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Antônio J. Roque da Silva (IFUSP), Adalberto Fazzio (IFUSP),

Workshop de Nanomagnetismo – 24 e 25/6/2004 Rede Virtual de Nanoci ência e Nanotecnologia do Estado do Rio de Janeiro/FAPERJ. Parametrization of Mn-Mn interactions in Ga 1-x Mn x As semiconductors. Antônio J. Roque da Silva (IFUSP), Adalberto Fazzio (IFUSP),

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Antônio J. Roque da Silva (IFUSP), Adalberto Fazzio (IFUSP),

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  1. Workshop de Nanomagnetismo – 24 e 25/6/2004 Rede Virtual de Nanociência e Nanotecnologia do Estado do Rio de Janeiro/FAPERJ Parametrization of Mn-Mn interactions in Ga1-xMnxAs semiconductors Antônio J. Roque da Silva (IFUSP), Adalberto Fazzio (IFUSP), Raimundo R. dos Santos (UFRJ), and Luiz Eduardo Oliveira (UNICAMP) • Financiamento: • CNPq • FAPERJ • FAPESP • Inst Milênio de Nanociências, • Rede Nacional de Materiais Nanoestruturados

  2. Motivation Combination of semiconductor technology with magnetismshould give rise to new devices: • Spin-polarized electronic transport •  long spin-coherence times (~ 100 ns) have been observed in semiconductors • manipulation of quantum states at a nanoscopic level

  3. Magnetic semiconductors • •Early 60’s: EuO and CdCr2S4 • very hard to grow • Mid-80’s: Diluted Magnetic Semiconductors • II-VI (e.g., CdTe and ZnS) II  Mn • difficult to dope • direct Mn-Mn AFM exchange interaction PM, AFM, or SG (spin glass) behavior • 90’s: • Low T MBE  (In,Mn)As • Uniform (Ga,Mn)As films on GaAs substrates: FM; heterostructures- Possibility of useful devices

  4. Ga1-xMnxAs Ga Ga: [Ar] 3d10 4s2 4p1 Mn: [Ar] 3d5 4s2 Mn atoms: provide both magnetic moments and holes  hole-mediated ferromagnetism As

  5. Ga1-xMnxAs • Resistance measurements on samples with different Mn concentrations: • Metal  R  as T  • Insulator  R  as T  •  Reentrant MIT [Ohno, JMMM 200, 110(1999)]

  6. Reproducibility?

  7. Hole concentration vs Mn concentration 1 hole/Mn atom

  8. 1h/Mn A simple mean field treatment† yields Notice maximum of p(x) within the M phase  correlate with MIT Early predictions log! †[RRdS, LE Oliveira, and J d’Albuquerque e Castro, JPCM (2002)] [Matsukura et al., PRB 57, R2037 (1999)]

  9. Experimental data very sensitive to growth conditions •  what are the dominant mechanisms behind the origin of ferromagnetism in DMS? • how delocalized are the holes (are effective mass theories meaningful)? • what is the effective Mn-Mn interaction? RKKY? • what is the role of disorder? First principles calculations should shed light into these issues

  10. Method Ab initio total energy calculations – DFT -VASP Ultra-soft pseudopotential Supercell calculations – 128/250 atoms (fcc) • Spin polarized • GGA (Perdew, Burke, Ernzerhof) for exchge-correl’n • Plane waves basis set – (cutoff of 230eV, k = L) • Final forces smaller than 0.02 eV/Å

  11. Single Mn atom As Mn Ga

  12. 20.3 Å

  13. Isosurfaces for the net local magnetization MnGa Green=0.004e/A3 Blue= -0.004e/A3 Ground state: quite localized hole interacting antiferromagnetically with S=5/2 of Mn(d 5 )

  14. Fit this energy difference to a Heisenberg interaction: We now consider two Mn atoms per unit cell  Assume all possible non-equivalent positions  For a given relative position, we consider FM and AFM relative Mn orientations, and work out the energy difference thus estimates for J (r1– r2)

  15. Mn Mn As As Mn-Mn 1st NN Ferromagnetic Antiferromagnetic

  16. Mn Mn Mn Mn As As As As Mn-Mn 1st NN Ferromagnetic Antiferromagnetic

  17. Mn Mn Mn Mn As As As As Mn-Mn 1st NN Mn-Mn 2nd NN Mn As Mn As Ferromagnetic Antiferromagnetic

  18. Again, note quite localized character of the holes Mn Mn Mn Mn As As As As Mn-Mn 1st NN Mn-Mn 2nd NN Mn Mn As As Mn Mn As As Ferromagnetic Antiferromagnetic

