Electronic structure and magnetic properties of II-VI DMS

1
Electronic structure and magnetic properties of
II-VI DMS
Thomas Chanier ISEN Engineer PhD student IM2NP,
MARSEILLE, France Co-workers R. Hayn, M.
Sargolzaei, I. Opahle, M. Lannoo
PhD defense - 29/08/2008 Faculté de St-Jérôme,
Marseille, France
2
Introduction

• Failure of Moores law
• The number of transistors / inch² on mP chips
  doubles every two years
• Current technology
• Based on electron charge
• Atomic scale
• Quantum nature of the electron
• Needed new science to replace classical micro-
• electronics

http//public.itrs.net/
LGlt50 nm (1000 at.)
dLG²
Fe corral on Au
MOS FET
TEM image
STM image, IBM
3
Spintronics

• SpinFET - Datta and Das, APL 56 665 (1990)
• Principals
• Rashbas precession
• Current challenge
• Injection of spin-polarized current
• in the SC channel
• Unsuccessful attempts
• S and D in FM metal weak injection
• due to conductivity mismatch with SC
• Schmidt et al., PRB 62 R4790 (2000)
• Alternative solution for spin injection
• DMS diluted magnetic SC
• - Classical SC doped with magnetic ions
• (TM or rare earth)

Scientific American
4
Basics on II-VI DMS
Host SC covalent bonds Zn2 -
A2- Substitutional impurity TM2 config. Ar
3dn 4s0 - for Co, n7 ? S 3/2 - for Mn,
n5 ? S 5/2 ZB only 1 NN exchange integral
JNN W 2 NN exch. Int. in-plane Jin
out-of-plane Jout
Ref. 1 Jamieson, J. Phys. Chem. Solids 41 963
Ref. 2 CRC Handbook of Chemistry and
Physics Ref. 3 Sabine, Acta Cryst. B 25
2254 Ref. 4 Reeber, JAP 38 1531 Ref. 5 Yim,
J. Electr Soc Sol-St.Sci. Tech 119 381
5
State of the art

• l

Dietl (2001)
FM prediction for ZnTMO - Sato et al., Physica
E 10 251 (2001) LSDA FM JNN in ZnCoO - Dietl
et al., PRB 63 195205 (2001) Zener model, p-type
ZnMnO AFM FM competition for ZnCoO
AFM for ZnMnO - Lee et al., PRB 69 085205
(2004) - Sluiter et al. , PRL 94 187204 (2005)
LSDA pseudopotential BUT
in contrast to experiments
Sati (2007)

• Our study AFM NN exchange constants
• - LSDAU Hubbard-type correction to LSDA ? AFM
  JNN
• T. Chanier et al., PRB 73 134418 (2006)
• Predictions confirmed AFM interactions in
  ZnCoO,
• P. Sati et al., PRL 98 137204 (2007)

LSDAU
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d-d exchange Hamiltonian

• Heisenberg Hamiltonian
• J gt 0 ? FM
• J lt 0 ? AFM
• Comparison of ?E in the Heisenberg model with
  ?ETotal obtained
• from FM and AFM First-principle calculations
• chain
• pair
• Where ST 2S the total spin for two
  magnetic impurities of spin S
• First-principle calculations
• FPLO full potential local orbital approximation
  (Koepernic et al., PRB 59 1743)
• LSDA Perdew-Wang 92 Vxc functional (Perdew and
  Wang, PRB 45 13244)

7
Supercell approach
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Exchange constants for ZnOCo

• LSDA competition between AFM and FM
  interactions
• for the two type of NN in constrast to exp.
• Necessity of better taking into account the
• strong electron correlation in the TM 3d-shell
• LSDAU AFM exchange constants for the two type
• of NN in quantitative agreement with exp.
• We use the same Slater parameters as those of
  CoO
• Two realistic values for U 6 and 8 eV
• Ref. Anisimov et al., PRB 44 943 (1991)
• Our values Jin -1.7 0.3 meV, Jout -0.8
  0.3 meV
• Experiments
• Tcw of magnetic susceptibility Jave -33 K
  -2.8 meV
• INS Jin -2.0 meV, Jout - 0.7 meV

Ref. 1 Lee and Chang, PRB 69 085205 (2004)
(LSDA, pseudopotential) Ref. 2 Sluiter et al.,
PRL 94 187204 (2005) (LSDA, pseudopotential)
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Exchange constants for ZnOMn

• LSDA underestimation of AFM exchange constants
  
• in either type of NN
• LSDAU AFM exchange constants in quantitative
• agreement with experiments (SP of MnO, U 6 8
  eV)
• Our values Jin -1.8 0.2 meV, Jout -1.1
  0.2 meV
• Experimental values two values of J (MST)
• J1 -2.08 meV, J2 -1.56 meV
• Ref. Gratens et al., PRB 69 125209 (2004)
• Ref. 2 Sluiter et al.,
  PRL 94 187204 (2005)

