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Thomas Chanier ISEN Engineer – PhD student IM2NP, MARSEILLE, France Co-workers : R. Hayn, M. Sargolzaei, I. Opahle, M. Lannoo 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 Electronic structure and magnetic properties of II-VI DMS

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IntroductionIntroduction Failure of Moores 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 Moores 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 L G <50 nm (~1000 at.) STM image, IBM TEM image Fe corral on AuMOS FET d~LG²d~LG²

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SpintronicsSpintronics SpinFET - Datta and Das, APL (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) - New class of DMS ? magnetic intrinsic defects (vacancy, interstitial) Needed : FM at room temperature for spintronic applications SpinFET - Datta and Das, APL (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) - New class of DMS ? magnetic intrinsic defects (vacancy, interstitial) Needed : FM at room temperature for spintronic applications Scientific American

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Basics on II-VI DMS Ref. 1 : Jamieson, J. Phys. Chem. Solids Ref. 2 : CRC Handbook of Chemistry and Physics Ref. 3 : Sabine, Acta Cryst. B Ref. 4 : Reeber, JAP Ref. 5 : Yim, J. Electr Soc Sol-St.Sci. Tech Host SC : covalent bonds Zn 2+ A 2- Substitutional impurity : TM 2+ config. : [Ar] 3d n 4s 0 : - for Co, n=7 S = 3/2 - for Mn, n=5 S = 5/2 ZB : only 1 NN exchange integral J NN W : 2 NN exch. Int. : in-plane J in & out-of-plane J out ZB W

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State of the art l l FM prediction for ZnTMO : - Sato et al., Physica E (2001) LSDA : FM J NN in ZnCoO - Dietl et al., PRB (2001) Zener model, p-type ZnMnO AFM & FM competition for ZnCoO & AFM for ZnMnO : - Lee et al., PRB (2004) - Sluiter et al., PRL (2005) LSDA + pseudopotential BUT : in contrast to experiments Our study : AFM NN exchange constants - LSDA+U : Hubbard-type correction to LSDA AFM J NN T. Chanier et al., PRB (2006) - Predictions confirmed: AFM interactions in ZnCoO, P. Sati et al., PRL (2007) Dietl (2001) Sati (2007) LSDA+U

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d-d exchange Hamiltonian Heisenberg Hamiltonian : J > 0 FM J < 0 AFM Comparison of E in the Heisenberg model with E Total obtained from FM and AFM First-principle calculations : chain : pair : Where S T = 2S the total spin for two magnetic impurities of spin S First-principle calculations : FPLO : full potential local orbital approximation (Koepernic et al., PRB ) LSDA : Perdew-Wang 92 Vxc functional (Perdew and Wang, PRB ) LSDA+U : atomic limit scheme (Anisimov et al., PRB ) No additional carrier codoping Heisenberg Hamiltonian : J > 0 FM J < 0 AFM Comparison of E in the Heisenberg model with E Total obtained from FM and AFM First-principle calculations : chain : pair : Where S T = 2S the total spin for two magnetic impurities of spin S First-principle calculations : FPLO : full potential local orbital approximation (Koepernic et al., PRB ) LSDA : Perdew-Wang 92 Vxc functional (Perdew and Wang, PRB ) LSDA+U : atomic limit scheme (Anisimov et al., PRB ) No additional carrier codoping

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Supercell approach

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Exchange 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 CoO Two realistic values for U = 6 and 8 eV Ref. : Anisimov et al., PRB (1991) Our values : J in = -1.7 ± 0.3 meV, J out = -0.8 ± 0.3 meV Experiments : –Tcw of magnetic susceptibility : J ave = -33 K = -2.8 meV –INS : J in = -2.0 meV, J out = meV Ref. : Yoon et al., JAP (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 CoO Two realistic values for U = 6 and 8 eV Ref. : Anisimov et al., PRB (1991) Our values : J in = -1.7 ± 0.3 meV, J out = -0.8 ± 0.3 meV Experiments : –Tcw of magnetic susceptibility : J ave = -33 K = -2.8 meV –INS : J in = -2.0 meV, J out = meV Ref. : Yoon et al., JAP (2003), Stepanov, private comm. (2008) Ref. 1 : Lee and Chang, PRB (2004) (LSDA, pseudopotential) Ref. 2 : Sluiter et al., PRL (2005) (LSDA, pseudopotential)

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Exchange 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 : J in = -1.8 ± 0.2 meV, J out = -1.1 ± 0.2 meV Experimental values : two values of J (MST) J 1 = meV, J 2 = meV Ref. : Gratens et al., PRB (2004) Ref. 2 : Sluiter et al., PRL (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 : J in = -1.8 ± 0.2 meV, J out = -1.1 ± 0.2 meV Experimental values : two values of J (MST) J 1 = meV, J 2 = meV Ref. : Gratens et al., PRB (2004) Ref. 2 : Sluiter et al., PRL (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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J NN for ZB II-VI DMS Chemical trends of J NN : Supercells TM 2 Zn 6 A 8 (ZB) A II B VI :Mn - U from Ref. : Gunnarson et al., PRB (1989) - Charge transfer from FPLO : A II B VI :Mn

