1. Band Structure and Phonons of Bulk NiO from Ellipsometry
Cayla M. Nelson, Travis I. Willett-Gies, Lina S. Abdallah, Stefan Zollner Department of Physics, New Mexico State University, Las Cruces, NM
Ayana Ghosh Department of Physics, University of Michigan-Flint
FTIR ellipsometry: 2 to 40 mm (Sandia)
NIR/VIS/QUV ellipsometry: 190 to 2500 nm, 77 to 800 K
NSF: DMR

2. Band Structure and Phonons of Bulk NiO
Crystal = Lattice + Basis
Atomic positions => point group, space group
Infrared Ellipsometry: Lattice vibrations (phonons)
NIR/VIS/UV Ellipsometry: Electronic band structure
Magnetic properties influence optical and electronic properties
Resistivity and reflectance of metallic Ni jump at Curie temperature.
Antiferromagnetism of NiO incluences IR-active phonons.
Complicated electronic band structure (Mott-Hubbard).
Bulk (111) NiO (purchased from SurfaceNet GmbH, Germany).
M. Cardona
New Mexico State University
Stefan Zollner, 08/12/2014, ICPS 2

3. Vibrational Properties (Phonons)
LaAlO3
Ran Liu et al., PRB, 1988
MgAl2O4
Space Group
LaAlO3
FTIR Ellipsometry
Loss function:
LO phonons
Dielectric function:
TO phonons LO LO
MgAl2O4 TO TO
Willett-Gies, Thin Solid Films, 2014
Zollner, Thin Solid Films, 2014
New Mexico State University
New Mexico State University
Stefan Zollner, March
Stefan Zollner, 06/02-05/2014, MFM-9 3
Stefan Zollner, March

4. Infrared Lattice Absorption of NiO
Silicon:
Diamond lattice
NiO or NaCl:
Rocksalt lattice
Si-Si bonds are non-polar.
Bonds: no dipole moment.
No infrared absorption.
Ni2+-O2- bonds are polar.
Ni-O vibration has dipole moment.
NiO
Typical Lorentz oscillator
Si: No IR absorption
e2=0
FTIR ellipsometry
New Mexico State University
Stefan Zollner, 08/12/2014, ICPS 4

5. Antiferromagnetism: Zone-folded TO phonon
Rocksalt Crystal Structure (FCC): Single optical phonon.
Antiferromagnetic ordering along (111).
Small rhombohedral distortion.
Lattice waves are reflected by the anti-parallel ordered spins along (111).
(Or: L-point phonon folded back to G due to doubling the crystal size.)
NiO cell
Rooksby, Nature, 1943
NiO Reststrahlen Band
Theory: e0=13.1 (Louie)
e0=11.3
e¥=5.0
Zone-folded phonon TO LO
Stefan Zollner, 06/02-05/2014, MFM-9 5
Stefan Zollner, 03/07/2014, APS March meeting 5

6. NiO Band Structure I
Atomic electron configurations: Ni: [Ar] 3d8 4s2 O: [He] 2s2 2p4
Ni2+O2-: 4s electrons of Ni are transferred to O 2p: Ni2+: [Ar] 3d8 4s0 O2-: [He] 2s2 2p6
This should be a metal, because only 8 of 10 d-states are filled.
However:
Transmission measurements show that NiO is an insulator with a fundamental band gap of about 0.8 eV
(Could be direct, indirect, or defect absorption at 0.8 eV.)
Compare: Newman, Phys. Rev
New Mexico State University
Stefan Zollner, 08/12/2014, ICPS 6