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Spin density
Co-O-Co plane, in-plane NN Co-O-Co plane,
out-of-plane NN
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JNN for ZB II-VI DMS

• Chemical trends of JNN Supercells TM2Zn6A8 (ZB)

AIIBVIMn
AIIBVIMn
- U from Ref. Gunnarson et al., PRB 40 10407
(1989) - Charge transfer from FPLO
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sp-d exchange constants

• Chemical trends of Na and Nb Supercells TMZn3A4
  (ZB)
• Mean Field Approx.
• With N the cation concentration
• sp-d exch cst for CBE and VBH at G

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LSDAU DOS
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LSDAU DOS
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LSDAU DOS
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LSDA DOS
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Main features of DOS

• The upper VB is formed by a semi-circle of width
  W
• LSDA BS inverted FM VB spin splitting DEv
  Ev - Ev gt 0
• too high position of TM 3d level, always a bound
  state
• LSDAU formation of a BS FM DEv if Vpd gt Vpd
• If U , the occupied 3d levels are shifted by
  -U/2 from VBM , 0 EBS-Ev
• Hyp. Vpd ? f(U)
• mm

c
e
l
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Analytical model

• Bethe Lattice Model
• - TB Hamiltonian
• - Basis set - Hamiltonian matrix
• - Local Creen Funct.

(t2g 3d orb. for TM2) (t2 p
orb. for A2-)
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Resolution

• Host Green function
• Local Green function
• No bound state f0 lt a e0 lt a-f0
• A bound state out of continuum f0 gt a e0 gt
  a-f0
• 2 bound states on both side of the continuum
• f0 gt a e0 lt a-f0

Vpd 0.90 eV
Vpd 0.90 eV
a 2 eV, e0 1 eV
a 2 eV, e0 1 eV
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Resolution

• Host Green function
• Local Green function
• No bound state f0 lt a e0 lt a-f0
• A bound state out of continuum f0 gt a e0 gt
  a-f0
• 2 bound states on both side of the continuum
• f0 gt a e0 lt a-f0

Vpd 0.90 eV
Vpd 0.90 eV
a 2 eV, e0 1 eV
a 2 eV, e0 1 eV
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Resolution

• Host Green function
• Local Green function
• No bound state f0 lt a e0 lt a-f0
• A bound state out of continuum f0 gt a e0 gt
  a-f0
• 2 bound states on both side of the continuum
• f0 gt a e0 lt a-f0

Vpd 0.90 eV
a 2 eV, e0 1 eV
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Formation of a Zhang-Rice Singlet

• Condition of formation of a bound state
• - Necessary condition for a BS
• f0 gt aW/2 e0 not too deep
• - for ZnOTM
• Two bound states

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Results

• Curve fitting - Results
• - Supercell MnZn31O32
• - Harrisons parametrization

24
Vpd for Host II-VI SC
c

• - Host SC DOS - Critical hybridization param.
  
• - Harrisons parametrization

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Vacancy in II-VI SC ab initio study

• - Basis set - NN relaxation
• - Electronic structure
• - LSDA results DE ELDA-ELSDA
• Zn4A3 calc. Neutral anion vacancy is
  non-magnetic

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Analytical model

• Molecular cluster model - sp3 molecular
  orbitals Yi (i1..4)
• - Hamiltonian
• Group Theory SALC of Yi
• - monoelectronic states
• A1 and T2 representations
• - polyelectronic states direct product group

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Results

• Monoparticule eigenenergies
• Biparticle eigenenergies
• D -4 4 eV, U 4 eV, V 1 eV
• VZn0 in ZnO S 1 state characterized by
  EPR
• Ref. D. Galland et al., Phys. Lett. 33A,
  1 (1970)

VA0 in ZnO, S 0 VZn0 in ZnO, S 1
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Conclusion

• Mn- and Co-doped DMS
• Necessity of taking into account the strong
  electron correlation on the TM 3d shell.
• The LSDAU exchange constants are in quantitative
  agreement with experiments.
• Importance of the hybridation parameter Vpd to
  describe correctly the DOS
• of DMS.
• Single vacancy in II-VI SC
• Neutral cation vacancy in more ionic ZnO carries
  a spin S 1 in agreement with experiments.
• This state is quasi-degenerate with a S 0 state
  in other less ionic II-VI SC.
• Neutral anion vacancy is non-magnetic.
• Publications T. Chanier et al. , PRB 73 134418
  (2006) T. Chanier et al. , PRL 100 026405 (2008)