  19. 24 <211> 12 <110> 6 <100> 8 <111> 24 <310> 12 <110>

  20. 24 8 12 6 24 12 The ferro-antiferro total energy differences yield... the effective coupling between Mn spins (JMn-MnSMn·SMn)

  21. Therefore: • impurity levels are localized • effective-mass picture for holes may be quite inadequate • Mn-Mn interaction mediated by AFM coupling Mn-hole • J Mn-Mn always ferromagnetic  non-RKKY • estimates for anisotropy and direction dependences for effective J Mn-Mn

  22. Our current agenda: • Effects of disorder? • Effects of concentration? •  Preliminary results

  23. J1 J4 J2 Strategy (in principle): Randomly place Mn atoms in the Ga sublattice and use a look up table for J’s Ga Mn

  24. We start with 4 Mn in our 128 atoms supercell: • Roadmap • Randomly place 4 Mn atoms in the Ga sublattice • Calculate, using same ab initio scheme, the total energies for: • (Mn1,Mn2,Mn3,Mn4)=(up,up,up,up) – Ferro • (Mn1,Mn2,Mn3,Mn4)=(down,up,up,up) – Flip Mn1 • (Mn1,Mn2,Mn3,Mn4)=(up,down,up,up) – Flip Mn2 • Etc. • Calculate energy differences E(Flip-Mn1)-Ferro, etc. • Write up same energy differences using an effective Heisenberg Hamiltonian, and extract effective Jn • Compare with previous results with only two Mn

  25. 4 Mn in 128 cell: - disorder inside unit cell - images are taken care of (unwanted order!) - Mn concentration – 0.0625 (6.25 %) - Different from 1 Mn in 32 atoms unit cell or 2 Mn in 64 atoms unit cell Ga Ji J1 Mn

  26. 4 Mn in 128 atoms unit cell Ab initio results Ferro = -553.737 eV Flip 1 = -553.547 eV Flip 2 = -553.586 eV Flip 3 = -553.302 eV Flip 4 = -553.508 eV Ferro - lowest energy configuration 1-Ferro = 0.190 eV 2-Ferro = 0.151 eV 3-Ferro = 0.435 eV 4-Ferro = 0.229 eV

  27. 4 Mn in 128 atoms unit cell Heisenberg Hamiltonian results For the particular realization, the Hamiltonian is Ferro = Flip 1 = Flip 2 = Flip 3 = Flip 4 = 1-Ferro = 2-Ferro = 3-Ferro = 4-Ferro =

  28. 2 Mn in 128 atoms unit cell Classical x Quantum Heisenberg Hamiltonian results J (meV) Same trend, Classical or Quantum

  29. 2 Mn x 4 Mn in 128 atoms unit cell Classical Heisenberg Hamiltonian J (meV)

  30. 2 Mn x 4 Mn in 128 atoms unit cell Classical Heisenberg Hamiltonian J (meV)

  31. 2 Mn x 3Mn x 4 Mn in 128 atoms unit cell Classical Heisenberg Hamiltonian 2Mn: x = 0.03125 3Mn: x = 0.046875 4Mn: x = 0.0625 J (meV)

  32. 2 Mn x 3Mn x 4 Mn in 128 atoms unit cell • Large reduction in the values of some of the J’s • – Possible reasons: • Effective Heisenberg Hamiltonian may not be appropriate to describe “magnetic” excitations • Effective Hamiltonian ok to describe low-energy magnetic excitations, but our spin flip excitations may have too high an energy (non-collinear spin ab initio calculations?) • Disorder and/or concentration may have an important effect in the effective J couplings

  33. Next steps (1): • Perform more calculations with random structures – obtain a distribution for effective J’s • Perform similar calculations for different Mn concentrations • Non-collinear spin calculations • If we conclude that we have a physically correct description through effective J’s + classical Heisenberg Hamiltonian, perform calculations for T > 0 (Monte Carlo) Next steps (2): • Study (ab initio) how defects (e.g., interstitial Mn) change this picture by placing them in the, for example, 4 Mn in 128 atoms supercell – local disorder + defects

  34. Conclusions: • Effective mass descriptions (and improvements thereof) not reliable • Effective Mn-Mn interactions not RKKY • Disorder strongly influences effective Mn-Mn interactions; simple model? • Heterostructures: -doping, Be co-doping

  35. Mn-hole exchange coupling Jhd = 0.083 eV; 250 atoms, x = 0.008 Jhd = 0.11 eV; 128 atoms, x = 0.0156

  36. We have performed total energy calculations based on the density-functional theory (DFT) within the generalized-gradient approximation (GCA) for the exchange-correlation potential. • The electron-ion interactions are described using ultra-soft pseudopotentials and plane wave expansion up to 200 eV as implemented in the VASP code. • We used a 128-atom and 250-atom fcc supercell and the L-point for the Brillouin sampling. The positions of all atoms in the supercell were relaxed until all the force components were smaller than 0.05 eV/Å.

