Thomas ChanierThomas ChanierISEN Engineer – PhD studentISEN Engineer – PhD student

IM2NP, MARSEILLE, FranceIM2NP, MARSEILLE, France

Co-workers : R. Hayn, M. Sargolzaei, I. Opahle, M. LannooCo-workers : R. Hayn, M. Sargolzaei, I. Opahle, M. Lannoo

Thomas ChanierThomas ChanierISEN Engineer – PhD studentISEN Engineer – PhD student

IM2NP, MARSEILLE, FranceIM2NP, MARSEILLE, France

Co-workers : R. Hayn, M. Sargolzaei, I. Opahle, M. LannooCo-workers : R. Hayn, M. Sargolzaei, I. Opahle, M. Lannoo

PhD defense - 29/08/2008 – Faculté de St-Jérôme, Marseille, France

Electronic structure and magnetic Electronic structure and magnetic properties of II-VI DMSproperties of II-VI DMS

Electronic structure and magnetic Electronic structure and magnetic properties of II-VI DMSproperties of II-VI DMS

IntroductionIntroductionIntroductionIntroduction

Failure of Moore’s law :– The number of transistors / inch² on P 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

Failure of Moore’s law :– The number of transistors / inch² on P 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

LG<50 nm (~1000 at.)

STM image, IBM

TEM image

http://public.itrs.net/

Fe corral on AuMOS FET

d~LG²

SpintronicsSpintronicsSpintronicsSpintronics SpinFET - Datta and Das, APL 56 665 (1990)

– Principals :• Rashba’s 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 SCSchmidt 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)

- New class of DMS ? magnetic intrinsic defects (vacancy, interstitial)

Needed : FM at room temperature for spintronic applications

SpinFET - Datta and Das, APL 56 665 (1990)– Principals :

• Rashba’s 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 SCSchmidt 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)

- New class of DMS ? magnetic intrinsic defects (vacancy, interstitial)

Needed : FM at room temperature for spintronic applications

Scientific American

Basics on II-VI DMSBasics on II-VI DMSBasics on II-VI DMSBasics on II-VI DMS

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

Host SC : covalent bonds Zn2+ ─ A2-

Substitutional impurity : TM2+ config. : [Ar] 3dn 4s0 : - for Co, n=7 → S = 3/2- for Mn, n=5 → S = 5/2

ZB : only 1 NN exchange integral JNN

W : 2 NN exch. Int. : in-plane Jin & out-of-plane Jout

ZB W

State of the artState of the artState of the artState of the art

ll

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

Our study : AFM NN exchange constants- LSDA+U : 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)

Dietl (2001)

Sati (2007)

LSDA+U

d-dd-d exchange Hamiltonian exchange Hamiltoniand-dd-d exchange Hamiltonian exchange Hamiltonian Heisenberg Hamiltonian :

• J > 0 → FM• J < 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) • LSDA+U : atomic limit scheme (Anisimov et al., PRB 44 943)

No additional carrier codoping

Heisenberg Hamiltonian :• J > 0 → FM• J < 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) • LSDA+U : atomic limit scheme (Anisimov et al., PRB 44 943)

No additional carrier codoping

Supercell approachSupercell approachSupercell approachSupercell approach

Exchange constants for ZnO:CoExchange constants for ZnO:CoExchange constants for ZnO:CoExchange constants for ZnO:Co 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

LSDA+U : AFM exchange constants for the two type of NN in quantitative agreement with exp.

We use the same Slater parameters as those of CoOTwo realistic values for U = 6 and 8 eVRef. : 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. : Yoon et al., JAP 93 7879 (2003), Stepanov, private comm. (2008)

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

LSDA+U : AFM exchange constants for the two type of NN in quantitative agreement with exp.

