Spin electronics at the nanoscale Michel Viret Service de Physique de l Etat Condensé CEA Saclay France
Principles of spin electronics: ferromagnetic metals spin accumulation Resistivity of homogeneous materials: AMR DWR Spin torque in DWs Reduced dimensions: Mesoscopic transport Atomic MR
Spin dependent electrical transport in ferromagnetic metals Different DOS for up and down spins : spin up E Spin down Transport is dominated by s electrons scattered into d bands d bands split by the exchange energy diffusion is spin dependent d bands s bands Two current model : Two conduction channels in parallel withρ ρ Resistivity : ρ= ρ ρ ρ ρ + s electrons : low density of states + high mobility d electrons : large density of states + low mobility or (with spin-flip) : ρ= ρ ρ ρ + + ρ ρ ( + ρ 4 ρ + ρ )
Current generated spin accumulation at a Ferro (Co) / Normal metal (Cu) interface: Typically, at 4.2 K : l sf (Co) 60 nm l sf (Cu) 500 nm
Introduction to spin electronics + - Conf igurat ion P M NM M R+= r r r + - Configuration AP M NM M R+ = (r +R)/ 2 r R Multilayers F metal / NM metal (ex : Fe / Cr, Co / Cu, etc ) V I 4 K R R R r R- = R R- = (R+r)/ 2 80% R P = Rr R + r r < R + R AP = 4 r GMR = R R AP R P P H (koe)
Example of FePd: Domain wall resistance 8.088 ρ CPW MFM image 2 x 2 µm 2 at zero field, in the virgin state and after saturation. The up domains are black and the down ones are white ρ (µωcm) 8.064 8.040 8.016 ρ CIW Resistive measurements : on a nanostructure with stripe width = 300nm 7.992 0.5 R/R = 8 % within the DWs Why is it so small? H (R. Danneau et al., Phys. Rev. Lett. 88, 157201 (2002))
Theory Spin transfer from the conduction electrons to the DW Two kinds of electrons: Current direction Localised Conduction electrons s-d Hamiltonian Action of a current: Globally, the conduction electrons transfer gµ B to the DW
Simple model : the particle approach s-d Hamiltonian : Precession equation : ( ) s : conduction electrons : localised spins In the rotating frame:
Spin evolution during DW crossing In the laboratory frame In the frame of the local moment : Local Moment φ 0 Electron spin
Spin evolution during DW crossing In the laboratory frame In the frame of the local moment : Local Moment φ 0 Electron spin
In the frame of the Spin local evolution moment during DW crossing direction : In the laboratory frame Local Moment φ 0 In the frame of the local moment : Electron spin R R ηvf φ0 = δ J w ex w 2 p F 1 = 2 2 (1 p ) J ex δ w Local Moment η v φ 0 Electron spin
In the frame of the Spin local evolution moment during DW crossing direction : In the laboratory frame Local Moment φ 0 In the frame of the local moment : Electron spin R R ηvf φ0 = δ J w ex w 2 p F 1 = 2 2 (1 p ) J ex δ w Local Moment η v φ 0 Electron spin
In the frame of the Spin local evolution moment during DW crossing direction : In the laboratory frame Local Moment φ 0 In the frame of the local moment : Electron spin R R ηvf φ0 = δ J w ex w 2 p F 1 = 2 2 (1 p ) J ex δ w Local Moment η v φ 0 Electron spin
In the frame of the Spin local evolution moment during DW crossing direction : In the laboratory frame Local Moment φ 0 In the frame of the local moment : Electron spin R R ηvf φ0 = δ J w ex w 2 p F 1 = 2 2 (1 p ) J ex δ w Local Moment η v φ 0 Electron spin
