1. UCSD

2. Tailoring spin interactions in artificial structures Joaquín Fernández-Rossier Work supported by and Spanish Ministry of Education

3. Part 1: theory ferromagnetic semicondutor heterostructures 2D structures of ferromagnetic semiconductor (Ga,Mn) As with L.J. Sham (UCSD) GaAsMn GaAs Experiment R. K. Kawakami et al., J. Appl. Phys., 87, 379 2000).

4. Part 2: Theory of the quantum mirage Phys. Rev. B. 63, 155406 (2001) With Diego Porras (UAM) Experiment: H.C. Manoharan,C.P. Lutz and D. Eigler, Nature 403,512 (2000) Cu(111) Cobalt Quantum Mirage Kondo effect in a quantum corral in a metallic surface

5. Localized magnetic moments + itinerant carriers : Kondo effect, ferromagnetism Artificial structures shape wave function of itinerant carriers: new physics, new devices. Main Ideas

6. Motivation Information technology trend: making smaller devices New strategies: spintronics Fun: exciting new physics

7. Outline of the first part Introduction –Main facts –Motivation –Origin of ferromagnetism Heterostructures –Experiments –Our theory: model and results Conclusions

8. Material: Ga (1-x) AsMn x Ferromagnetic below 110 kelvin Homogeneous alloy for x<0.08 Transport: p-doped semiconductor (p<c Mn ) FERRO PARA

9. Doping GaAs with Mn : 1) Mn is an acceptor 2) Mn has a magnetic moment ( 5/2 ? ) Ga Mn Acceptor Magnetic Moment

10. Motivation 3 things you can do with GaAsMn (better than with Fe) 1.Ferromagnetic-Semiconductor heterostructures 2.Electrical Control of Curie Temperature 3.Spin injection in a semiconductor

11. Digital Multilayer R. K. Kawakami et al., J. Appl. Phys., 87, 379 2000).

12. Low energy 2 Mn, 1 hole 1 donor The origin of ferromagnetism 1 Mn, 1 hole High energy RKKY Low density of holes

13. Itinerant holes, effective mass approximation Localized d electrons Local hole-Mn exchange interaction Virtual Crystal approximation Mean Field approximation The ‘standard’ model k.p Luttinger holes (SPIN-ORBIT) Spin wave fluctuations (beyond mean field theory)

14. Our model for heterostructures 1.Calculation of the electronic structure of the heterostructure (self- consistent Poisson-Schrödinger multi sub-band approach). Calculation of the non-local spin susceptibility 2.T C : Solution of an integral equation

15. Modeling for Delta Doping 1c Mn =2 10 14 cm -2 3 Gaussian distribution Of impurities:  p=2 10 13 cm -2 Mn=Comp+ Holes 2 -60-40-2002040 60 0 Holes Impurities (Mn+comp) Gaussian:  (c Mn, p,  )

16. Self consistent Electronic Structure -60-40-2002040 60 0 Holes Impurities (Mn+comp) 200 00.050.1 k || (A ) 0 50 100 150 -100-50050 z(A) 0 50 100 150 200 Energy (meV) hh lh Envelope function Kohn-Luttinger Hamiltonian Spin-Orbit Interaction D=5 A. p=2.5 10 13 cm -2 c Mn =2 10 14 cm -2

17. Mean Field Critical Temperature S=5/2 x= Mn Concentration J= Exchange constant  = Spin Susceptibility of bare GaAs T c does not depend on the sign of J T c is linearly proportional to c Mn T c depends A LOT on |J| T c is hole density dependent PLANAR HETEROSTRUCTURE BULK

18. J=150 mev nm 3 c Mn =2 10 14 cm -2 Single layer results 0 1e+142e+14 0 50 100 150 200  =5A  =10A  =15A  =20A Critical Temperature (K)  =0 Density of Holes (cm -2 )

19. 0 1e+14 2e+14 0 5 10 15 20 Critical Temperature (K)  (A) Density of Holes (cm -2 ) Tc=35 Kelvin Impurities Holes 05101520  (A) 0 50 100 150 75% 50% 40% 20% 10%

20. T C (K) -150-5050150 10 ML 20ML 40ML -150-5050150 0 2e-05 4e-05 6e-05 8e-05 0.00010 2e-05 4e-05 6e-05 8e-05 0.00010 2e-05 4e-05 6e-05 8e-05 0.0001  =5 A. p=2.5 10 13 cm -2 01020304050 30 40 50 60 Theory EXPERIMENT Interlayer Distance (ML) 1020304050 30 40 50 60  =15 A, p=8 10 13 cm -2 T C (K) Interlayer Distance (ML) 10 ML 20 ML 40 ML

21. Engineering T c : Digital layer in a QW -50050 z (A) -300 -200 -100 0 100 V (meV) V} Ga 1-x Al x As

22. -50050 0 5e+11 1e+12 Density (cm -3 ) 0 5e+11 1e+12 Density (cm -3 ) -50050 Position (Amstrongs) -50050 0100200300400500 V (meV) 30 40 50 60 70 80 T c (kelvin) Density profiles for different barrier heights (V) T c vs barrier height DOUBLING T c !!!

23. Conclusions (Part I) GaAsMn is a ferromagnetic semiconductor. Exchange and itinerant carriers produce Ferromagnetism Planar heterostructures of GaAsMn: –Tailoring Mn-hole interaction and T C – Promising for new physics and devices

24. Part 2: Theory of the quantum mirage Phys. Rev. B. 63, 155406 (2001) With Diego Porras (UAM) Experiment: H.C. Manoharan,C.P. Lutz and D. Eigler, Nature 403,512 (2000) Cu(111) Cobalt Quantum Mirage Kondo effect in a quantum corral in a metallic surface

25. STM BASICS 1) READ : measure I(V,x,y,z) 2) WRITE

26. The Kondo effect Cobalt Conduction electrons screen the magnetic moment of the impurity Collective many body state: Enhancement of DOS at E F

27. Single magnetic atom in a surface H.C. Manoharan, C.P. Lutz and D. Eigler, Nature 403,512 (2000) V. Madhavan et. al., SCIENCE 280, 567(1998)

28. Elliptical Quantum Corral H.C. Manoharan, C.P. Lutz and D. Eigler, Nature 403,512 (2000) QUANTUM MIRAGE Kondo dip Phantom dip

29. 10Å 80Å

30. The questions What is the explanation? –Black box Green function theory –Hand-waving explanation Is the ellipse necessary?

31. t Black Box Theory Surface electrons Impurity electrons Coupling

32. The Ellipse LDOS LDOS(E F ) LDOS in the foci

33. Decays for (|R-R I| ) >>k F -1  10 Å

34. EXPERIMENTS H.C. Manoharan, C.P. Lutz and D. Eigler, Nature 403,512 (2000) Our theory D. Porras, J.Fernandez-Rossier and C. Tejedor Phys. Rev. B. 63, 155406 (2001)

35. Summary part II Mirage: projection of the local Kondo resonance to a ‘remote’ location Explanation: Single ‘confined’ state at the Fermi level carries information. No destructive interference. Ellipse: convenient, not necessary. ‘Semiclassical geometrical interpretation’: not needed.

36. Exchange Interaction Coulomb Exchange: ferromagnetic (Reduction of Coulomb repulsion ) Kinetic Exchange: Antiferromagnetic d5d5 d6d6 AsMn d5d5 d6d6 AsMn

37. Cobalt Copper