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sp-d exchange constants Chemical trends of N and N : Supercells TMZn 3 A 4 (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 TMZn 3 A 4 (ZB) –Mean Field Approx. : With N the cation concentration sp-d exch cst for CBE and VBH at

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LSDA+U 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 E v = E v - E v > 0 –too high position of TM 3d level, always a bound state LSDA+U : formation of a BS & FM E v if V pd > V pd –If U, the occupied 3d levels are shifted by ~ -U 2 from VBM, 0 = E BS -E v –Hyp. : V pd f(U) –mm The upper VB is formed by a semi-circle of width W LSDA : BS & inverted FM VB spin splitting E v = E v - E v > 0 –too high position of TM 3d level, always a bound state LSDA+U : formation of a BS & FM E v if V pd > V pd –If U, the occupied 3d levels are shifted by ~ -U 2 from VBM, 0 = E BS -E v –Hyp. : V pd f(U) –mm c l

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Analytical 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. : (t 2g 3d orb. for TM 2+ ) (t 2 p orb. for A 2- )

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ResolutionResolution Host Green function Local Green function (i)No bound state : f 0 < a & | 0 | < |a-f 0 | (ii)A bound state out of continuum : f 0 > a & | 0 | > |a-f 0 | (iii)2 bound states on both side of the continuum : f 0 > a & | 0 | < |a-f 0 | Host Green function Local Green function (i)No bound state : f 0 < a & | 0 | < |a-f 0 | (ii)A bound state out of continuum : f 0 > a & | 0 | > |a-f 0 | (iii)2 bound states on both side of the continuum : f 0 > a & | 0 | < |a-f 0 | Vpd = 0.90 eV a = 2 eV, 0 = 1 eV Vpd = 0.90 eV

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ResolutionResolution Host Green function Local Green function (i)No bound state : f 0 < a & | 0 | < |a-f 0 | (ii)A bound state out of continuum : f 0 > a & | 0 | > |a-f 0 | (iii)2 bound states on both side of the continuum : f 0 > a & | 0 | < |a-f 0 | Host Green function Local Green function (i)No bound state : f 0 < a & | 0 | < |a-f 0 | (ii)A bound state out of continuum : f 0 > a & | 0 | > |a-f 0 | (iii)2 bound states on both side of the continuum : f 0 > a & | 0 | < |a-f 0 | Vpd = 0.90 eV a = 2 eV, 0 = 1 eV Vpd = 0.90 eV

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ResolutionResolution Host Green function Local Green function (i)No bound state : f 0 < a & | 0 | < |a-f 0 | (ii)A bound state out of continuum : f 0 > a & | 0 | > |a-f 0 | (iii)2 bound states on both side of the continuum : f 0 > a & | 0 | < |a-f 0 | Host Green function Local Green function (i)No bound state : f 0 < a & | 0 | < |a-f 0 | (ii)A bound state out of continuum : f 0 > a & | 0 | > |a-f 0 | (iii)2 bound states on both side of the continuum : f 0 > a & | 0 | < |a-f 0 | a = 2 eV, 0 = 1 eV Vpd = 0.90 eV

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Formation of a Zhang-Rice Singlet Condition of formation of a bound state : - Necessary condition for a BS : f 0 > 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 : f 0 > a=W/2 & 0 not too deep - for ZnO:TM : Two bound states :

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ResultsResults Curve fitting - Results : - Supercell MnZn 31 O 32 : - Harrisons parametrization : Curve fitting - Results : - Supercell MnZn 31 O 32 : - Harrisons parametrization :

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V pd for Host II-VI SC - Host SC DOS- Critical hybridization param. : - Harrisons parametrization : - Host SC DOS- Critical hybridization param. : - Harrisons parametrization : c

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Vacancy in II-VI SC : ab initio study - Basis set :- NN relaxation : - Electronic structure : - LSDA results : E = E LDA -E LSDA Zn 4 A 3 calc. : Neutral anion vacancy is non-magnetic - Basis set :- NN relaxation : - Electronic structure : - LSDA results : E = E LDA -E LSDA Zn 4 A 3 calc. : Neutral anion vacancy is non-magnetic

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Analytical model Molecular cluster model : - sp 3 molecular orbitals : i (i=1..4) - Hamiltonian : Group Theory : SALC of i - monoelectronic states : A 1 and T 2 representations - polyelectronic states : direct product group Molecular cluster model : - sp 3 molecular orbitals : i (i=1..4) - Hamiltonian : Group Theory : SALC of i - monoelectronic states : A 1 and T 2 representations - polyelectronic states : direct product group

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ResultsResults Monoparticule eigenenergies : Biparticle eigenenergies : = -4 & 4 eV, U = 4 eV, V = 1 eV V Zn 0 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 V Zn 0 in ZnO : S = 1 state characterized by EPR Ref. : D. Galland et al., Phys. Lett. 33A, 1 (1970) V A 0 in ZnO, S = 0 V Zn 0 in ZnO, S = 1

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ConclusionConclusion 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 V pd 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 (2006) ; T. Chanier et al., PRL (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 V pd 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 (2006) ; T. Chanier et al., PRL (2008)

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