Spin evolution during DW crossing In the laboratory frame In the frame of the local moment : Local Moment φ 0 Electron spin
Spin evolution during DW crossing In the laboratory frame In the frame of the local moment : Local Moment φ 0 Electron spin
Spin evolution during DW crossing In the laboratory frame In the frame of the local moment : Local Moment φ 0 Electron spin
Spin evolution during DW crossing In the laboratory frame In the frame of the local moment : Local Moment φ 0 Electron spin
For a long wall and Precession around the effective field : Rotating frame Magnetisation Magnetic moment Laboratory frame The mistracking angle is small (a few degrees) and the induced spin scattering is weak Direction of electron propagation
Reaction on the wall Effect of the current : Globally, the conduction electrons transfer gµ B to the DW Spin torque The total moment is conserved The torque can be decomposed into a constant and periodic part For long walls, the periodic part averages to zero and the constant part reads: P = polarisation, j = current density Conclusions : distortion (steady state) pressure Torques: non-homogeneous within the walls + small pressure term Importance of the magnetic structure of the DW Very thin DWs: Enhanced pressure oscillating with thickness
Preliminary conclusions Question: Can we build spin electronics devices with domain walls? DW: topological soliton which can be moved by a current and which scatters electrons Russel Cowburn (Durham/London) : magnetic logic based on DWs Stuart Parkin (IBM San Jose) : registery memory Problems: DWs are not very resistive and cannot be pushed by small currents Solution : 1D structures
Different transport regimes Ohm s law: I = G V G = σ S / L if L >> l F Fermi wavelength (quantum) l mean free path (elastic) L j coherence length (inelastic) atomic ballistic diffusive macroscopic
Magnetoresistance in reduced dimensions: the constriction Perfect case: continuous materials of cross section close to λ F (ex: 2DEG) : k quantized conductance quantized : G = ΣT i G 0 (G 0 = e 2 /h = 1/26kOhm) 2D electron gases : σ quantized in units of 2G 0, but large H : quantization in G 0 + magnetism : Spin degeneracy removed by the exchange energy Fermi wavelength for up and down electrons the size of the constriction at which the number of transmitted channels changes is spin dependent H = k k perp, long = = 2 η 2m 2π n. d 2m 2 η * 2 + V ( E F ( r ) + J ± E ex ex. σ ) k 2 perp N N
Introduction of a DW in a constriction (ideal case) : DW width = size of constriction (P. Bruno, PRL83, 2425 (1999), Y. Labaye et al., J.A.P.91, 5341 (2002)) Constricted DW width constriction diameter or length + Potential barrier of magnetic (exchange) origin (Imamura et al. PRL 84, 1003 (2000)) : large MR effects because a DW can close the conductance channel. Closer to real life : Metals : λ F 2Å quantization requires atomic contacts! Conducting channels defined by overlap of atomic orbitals atomic calculation needed + In the single atomic regime more than one conduction channels are opened for 3d elements. Ni: 4s 2 3d 8 potentially 4 + 6 channels Magnetic problems : DWs not infinitely thin: Micromagnetic configuration of the relevant atoms? Experimental problems : Magnetostriction?? For Ni : λ -40 ppm 100 µm wire shrinks by 4 nm!
