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 Moore’s 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/ LG<50 nm (~1000 at.) d~LG² MOS FET Fe corral on Au TEM image STM image, IBM

3. Spintronics • 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 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

4. ZB W Basics on II-VI DMS • 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 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 • - 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) LSDA+U

6. d-d 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

7. Supercell approach

8. 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 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)

9. 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 : 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)

10. Spin density Co-O-Co plane, in-plane NN Co-O-Co plane, out-of-plane NN

11. JNN for ZB II-VI DMS • Chemical trends of JNN: Supercells TM2Zn6A8 (ZB) AIIBVI:Mn AIIBVI:Mn - U from Ref. : Gunnarson et al., PRB 40 10407 (1989) - Charge transfer from FPLO :

12. 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

13. LSDA+U DOS

14. LSDA+U DOS

15. LSDA+U DOS

16. LSDA DOS

17. 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 > 0 • too high position of TM 3d level, always a bound state • LSDA+U : formation of a BS & FM DEv if Vpd > Vpd • If U , the occupied 3d levels are shifted by ~ -U/2from VBM , 0 = EBS-Ev • Hyp. : Vpd ≠ f(U) • mm c e l

18. Analytical model • Bethe Lattice Model : - TB Hamiltonian : - Basis set : - Hamiltonian matrix : - Local Creen Funct. : (t2g 3d orb. for TM2+) (t2 p orb. for A2-)

19. Resolution • Host Green function • Local Green function • No bound state : f0 < a & |e0| < |a-f0| • A bound state out of continuum : f0 > a & |e0| > |a-f0| • 2 bound states on both side of the continuum : f0 > a & |e0| < |a-f0| Vpd = 0.90 eV Vpd = 0.90 eV a = 2 eV, e0= 1 eV a = 2 eV, e0= 1 eV

20. Resolution • Host Green function • Local Green function • No bound state : f0 < a & |e0| < |a-f0| • A bound state out of continuum : f0 > a & |e0| > |a-f0| • 2 bound states on both side of the continuum : f0 > a & |e0| < |a-f0| Vpd = 0.90 eV Vpd = 0.90 eV a = 2 eV, e0= 1 eV a = 2 eV, e0= 1 eV

21. Resolution • Host Green function • Local Green function • No bound state : f0 < a & |e0| < |a-f0| • A bound state out of continuum : f0 > a & |e0| > |a-f0| • 2 bound states on both side of the continuum : f0 > a & |e0| < |a-f0| Vpd = 0.90 eV a = 2 eV, e0= 1 eV

22. Formation of a Zhang-Rice Singlet • Condition of formation of a bound state : - Necessary condition for a BS : f0 > a=W/2 & e0 not too deep - for ZnO:TM : • Two bound states :

23. Results • Curve fitting - Results : - Supercell MnZn31O32 : - Harrison’s parametrization :

24. Vpd for Host II-VI SC c - Host SC DOS - Critical hybridization param. : - Harrison’s parametrization :

25. 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

26. Analytical model • Molecular cluster model : - sp3 molecular orbitals : Yi (i=1..4) - Hamiltonian : • Group Theory : SALC of Yi - monoelectronic states : A1 and T2 representations - polyelectronic states : direct product group

27. 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 = 0VZn0 in ZnO, S = 1

28. Conclusion • 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)