Material Science II. d Electron systems 1. Electronic structure of transition-metal ions (May 23) 2. Crystal structure and band structure (June 13) 3. Mott s (June 20) 4. Metal- transition (June 27) 5. High-temperature superconductivity (July 4) 6. Spin-related phenomena (July 11)
- Materials, physical properties - Electronic structure 6.2 Magnetic semiconductors - Materials, physical properties - Electronic structure
4. Metal- transition 4.3 Filling-controlled metal- transition Bandwidth control Mn 4+ Mn 3+ Fermi-liquid to Mott : Ti, V Giant magnetoresistance: Mn Filling control Giant thermopower: Co M. Imada, A. Fujimori and Y. Tokura, Rev. Mod. Phys. 1998
U/W or /W Insulator BANDWIDTH U/W or /W ~ 1 n 4 Filling-controlled MIT Bandwidth-controlled MIT n M. Imada, A. Fujimori and Y. Tokura, Rev. Mod. Phys. 1998
Tc Giant magneto-resistance La 1-x Sr x MnO 3 Resistance Resistance La 1-x Sr x MnO 3 Temperature Magnetic field Y. Tokura et al., J. Phys. Soc. Jpn. 1994
4. Metal- transition 4.3 Filling-controlled metal- transition Bandwidth control Nd Pr Fermi-liquid to Mott :Ti, V Mn 4+ Mn 3+ Giant magnetoresistance: Mn Filling control Giant thermopower: Co M. Imada, A. Fujimori and Y. Tokura, Rev. Mod. Phys. 1998
Filling-controlled MIT /W Insulator Pr 1-x Ca x MnO 3 BANDWIDTH /W ~ 1 Hole doping Nd 1-x Sr x MnO 3 La 1-x Sr x MnO 3 n 4 Bandwidth-controlled MIT
Electronic phase diagram La 1-x Sr x MnO 3 Nd 1-x Sr x MnO 3 Pr 1-xCa x MnO 3 T C T C Ferromagnetic metal Insulator Ferromagnetic metal Charge-ordered Large Doped hole content x Doped hole content x Bandwidth W Doped hole content x Small W cos 2 Y. Tokura and Y. Tomioka, J. Magn. Magn. Mater. 1999
Spin-charge-orbital ordering Pr 1-x Ca x MnO 3 Charge-ordered Mn 3+ :Mn 4+ =1:1 Mn 3+ :Mn 4+ =1:2 Large Doped hole content x Jahn-Teller distortion of MnO 6 octahedron for the Mn 3+ ion Mn 3+ (t 2g3 e g ) Mn 4+ (t 2g3 ) d 3z2-r2 d x2-y2
Colossal magneto-resistance Resistivity change by pulsed electric field Insulator-to-metal transition induced by magnetic or electric field Y. Tomioka et al., Phys. Rev. B 1996 A. Asamitsu et al., Nature 1997
Tc Giant magneto-resistance La 1-x Sr x MnO 3 Resistance Resistance La 1-x Sr x MnO 3 Temperature Magnetic field Y. Tokura et al., J. Phys. Soc. Jpn. 1994
- Materials, physical properties - Electronic structure 6.2 Magnetic semiconductors - Materials, physical properties - Electronic structure
Parent compounds 6. Spin-related phenomena Electronic phase diagram La 1-x Sr x MnO 3 Nd 1-x Sr x MnO 3 Pr 1-xCa x MnO 3 T C T C Ferromagnetic metal Insulator Ferromagnetic metal Charge-ordered Large Doped hole content x Doped hole content x Bandwidth W Doped hole content x Small W cos 2 Y. Tokura and Y. Tomioka, J. Magn. Magn. Mater. 1999
small Charge-transfer energy Valence: 2-1-. + 2+ 3+ 4+ 5+ 1.0 1.5 large small 3.5 4.0 large Transition-metal ions 1.5 1.6 1.5 1.8 2.5 S 0.8 1.0 2.1 1.2 1.8 2.2 Non-TM ions large large small small small large
Zaanen-Sawatzky-Allen phase diagram Schematic Real materials W p-band metal Charge-transfer Mott-Hubbard d-band metal U Negative charge-transfer energy p-band metal RNiO 3 Charge-transfer Mott-Hubbard W d-band metal
Mott-Hubbard-type Charge-transfer-type 3d 3d O 2p W W U 3d ZR-like O 2p 3d U Zhang-Ricelike states strong p-d hybridization U < U > Gap ~ U - W Gap ~ -W W: Band width U : Atomic Coulomb energy (Coulomb integral) : Charge-transfer enrgy
Electronic states of Mn ion O 2p orbitals Mn 3d orbitals (d 4 L, Jahn-Teller distortion of Mn 3+ ion octahedron Y. Tokura Hund s rule 3 > Crystal field High-spin state
Electronic phase diagram La 1-x Sr x MnO 3 Nd 1-x Sr x MnO 3 Pr 1-xCa x MnO 3 T C T C Ferromagnetic metal Insulator Ferromagnetic metal Charge-ordered Large Doped hole content x Doped hole content x Bandwidth W Doped hole content x Small W cos 2 Y. Tokura and Y. Tomioka, J. Magn. Magn. Mater. 1999
