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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) http://ellipsometry.nmsu.edu NSF: DMR-11104934 NIR/VIS/QUV ellipsometry: 190 to 2500 nm, 77 to 800 K 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 M. Cardona 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). New Mexico State University Stefan Zollner, 08/12/2014, ICPS

2 Vibrational Properties (Phonons) LaAlO3 Ran Liu et al., PRB, 1988 MgAl2O4 D36d or R 3 c Space Group Oh7 or Fd 3m R N R det R 2 cos LaAlO3 LO s FTIR Ellipsometry 2 s i2,LO 22.3 0.3 i i ,TO TO Stefan Zollner, March 2014 3 06/02-05/2014, MFM-9

LO Loss function: LO phonons Dielectric function: TO phonons 3 i i2,LO 7.8 0.2 i2,TO Willett-Gies, Thin Solid Films, 2014 Zollner, Thin Solid Films, 2014 TO MgAl2O4 New Mexico State University 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 Silicon dielectric function (IR) 11.700 11.698 Si: No IR absorption Typical Lorentz oscillator <1> 11.696 11.694 11.692 2=0 11.690 11.688 200 400 600 Wave Number (cm Stefan Zollner, 08/12/2014, ICPS

800 -1) 4 1000 FTIR ellipsometry New Mexico State University 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 Rooksby, Nature, 1943 anti-parallel ordered spins along (111). NiO cell (Or: L-point phonon folded back to G due to doubling the crystal size.) NiO Reststrahlen Band Theory: 0=13.1 (Louie) 0=11.3 =5.0 TO Stefan Zollner,

06/02-05/2014, MFM-9meeting5 Stefan Zollner, 03/07/2014, APS March 5 Zone-folded phonon LO 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 Compare: Newman, Phys. Rev. 1959. 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.) New Mexico State University Stefan Zollner, 08/12/2014, ICPS

6 NiO Band Structure: Charge-transfer insulator Lets double the unit cell: 2 Ni and 2 O atoms per crystal cell: Ni(1): [Ar] 3d8 4s0 Mixed valence Ni(2): [Ar] 3d9 4s0 Sawatzky & Allen, PRL, 1984 O(1): [He] 2s2 2p6 Powell & Spicer, PRB,1970 1 6 Kunes & Vollhardt, PRL, 2007 O(2): [He] 2s 2p 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 Charge-transfer gap at 3.97 eV assumed to be 4.0-4.5 eV. Most evidence from photoemission. Optical spectroscopy (transmission, ellipsometry) is usually ignored. 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 NiO looks just like Silicon 60 50 40 1 20 0 -20 -40 0 30 Silicon: E1 at 3.4 eV 1 2 20 10 NiO:Charge-transfer gap at 3.97 eV 2 Real(Dielectric Constant),

40 Imag(Dielectric Constant), 1 2 3 4 Photon Energy (eV) 5 6 0 7 ? 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

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. Li, Riganese, Louie, Phys. Rev. B 71, 193102 (2005). NiO TN=530 K Derivative analysis Charge-transfer gap at 3.97 eV Several critical points Lowest gap at 1.5 eV New Mexico State University Stefan Zollner, 08/12/2014, ICPS 9 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 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 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 Email: [email protected] http://ellipsometry.nmsu.edu

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