UCSD

1. UCSD

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

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

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

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

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) AsMnx • Ferromagnetic below 110 kelvin • Homogeneous alloy for x<0.08 • Transport: p-doped semiconductor (p<cMn) PARA FERRO

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

10. Motivation3 things you can do with GaAsMn (better than with Fe) • Ferromagnetic-Semiconductor heterostructures • Electrical Control of Curie Temperature • Spin injection in a semiconductor

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

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

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

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

15. Impurities (Mn+comp) Gaussian: 1 cMn=2 1014 cm-2 0 2 Mn=Comp+ Holes 60 -60 -40 -20 0 20 40 p=2 1013 cm-2 Gaussian distribution Of impurities: 3 Modeling for Delta Doping Holes (cMn, p, )

16. 0 60 -60 -40 -20 0 20 40 200 200 150 150 hh Energy (meV) 100 100 lh • Envelope function • Kohn-Luttinger Hamiltonian • Spin-Orbit Interaction 50 50 hh 0 0 -100 -50 0 50 0 0.05 0.1 -1 k (A ) z(A) || Self consistent Electronic Structure Impurities (Mn+comp) Holes • =5 A. p=2.5 1013 cm-2 cMn=2 1014 cm-2

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

18. Single layer results 200  =0 150  =5A Critical Temperature (K) 100  =10A  =15A 50  =20A 0 0 1e+14 2e+14 Density of Holes (cm-2) J=150 mev nm3 cMn=2 1014 cm-2

19. -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 Tc=35 Kelvin 75% 150 50% 20 40% 20% 10% 15 100 Critical Temperature (K) (A) 10 50 5 0 0 0 2e+14 1e+14 0 5 10 15 20 (A) Density of Holes (cm-2) Impurities Holes Holes

20. 60  =5 A. p=2.5 1013 cm-2 Theory 0.0001 EXPERIMENT 10 ML 8e-05 50 6e-05 4e-05 TC (K) 2e-05 0.0001 0 8e-05 20 ML 40 6e-05 4e-05 2e-05 0.0001 0 8e-05 40 ML 6e-05 30 4e-05 0 10 20 30 40 50 2e-05 Interlayer Distance (ML) 0 -150 -50 50 150 60  =15 A, p=8 1013 cm-2 10 ML 50 TC (K) 40 20ML 30 40ML 10 20 30 40 50 Interlayer Distance (ML) -150 -50 50 150

21. Engineering Tc: Digital layer in a QW Ga1-xAlxAs 100 0 V (meV) V} -100 -200 -300 -50 0 50 z (A)

22. Density profiles for different barrier heights (V) Tc vs barrier height 80 ) -3 1e+12 70 Tc (kelvin) Density (cm 5e+11 60 50 0 ) -3 40 1e+12 30 Density (cm 5e+11 0 100 200 300 400 500 V (meV) 0 -50 0 50 -50 0 50 -50 0 50 DOUBLING Tc !!! Position (Amstrongs)

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

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

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

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

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

29. 10Å 80Å

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

31. Surface electrons Impurity electrons Coupling t Black Box Theory

32. The Ellipse LDOS LDOS(EF) LDOS in the foci

33. Decays for (|R-RI|) >>kF-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. d6 d6 d5 d5 As Mn As Mn Exchange Interaction • Coulomb Exchange: ferromagnetic (Reduction of Coulomb repulsion ) • Kinetic Exchange: Antiferromagnetic

37. Copper Cobalt