  37. Isosurfaces for the difference between calculated for the MnGa ground state and the GaAs host

  38. m(r) = (r)-(r) m(r) = +0.5 e-/Å3

  39. Sub-Si n=p

  40. n.5p.oo5

  41. t2 As As As Ga a1 As As t2 As As a1 As t2 As e t2 As As Mn a1 As

  42. F. Matsukura, H. Ohno, A. Shen, and Y. Sugawara, Phys. Rev. B 57, R2037 (1998) • MBE at low growth T (200 - 300 OC) on GaAs (001) substrates • x = 0.015 – 0.071 • 200 nm thick Ga1-xMnxAs samples • A. van Esch et al, PRB 56, 13103 (1997) • Ga1-xMnx As layers grown on GaAs (100) substrates • GaAs grown by MBE at low temperatures (200 – 300 OC) • samples of 3 m thick with Mn concentrations up to 9% • K. W. Edmonds et al, APL 81, 3010 (2002) • metallic behavior for 0.015 x  0.08 • Ga1-xMnxAs layers grown on semi-insulating GaAs (001) substrates by low-temperature (180 – 300 OC) MBE using As2 • samples: 45 nm thick • S. J. Potashnik et al, APL 79, 1495 (2001) • temperature during growth:  250 OC • Ga1-xMnxAs layers: thicknesses in range 110 – 140 nm

  43. M. J. Seong et al, PRB 66, 033202 (2002) • samples grown as in Potashnik et al:  250 OC and  120 nm • used a Raman-scattering intensity analysis of the coupled plasmon-LO phonon mode • and the unscreened LO phonon. • H. Asklund et al, PRB 66, 115319 (2002) • angle-resolved photoemission; 1% - 6% • growth temperature of LT-GaAs and GaMnAs was typically 220 0C • Mn concentrations accurate within 0.5 % • NOTE THAT • T. Hayashi et al, APL 78, 1691 (2001) • “a 10 oC difference in the substrate temperature during growth can lead to a • considerable difference in the transport properties as well as in magnetism even • though there is no difference in the growth mode as observed by electron diffraction

  44. 2 Mn atoms as nearest-neighbors (Ga sub-lattice) m(r) = -0.004 e-/Å3 m(r) = +0.004 e-/Å3 Antiferromagnetic coupling

  45. VERY DILUTED DOPING LIMIT: Mn FORMS ACCEPTOR LEVEL 110 meV ABOVE VALENCE BAND • ANGLE-RESOLVED PHOTOEMISSION SPECTROSCOPY OBSERVES IMPURITY BAND NEAR EF. • INFRARED MEASUREMENTS OF THE ABSORPTION COEFFICIENT ALSO REVEAL A STRONG RESONANCE NEAR THE ENERGY OF THE Mn ACCEPTOR IN GaAs. • E. J. Singley, R. Kawakami, D. D. Awschalom, and D. N. Basov, PRL 89, 097203 (02) conductivity data: estimate the effective mass to be 0.7 mo < m* < 15 mo for the x = 0.052 sample, and larger at all other dopings, which suggest that the carriers do not simply reside in the unaltered GaAs valence band

  46. favor a picture of the electronic structure involving impurity states at EF rather than of holes doped into an unaltered GaAs valence band work obtained by using “complete” Kohn-Luttinger formalism (magnetic anisotropy, strain, etc): • M. Abolfath, T. Jungwirth, J. Brum, and A. H. MacDonald, PRB 63, 054418 (2001). • T. Dietl, H. Ohno, and F. Matsukura, PRB 63, 195205 (2001).

  47. Isosurfaces for the net local magnetization: two MnGa defects Mn Mn As As Green=0.004e/A Blue= -0.004e/A Mn-Mn 1st nn Mn Mn As As In (a) and (b) the two Mn are nearest neighbors with their S=5/2 spins alligned parallel and antiparallel, respectively

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