Break junction technique : MR in ferromagnetic atomic contacts Samples : ferromagnetic bridges suspended with pads of different shapes made in polycrystalline Ni, Co, Fe : Micromagnetics: Program OOMMF (NIST)
Bending system in a cryostat Pulling 1 nm/turn Experimental setup
H. Ohnishi, Y. Kondo and K. Takayanagi, Nature 295, 780 (1998) TEM pictures while pulling an Au tip from a Au film :
Measurements : breaking (e 2 /h) 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0-1 -0.8-0.6-0.4-0.2 0 0.2 d (nm) ln(r) 11 10 9 8 7 6 5 4 3 Tunneling regime - H=0.4T perp 0 0.01 0.02 0.03 0.04 0.05 gap (nm) Conductance steps : atomic reorganization (+ quantization) Tunnelling : R = R 0 exp(x/x 0 ), x 0 =0.045 nm
Two types of measurements R(θ) AMR: 1.2 Resistance 1 0.8 0.6 0.4 0.2 0-90 -60-30 0 30 60 90 120 150 180 210 240 270 Angle (degree) R(Η) DWR :
Atomic contact regime (Fe, 4.2K) R(θ) curves : 1 8 0 0 0 1 7 0 0 0 1 6 0 0 0 1 5 0 0 0 1 4 0 0 0 Atomic contact: R/R min = 75% Significant effect Clear departure from cos 2 (θ) 1 3 0 0 0 1 2 0 0 0 1 1 0 0 0 1 0 0 0 0 9 0 0 0 3e 2 /h R (Ohm) 8800 8600 8400 8200 2T, Vdc=0mV R ( O h m ) 8 8 0 0 8 6 0 0 8 4 0 0 8 2 0 0 8 0 0 0 7 8 0 0 Atomic contact: R/R min = 21% 8000 7 6 0 0 7800 7 4 0 0 7600 7 2 0 0 3.5e 2 /h 7400 7200 angle ( ) 7000-100 -50 0 50 100 150 200 7 0 6 7 0 4 Nanostructure: R/R min = 1.1% Channels closing? 7 0 2 Parallel with evolution of conductance with stretching 7 0 0 6 9 8-9 0-6 0-3 0 0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 0 A n g l e ( d e g r e e )
Tentative explanation of the AMR effects : Orbitals overlap responsible for the opened channels Distortion with field because of spin-orbit coupling? + enhanced effects in reduced dimensions
Ab-initio calculations Pseudo potential plane wave method + spin-orbit coupling Fe atomic chain: magnetisation parallel and perpendicular Tight binding calculations fcc (111) bcc (001) The exact geometry of the contact is important, especially the coordination number of the central atom.
Tunnelling regime, Fe (4.2K) : Measurements quite erratic because different configurations can give the same resistance AMR still large in tunnelling Tunnelling defined by the overlap of evanescent orbitals Spin-orbit coupling of the same nature but on the evanescent orbitals
Summary of AMR measurements in Fe
Domain wall effects 6.6 6.55 Fe (4.2K) R(kohms) R(kohms) 6.5 6.45 6.4 6.35 6.3 6.25 6.2-60 -40-20 0 20 40 60 80 100 120 140 160 180 200 Angle(degrees) 90 <--180 7.1 7 6.9 6.8 6.7 6.6 6.5 6.4 6.3 6.2-2.5-1.5-0.5 H(T) 0.5 1.5 2.5 7.6 DWR 10% 20% Co (4.2K) 37 36 R(kohms) 7.4 7.2 7 6.8 6.6 12% 180 R(kohms) 35 34 33 32 31 30 21% 90 6.4 90 6.2 6-2.5-2 -1.5-1 -0.5 0 0.5 1 1.5 2 2.5 H(T) 29 28 180 27-0.3-0.2-0.1 0 0.1 0.2 0.3 H(T)
Electric field effects, Fe (4.2K): E-field efects 4700 R (Ohm) field at 0 4600 4500 4400 4300 4200 4100 4000 3900 3800 Vdc=100mV Vdc=50mV Vdc=0 differential conductance for two different magnetic configurations 3700-0.3-0.2-0.1 0 0.1 0.2 0.3 H (T) 17000 H=1T 16000 di/dv (Ohm) 15000 14000 13000 12000 11000 H=0 10000 9000 8000-0.12-0.1-0.08-0.06-0.04-0.02 0 0.02 0.04 0.06 0.08 Vbias (V) Effect of the electric field: Evidence for spin torque? At 50mV, j 5 10 8 A/cm 2
Conclusions for the MR at the atomic scale Contact: AAMR : 50 % DWR : 20% AAMR>DWR conductance depends on orbital overlap S-O coupling = atomic AMR effect In reduced dimensions: large S + large O! Tunnelling TAMR : 100 % TMR : 35% TAMR>TMR tunnelling AMR : same with evanescent orbitals See: M. Viret et al., Eur. Phys. J. B 51, 1 (2006)
Conclusions Can DWs be used for spin electronics? In the bulk : DW resistance too small + current induced pressure too weak In atomic constrictions: Importance of orbital effects (AMR) DW Resistance enhanced (20%) Pushing with a current impossible (destruction of the contacts) The ideal : 1D atomic chains