3. Mott s 3.7 Insulator-to-metal transition Carrier doping (Filling control) Mott-Hubbard type Charge-transfer type U > W > W 3d W 3d 3d W U O 2p U O 2p Gap ~ U - W 3d Gap ~ -W
Double exchange model (ZR-like) (ZR-like) e g 10Dq t 2g S: i : i e t g 2 g spin spin J H Hund s rule
Electronic phase diagram La 1-x Sr x MnO 3 Nd 1-x Sr x MnO 3 Pr 1-xCa x MnO 3 T C T C Ferromagnetic metal Insulator Ferromagnetic metal Charge-ordered Large Doped hole content x Doped hole content x Bandwidth W Doped hole content x Small W cos 2 Y. Tokura and Y. Tomioka, J. Magn. Magn. Mater. 1999
Band structure of La 1-x Sr x MnO 3 Photoemission spectra Band-structure calculation e g band t 2g band O2p band X X A. Chikamatsu et al., Phys. Rev. B 2006
Fermi surfaces of La 1-x Sr x MnO 3 Band dispersion and self-energy Jahn-Teller phonon mode Re(k,) Re(k,) 0 Im(k,) Fermi liquid K. Horiba et al., Phys. Rev. Lett. 2016-0.5 0 (ev)
- Materials, physical properties - Electronic structure 6.2 Magnetic semiconductors - Materials, physical properties - Electronic structure
6.2 Magnetic semiconductors Antiferromagnetic/spin-glass Random Mn substitution Mn 2+ (d 5 ) II-VI semiconductors Cd 2+ Te Zn 2+ S Cd 2+ 1-xMn 2+ xte: Giant Faraday rotation Optical isolator Zn 2+ 1-xMn 2+ xs: Luminescent material
6.2 Magnetic semiconductors Ferromagnetic metal/conductor III-V semiconductors In 3+ As Ga 3+ As Non-thermal equilibrium growth by MBE In 3+ 1-xMn 2+ (d 5 ) x As + (hole) x Ga 3+ 1-xMn 2+ (d 5 ) x As + (hole) x Curie temperature Mn H. Ohno et al., J. Magn. Magn. Mater., 1999 H. Munekata et al., Phys. Rev. Lett. 1989
6.2 Magnetic semiconductors High-temperature ferromagnetic semiconductors for future spintronics Non-volatile memories GMR devices Novel devices utilizing spin injection Mn Si, Ge Mn in GaAs, InAs,... Y. Ohno et al., Nature 1999
6.2 Magnetic semiconductors Giant magneto-resistance Tc ~ Magnetization A. Oiwa et al., Solid State Commun. 1997 F. Matsukura et al. Phys. Rev. B 1998
Tc Giant magneto-resistance La 1-x Sr x MnO 3 Resistance Resistance La 1-x Sr x MnO 3 Temperature Magnetic field Y. Tokura et al., J. Phys. Soc. Jpn. 1994
6.2 Magnetic semiconductors Ferromagnetic metal/conductor III-V semiconductors Ga 3+ As Ga 3+ 1-xMn 2+ (d 5 ) x As + (hole) In 3+ As In 3+ 1-xFe 3+ (d 5 ) x As:Be + (electron) Curie temperature Fe H. P. Ohno N. Hai et al., J. Appl. Magn. Phys. Magn. Lett. Mater., 2012 1999 H. Munekata et al., Phys. Rev. Lett. 1989
6.2 Magnetic semiconductors Fe-based high-t c superconductor Ba 1-x K x Fe 2 As 2 New diluted magnetic semiconductor Ba 1-x K x (Zn 1-y Mn y ) 2 As 2 Magnetization Ba Zn As Resistivity Fe(d 6 ) hole e - Mn(d 5 ) hole e - Ba 2+ K + Ba 2+ K + K. Zhao et al., Nat. Commun. 2013
- Materials, physical properties - Electronic structure 6.2 Magnetic semiconductors - Materials, physical properties - Electronic structure
Mn 3d band 6. Spin-related phenomena 6.2 Magnetic semiconductors Carrier-induced ferromagnetism through p-d via exchange p hole U Hole Conduction band N-1 ev Mn 3d band valence p band p-d exchange ingteraction N~ - 1 ev Ga 3+ Mn 3+ Mn 2+ + hole Atom substitution Strong p-d hybridization
6.2 Magnetic semiconductors Search for high-temperature ferromagnetic semiconductors Theoretical prediction Mn content ~ hole content ~ 5% T. Dietl et al, Science, 2000 Room temperature ferromagnetic semiconductors wide-gap semiconductor-based materials: Ga 1-x Mn x N,Zn 1-x Co x O,Ti 1-x Co x O 2,.
6.2 Magnetic semiconductors Soft x-ray ARPES of Ga 1-x Mn x As Calculated band structure of GaAs Resonance ARPES of Ga 1-x Mn x As Off res. On res. E F ~100 mev VBM HH SO LH Impurity band Mn 3d M. Kobayashi et al., Phys. Rev. B 2014