We use the same Slater parameters as those of CoOTwo realistic values for U = 6 and 8 eVRef. : 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. : Yoon et al., JAP 93 7879 (2003), Stepanov, private comm. (2008)Ref. 1 : Lee and Chang, PRB 69 085205 (2004) (LSDA, pseudopotential)Ref. 2 : Sluiter et al., PRL 94 187204 (2005) (LSDA, pseudopotential)

Exchange constants for ZnO:MnExchange constants for ZnO:MnExchange constants for ZnO:MnExchange constants for ZnO:Mn

LSDA : underestimation of AFM exchange constants in either type of NN

LSDA+U : 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)

LSDA : underestimation of AFM exchange constants in either type of NN

LSDA+U : 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)

Spin densitySpin densitySpin densitySpin density

Co-O-Co plane, in-plane NN Co-O-Co plane, out-of-plane NN

JJNNNN for ZB II-VI DMS for ZB II-VI DMSJJNNNN for ZB II-VI DMS for ZB II-VI DMS

Chemical trends of JNN : Supercells TM2Zn6A8 (ZB) Chemical trends of JNN : Supercells TM2Zn6A8 (ZB)

AIIBVI:Mn

- U from Ref. : Gunnarson et al., PRB 40 10407 (1989)- Charge transfer from FPLO :

AIIBVI:Mn

sp-dsp-d exchange constants exchange constantssp-dsp-d exchange constants exchange constants

Chemical trends of N and N : Supercells TMZn3A4 (ZB)– Mean Field Approx. :

With N the cation concentration

sp-d exch cst for CBE and VBH at

Chemical trends of N and N : Supercells TMZn3A4 (ZB)– Mean Field Approx. :

With N the cation concentration

sp-d exch cst for CBE and VBH at

LSDA+LSDA+UU DOS DOSLSDA+LSDA+UU DOS DOS

LSDA+LSDA+UU DOS DOSLSDA+LSDA+UU DOS DOS

LSDA+LSDA+UU DOS DOSLSDA+LSDA+UU DOS DOS

LSDA DOSLSDA DOSLSDA DOSLSDA DOS

Main features of DOSMain features of DOSMain features of DOSMain features of DOS

The upper VB is formed by a semi-circle of width W LSDA : BS & inverted FM VB spin splitting Ev = Ev - Ev > 0

– too high position of TM 3d level, always a bound state LSDA+U : formation of a BS & FM Ev if Vpd > Vpd

– If U , the occupied 3d levels are shifted by ~ -U2 from VBM , 0 = EBS-Ev

– Hyp. : Vpd ≠ f(U)

– mm

The upper VB is formed by a semi-circle of width W LSDA : BS & inverted FM VB spin splitting Ev = Ev - Ev > 0

– too high position of TM 3d level, always a bound state LSDA+U : formation of a BS & FM Ev if Vpd > Vpd

– If U , the occupied 3d levels are shifted by ~ -U2 from VBM , 0 = EBS-Ev

– Hyp. : Vpd ≠ f(U)

– mm

c

l

Analytical modelAnalytical modelAnalytical modelAnalytical model

Bethe Lattice Model :- TB Hamiltonian :

- Basis set : - Hamiltonian matrix :

- Local Creen Funct. :

Bethe Lattice Model :- TB Hamiltonian :

- Basis set : - Hamiltonian matrix :

- Local Creen Funct. :

(t2g 3d orb. for TM2+)

(t2 p orb. for A2-)

ResolutionResolutionResolutionResolution

Host Green function

Local Green function

(i) No bound state : f0 < a & |0| < |a-f0|

(ii) A bound state out of continuum : f0 > a & |0| > |a-f0|

(iii) 2 bound states on both side of the continuum :

f0 > a & |0| < |a-f0|

Host Green function

Local Green function

(i) No bound state : f0 < a & |0| < |a-f0|

(ii) A bound state out of continuum : f0 > a & |0| > |a-f0|

(iii) 2 bound states on both side of the continuum :