7. NiO Band Structure: Charge-transfer insulator
Let’s double the unit cell: 2 Ni and 2 O atoms per crystal cell: Ni(1): [Ar] 3d8 4s0 Ni(2): [Ar] 3d9 4s0 O(1): [He] 2s2 2p6 O(2): [He] 2s1 2p6
Every other O atom (ligand) transfers one electron to a Ni atom. Ligand (O) hole adds an extra d-electron to Ni.
Antiferromagnetic ordering.
Charge-transfer gap commonly assumed to be eV.
Most evidence from photoemission.
Optical spectroscopy (transmission, ellipsometry) is usually ignored.
Mixed valence
Sawatzky & Allen, PRL, 1984
Powell & Spicer, PRB,1970
Kunes & Vollhardt, PRL, 2007
Charge-transfer gap at 3.97 eV
Newman & Chrenko, Phys. Rev. 114, 1507 (1959). Kang, Lee, & Lee, J. Kor. Phys. Soc. 50, 632 (2007). ?
New Mexico State University
Stefan Zollner, 08/12/2014, ICPS 7

8. NiO looks just like Silicon
NiO:Charge-transfer gap at 3.97 eV
Silicon: E1 at 3.4 eV ?
The charge-transfer gap (CTG) of NiO at 4 eV looks just like the E1 gap of Si.
Energy decreases with increasing temperature.
Broadening increases with temperature.
Just like Si: Phonon-related ?
Compare: Vina, PRB, 1984 (Ge); Lautenschlager, PRB, 1987 (Si).
New Mexico State University
Stefan Zollner, 08/12/2014, ICPS 8

9. Failures of the Charge-Transfer Model for NiO
Optical absorption from 0.8 to 3.5 eV: Electronic states below CTG. Too strong to be defect-related. Too weak for photoemission.
Absorption decreases near and above Neel temperature (525 K).
Several weak critical points between 0.8 and 4.0 eV.
Charge-gap model is flawed.
We need a full-zone band structure for NiO to compare with optical experiments.
NiO
TN=530 K
Derivative analysis
Charge-transfer gap at 3.97 eV
Li, Riganese, Louie, Phys. Rev. B 71, (2005).
Several critical points
Lowest gap at 1.5 eV
New Mexico State University
Stefan Zollner, 08/12/2014, ICPS 9

10. Electron Structure: Band Gaps Peaks indicate interband transitions
Valence band (flat): Ni(3d) states with some O
Conduction band: Flat: Ni(3d) states (unfilled) Curved: Unfilled Ni(4s) states
Strong 4.0 eV peak goes from Ni(3d) VB to Ni(3d) CB.
Also observed in photoemission
Weak peaks are transitions from many Ni(3d) VB states to the Ni(4s) band, only at G.
Explains all experimental evidence.
Several critical points
Lowest gap at 1.5 eV
J.L. Li & S.G. Louie, PRB, 2005
New Mexico State University
Stefan Zollner, 08/12/2014, ICPS 10

11. NiO is a fascinating material.
Summary: Interactions of Magnetism with Electronic and Vibrational Properties of NiO
NiO is a fascinating material.
The antiferromagnetic ordering of the electron spins doubles the size of the crystal cell (4 atoms per cell instead of 2).
This cell doubling causes a side-band of the Ni-O vibration (L-point phonon folded back to G).
The cell doubling also makes NiO a charge-transfer insulator.
A full-zone band structure is needed to understand the weak optical transitions below the charge-transfer gap at 4.0 eV.
New Mexico State University
Stefan Zollner, 08/12/2014, ICPS 11

12. Graduate Students: Lina Abdallah, Travis Willett-Gies, Nalin Fernando, Tarek Tawalbeh (Theory) Undergraduate Students: Cesar Rodriguez, Nathan Nunley, Khadijih Mitchell, Cayla Nelson, Laura Pineda, Eric DeLong, Chris Zollner (Cornell), Amber Medina, Maria Spies, Ayana Ghosh (Michigan-Flint) Collaborators: Igal Brener (CINT), Neha Singh, Harland Tompkins (J.A. Woollam Co.), S.G. Choi (NREL) Samples: Demkov (UT Austin), Alpay (Uconn), Droopad (Motorola), MTI (LAO), SurfaceNet (NiO)
Flat & uniform films, at least 5 by 5 mm2, low surface roughness, films on single-side polished substrate
New Mexico State University