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UCSD
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Tailoring spin interactions in artificial structures Joaquín Fernández-Rossier Work supported by and Spanish Ministry of Education
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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).
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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
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Localized magnetic moments + itinerant carriers : Kondo effect, ferromagnetism Artificial structures shape wave function of itinerant carriers: new physics, new devices. Main Ideas
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Motivation Information technology trend: making smaller devices New strategies: spintronics Fun: exciting new physics
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Outline of the first part Introduction –Main facts –Motivation –Origin of ferromagnetism Heterostructures –Experiments –Our theory: model and results Conclusions
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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
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Doping GaAs with Mn : 1) Mn is an acceptor 2) Mn has a magnetic moment ( 5/2 ? ) Ga Mn Acceptor Magnetic Moment
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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
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Digital Multilayer R. K. Kawakami et al., J. Appl. Phys., 87, 379 2000).
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Low energy 2 Mn, 1 hole 1 donor The origin of ferromagnetism 1 Mn, 1 hole High energy RKKY Low density of holes
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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)
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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
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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, )
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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
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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
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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 )
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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%
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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
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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
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-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 !!!
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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
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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
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STM BASICS 1) READ : measure I(V,x,y,z) 2) WRITE
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The Kondo effect Cobalt Conduction electrons screen the magnetic moment of the impurity Collective many body state: Enhancement of DOS at E F
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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)
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Elliptical Quantum Corral H.C. Manoharan, C.P. Lutz and D. Eigler, Nature 403,512 (2000) QUANTUM MIRAGE Kondo dip Phantom dip
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10Å 80Å
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The questions What is the explanation? –Black box Green function theory –Hand-waving explanation Is the ellipse necessary?
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t Black Box Theory Surface electrons Impurity electrons Coupling
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The Ellipse LDOS LDOS(E F ) LDOS in the foci
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Decays for (|R-R I| ) >>k F -1 10 Å
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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)
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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.
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Exchange Interaction Coulomb Exchange: ferromagnetic (Reduction of Coulomb repulsion ) Kinetic Exchange: Antiferromagnetic d5d5 d6d6 AsMn d5d5 d6d6 AsMn
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Cobalt Copper
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