f0 > a & |0| < |a-f0|

Vpd = 0.90 eV

a = 2 eV, 0= 1 eVa = 2 eV, 0= 1 eV

Vpd = 0.90 eV

ResolutionResolutionResolutionResolution

Host Green function

Local Green function

(i) No bound state : f0 < a & |0| < |a-f0|

(ii) A bound state out of continuum : f0 > a & |0| > |a-f0|

(iii) 2 bound states on both side of the continuum :

f0 > a & |0| < |a-f0|

Host Green function

Local Green function

(i) No bound state : f0 < a & |0| < |a-f0|

(ii) A bound state out of continuum : f0 > a & |0| > |a-f0|

(iii) 2 bound states on both side of the continuum :

f0 > a & |0| < |a-f0|

Vpd = 0.90 eV

a = 2 eV, 0= 1 eVa = 2 eV, 0= 1 eV

Vpd = 0.90 eV

ResolutionResolutionResolutionResolution

Host Green function

Local Green function

(i) No bound state : f0 < a & |0| < |a-f0|

(ii) A bound state out of continuum : f0 > a & |0| > |a-f0|

(iii) 2 bound states on both side of the continuum :

f0 > a & |0| < |a-f0|

Host Green function

Local Green function

(i) No bound state : f0 < a & |0| < |a-f0|

(ii) A bound state out of continuum : f0 > a & |0| > |a-f0|

(iii) 2 bound states on both side of the continuum :

f0 > a & |0| < |a-f0|

a = 2 eV, 0= 1 eV

Vpd = 0.90 eV

Formation of a Zhang-Rice SingletFormation of a Zhang-Rice SingletFormation of a Zhang-Rice SingletFormation of a Zhang-Rice Singlet

Condition of formation of a bound state :- Necessary condition for a BS :

f0 > a=W/2 & 0 not too deep

- for ZnO:TM :

Two bound states :

Condition of formation of a bound state :- Necessary condition for a BS :

f0 > a=W/2 & 0 not too deep

- for ZnO:TM :

Two bound states :

ResultsResultsResultsResults

Curve fitting - Results :

- Supercell MnZn31O32 :

- Harrison’s parametrization :

Curve fitting - Results :

- Supercell MnZn31O32 :

- Harrison’s parametrization :

VVpd pd for Host II-VI SCfor Host II-VI SCVVpd pd for Host II-VI SCfor Host II-VI SC

- Host SC DOS - Critical hybridization param. :

- Harrison’s parametrization :

- Host SC DOS - Critical hybridization param. :

- Harrison’s parametrization :

cc

Vacancy in II-VI SC :Vacancy in II-VI SC : ab initio ab initio study studyVacancy in II-VI SC :Vacancy in II-VI SC : ab initio ab initio study study

- Basis set : - NN relaxation :

- Electronic structure :

- LSDA results : E = ELDA-ELSDA

Zn4A3 calc. : Neutral anion vacancy is non-magnetic

- Basis set : - NN relaxation :

- Electronic structure :

- LSDA results : E = ELDA-ELSDA

Zn4A3 calc. : Neutral anion vacancy is non-magnetic

Analytical model Analytical model Analytical model Analytical model

Molecular cluster model : - sp3 molecular orbitals : i (i=1..4)

- Hamiltonian :

Group Theory : SALC of i

- monoelectronic states :

A1 and T2 representations

- polyelectronic states : direct product group

Molecular cluster model : - sp3 molecular orbitals : i (i=1..4)

- Hamiltonian :

Group Theory : SALC of i

- monoelectronic states :

A1 and T2 representations

- polyelectronic states : direct product group

Results Results Results Results Monoparticule eigenenergies :

Biparticle eigenenergies :

= -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)

Monoparticule eigenenergies :

Biparticle eigenenergies :

= -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 VZn

0 in ZnO, S = 1

ConclusionConclusionConclusionConclusion

Mn- and Co-doped DMS– Necessity of taking into account the strong electron correlation on the TM 3d

shell. – The LSDA+U 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)

Mn- and Co-doped DMS– Necessity of taking into account the strong electron correlation on the TM 3d

shell. – The LSDA+U 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)