ →→→→ d1 TM Ion

EF

DOS

M-M π π π π →→→→ d2 TM IonM-M δ/δδ/δδ/δδ/δ∗∗∗∗

M-M π∗ π∗ π∗ π∗ →→→→ d5 TM IonM-M σ∗ σ∗ σ∗ σ∗ →→→→ d6 TM Ion

M-O ππππ∗∗∗∗

M-O π* ~ M-M σ > M-M π > M-M δ

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+ M-M σσσσ

Tetragonal Structure (TiOTetragonal Structure (TiO22,CrO,CrO2,2,RuORuO22))

d d eegg

d td t2g2g

Oxygen 2pOxygen 2pTransition Transition

MetalMetal

M-O σσσσ

M-O ππππO 2p NB

M-O π∗π∗π∗π∗ [2]

M-O σ∗σ∗σ∗σ∗ [4]

+ M-M σ∗σ∗σ∗σ∗

Z = 2 (MZ = 2 (M22OO44))

EEFF TiOTiO22

EEFF VOVO22

EEFF CrOCrO22

EEFF RuORuO22

Delocalized Delocalized ElectronsElectrons


Band Structure CalculationsBand Structure Calculations

10

15

20

25

DOS (e/eV) 12

DOS (e/eV)12

k

Ener

gy (v

s. O

2s)

10

15

20

25

kX R M Γ R Z α M Γ Z R X Γ

SrTiOSrTiO33 TiOTiO22

10


k

Ener

gy (v

s. O

2s)

10

15

20

25

Z α M Γ Z R X Γ

10

15

20

25

10

15

20

25

Z α M Γ Z R X Γ Z α M Γ Z R X Γ

TiOTiO22 VOVO22 CrOCrO22

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


TiOTiO22 VOVO22 CrOCrO22

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

DOS (electrons/eV)

4 8 12

Ener

gy (v

s. O

2s)

10

15

20

25

4 8 12

10

15

20

25

4 8 12

10

15

20

25

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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

TiOTiO22Tetragonal Z=2Tetragonal Z=2

MoOMoO22Monoclinic Z=4Monoclinic Z=4

ΖΖΖΖ point

ΓΓΓΓ point

BondingBonding

AntibondingAntibonding

MM--M Short=BondingM Short=BondingMM--M Long=BondingM Long=Bonding

MM--M Short=ABM Short=ABMM--M Long=ABM Long=AB

MM--M Short=BondingM Short=BondingMM--M Long=ABM Long=AB

MM--M Short=ABM Short=ABMM--M Long=BondingM Long=Bonding


PierlsPierls DistortionDistortionThe The dimerization dimerization which occurs in the which occurs in the rutile rutile structure and it�s structure and it�s

effects on the band structure are similar to the effects on the band structure are similar to the Pierls 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 Mexcept that it occurs on top of the M--O O ππ* interactions.* interactions.

a

a

a

a

a

a

E

k0 π/a

EF

E

k0 π/a

EF

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M-O σσσσ

M-O ππππO 2p NB

M-M σσσσ [2]

M-O π∗π∗π∗π∗ [8]

M-O σ∗σ∗σ∗σ∗ [8]

M-M σ∗σ∗σ∗σ∗ [2]d d eegg

d td t2g2g

Z = 4 (MZ = 4 (M44OO88))

EEFF VOVO22

EEFF MoOMoO22

Oxygen 2pOxygen 2p

Monoclinic Structure (VOMonoclinic Structure (VO22,MoO,MoO22))

Delocalized Delocalized ElectronsElectrons

MM--O O AntibondingAntibonding

Localized Localized ElectronsElectrons

MM--M BondingM Bonding


DOS (e/eV)

13

k

Ener

gy (v

s. O

2s)

10

15

20

25

Z α M Γ Z R X Γ

10

15

20

25

DOS (e/eV) 13Z Γ Y α β ∆ ε C

k

MoOMoO22Monoclinic (Z=4)Monoclinic (Z=4)

CrOCrO22Tetragonal (Z=2)Tetragonal (Z=2)

Mo-Mo σσσσMo-O ππππ∗∗∗∗

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CrOCrO22 and RuOand RuO22Why are alternating longWhy are alternating long--short Mshort M--M contacts, indicative of M contacts, indicative of MetalMetal--Metal bonding not observed in CrOMetal bonding not observed in CrO22 and RuOand RuO22. The . The

electron count suggests that the Melectron count suggests that the M--M M σσσσσσσσ levels should be full levels should be full and the Mand the M--M M σσσσσσσσ** levels empty?levels empty?

There is a competition between localized MThere is a competition between localized M--M bonding (prefers M bonding (prefers dimersdimers) and ) and delocalized delocalized electronic transport in the Melectronic transport in the M--O O ππππππππ** band band

(prefers equal spacing). (prefers equal spacing).

Favors MFavors M--M bonding M bonding and localized eand localized e-

Dominant in MoODominant in MoO22

Favors Favors delocalizeddelocalizedtransport in the Mtransport in the M--O O ππππππππ**

bandband

Dominant in Dominant in CrOCrO22 (poor overlap) (poor overlap)

RuORuO22 (electron count)(electron count)

VOVO22IntermediateIntermediate


Double ExchangeDouble ExchangeCrOCrO22 is ferromagnetic. A property which leads to it�s use in magnetis ferromagnetic. A property which leads to it�s use in magnetic ic

cassette tapes. What stabilizes the ferromagnetic state?cassette tapes. What stabilizes the ferromagnetic state?

Localized tLocalized t||||electronselectrons

No MNo M--M BondingM Bonding

M

M

MM

M

M

Delocalized Delocalized tt2g2g ππππππππ**

electronselectrons

Ferromagnetic:Ferromagnetic: DelocalizedDelocalizedtransport of transport of ttππππππππ** electrons allowedelectrons allowed..

tt||||

ttππππππππ**

tt||||

ttππππππππ**

AntiferromagneticAntiferromagnetic:: DelocalizedDelocalizedtransport violates transport violates Hund�sHund�s RuleRule..

Localized tLocalized t|||| electrons polarize itinerant (electrons polarize itinerant (delocalizeddelocalized) t) t2g2g ππππππππ**

electrons. Magnetism and conductivity are correlated.electrons. Magnetism and conductivity are correlated.

transition metal oxides rock salt and rutile: metal-metal bonding

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