Material Science II. d Electron systems

Transcription

1 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)

2 - Materials, physical properties - Electronic structure 6.2 Magnetic semiconductors - Materials, physical properties - Electronic structure

3 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

4 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

5 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 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

7 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

8 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

9 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

10 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

11 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

12 - Materials, physical properties - Electronic structure 6.2 Magnetic semiconductors - Materials, physical properties - Electronic structure

13 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

14 small Charge-transfer energy Valence: large small large Transition-metal ions S Non-TM ions large large small small small large

15 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

16 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

17 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

18 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

19 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

20 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

21 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

22 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

23 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 (ev)

24 - Materials, physical properties - Electronic structure 6.2 Magnetic semiconductors - Materials, physical properties - Electronic structure

25 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

26 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

27 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

28 6.2 Magnetic semiconductors Giant magneto-resistance Tc ~ Magnetization A. Oiwa et al., Solid State Commun F. Matsukura et al. Phys. Rev. B 1998

29 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

30 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., H. Munekata et al., Phys. Rev. Lett. 1989

31 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

32 - Materials, physical properties - Electronic structure 6.2 Magnetic semiconductors - Materials, physical properties - Electronic structure

33 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

34 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,.

35 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