1. THE BIGGER PICTURE - TRENDS IN REAL SYSTEMS
Band description of unique ferromagnetism of Fe, Co, Ni group
Need to consider properties of each valence band:
Energy
Width
Degeneracy
Curvature
Overlap
Occupancy
Density of states
With increasing number of 3d, 4s, 4p valence electrons and effective nuclear charge

2. THE BIGGER PICTURE - TRENDS IN REAL SYSTEMS
3d less diffuse than 4s,4p, poor shielding from Z
3d penetrates closer to core, less orbital overlap, creates narrower bands
orbital degeneracy 3d > 4p > 4s
3d electron occupancy greater
higher DOS for 3d than 4s,4p
DOS near EF important for magnetic, electrical, optical properties

3. THE BIGGER PICTURE - TRENDS IN REAL SYSTEMS
ferromagnetism requires partially filled bands and unpaired spins
strong cooperative magnetic dipole and exchange coupling
enabled by localized narrow bands, 3dn
high DOS of strongly magnetically coupled and hence aligned electron spins near the Fermi level
optimized at Fe, Co, Ni
let us consider the change in band properties across the transition element group and how this affects the magnetism

4. MAGNETIC PROPERTIES OF TRANSITION METALS
Real world - partially filled overlapping 4sp/3d bands in transition metals
4sp band - good overlap and hence broad
3d band poorer overlap - narrower, decreasing energy and band width across transition series with increasing Z*
3d bands high orbital degeneracy
Bloch-Wilson band picture for valence bands

5. MAGNETIC PROPERTIES OF TRANSITION METALS
Note the low DOS at the Fermi energy for the elements at the left and right of the first transition series
Arising from diffuse (3d Ti, 4sp Cu) delocalized bands
Gives rise to weak Pauli paramagnetism

6. MAGNETIC PROPERTIES OF TRANSITION METALS
High DOS for Fe, Co, Ni, near the centre of the transition series
Large number of unpaired electrons in localized narrow 3d band
Many degenerate levels close together
High e count/M - aligned spins, strong magnetic and exchange coupling
Gives rise to ferromagnetism
Note: more diffuse 4d, 5d orbitals and lower DOS
Preclude ferromagnetism for 2nd/3rd TEs

7. ROCK SALT TRANSITION METAL OXIDE (MO) CRYSTAL STRUCTURE
Face centered cubic fcc B anions with A cations in every octahedral site – coordination number 6 for A and B - hence stoichiometry is 1:1

8. BANDS IN d-BLOCK SOLIDS, TM MONOXIDES
TiO, VO rock salt metallic, Pauli paramagnets
Overlap of diffuse t2g orbitals at LHS of TS
Partially filled t2g band, 6N electron states, delocalized orbitals
Ti(II) Oh, HS, d2, 2N/6N filled; V(II), Oh, HS, d3, 3N/6N filled
Hence Pauli paramagnet

9. STOICHIOMETRIC TiO, A ROCK SALT TYPE METALLIC PAULI PARAMAGNETIC
TiO rock salt structure type
Ti(ll) Oh d2 t2g2 (dxz,yz,xy)2
LHS of 1st transition series
Low effective nuclear charge
Expanded diffuse d-orbitals
Poor overlap of dxz,yz,xy with O(-ll) 2p pi-orbitals
Delocalized partially filled t2g2 (dxz,yz,xy)2 d-band
Only two electrons hence low DOS
Weak magnetic coupling of unpaired electrons
Hence behaves as a Pauli paramagnetic metal

10. BANDS IN d-BLOCK SOLIDS, TM MONOXIDES
MnO, FeO, CoO, NiO, semiconductors, antiferromagnets
Contracted, more tightly bound, t2g, eg orbitals with increasing Z*
Oh, Mn(II), HS, d5, Fe(II), HS, d6, Co(II), HS, d7, Ni(II), HS, d8
Greater inter-electronic repulsion of electrons on same atom
Less facile electron transport
Electrons become localized
Shorter stronger sigma M-O-M bonds favor super-exchange coupling
Hence behave as antiferromagnetic semiconductors

11. STOICHIOMETRIC NiO, A GREEN ROCK SALT TYPE ANTIFERROMAGNETIC SEMICONDUCTOR
NiO rock salt structure type
Ni(ll) Oh d8
t2g6 (dxz,yz,xy)6eg2 (dz2,x2-y2)2
RHS of 1st transition series
High effective nuclear charge Z*
Contracted d-orbitals
Narrow localized eg2 (dz2,x2-y2)2 d-band
Overlap of dz2,x2-y2 with O(-ll) 2p sigma-orbitals
UPEs super-exchange coupled
Behaves as antiferromagnetic semiconductor with t2geg electronic band gap

12. ROCK SALT NiO ANTIFERROMAGNETIC SUPER-EXCHANGE OF Ni2+O2-Ni2+ CENTERS
Oh Ni(2+) adjacent sites in rock salt lattice, d8(t2g6eg2)
Unpaired eg electrons occupy symmetry equivalent dz2/dx2-y2
Couple electronically via p-type electrons of bridging oxygens, “super-exchange”
Give antiferromagnetically coupled eg electrons

13. ELECTRONIC BAND SCHEMES FOR TiO AND NiOEg

15. RUTILE TITANIUM DIOXIDE TiO2 AND CADMIUM IODIDE TITANIUM DISULFIDE TiS2 CRYSTAL STRUCTURES
Body centered cubic bcc six coordinate Ti(IV) with O(-II) in three coordinate sites (Rutile archetype)
Hexagonal close packed hcp three coordinate S(-II) sites with Ti(IV) in six coordinate octahedral sites (Cadmium Iodide archetype)

16. BANDS IN d-BLOCK SOLIDS TM DIOXIDES AND DISULFIDES
Broad diffuse delocalized bands early TMs
TiO2 rutile, Oh, Ti(IV), d0, insulator
TiS2 layered CdI2 type, D3h, Ti(IV), d0, semiconductor
Full O2p and S3p pi-type bands
Empty 3d bands

17. BANDS IN d-BLOCK SOLIDS TM DIOXIDES AND DISULFIDES
Greater Ti-S bond overlap and co-valency than more ionic Ti-O bonds
Larger band widths for VB and CB of TiS2 vs TiO2
Smaller Eg for TiS2 vs TiO2
TiS2 semiconductor
TiO2 insulator
n-doped TiO2 as photocathode in solar cells
TiS2 as intercalation cathode in solid state rechargeable batteries