Spin-dependent transport in layered magnetic metals Patrick Bruno Max-Planck-Institut für Mikrostrukturphysik, Halle, Germany Summary: introduction: what is spin-electronics giant magnetoresistance (GMR) tunneling magnetoresistance (TMR) hot-electron spin-transistor magnetization switching due to spin-injection ab initio calculations of perpendicular current GMR domain wall magnetoresistance theory of TMR introduction: what is spin-electronics?
what is an electron? particle with negative electric charge q=-e and spin 1/2 (magnetic moment m=µ B ) - - - - - - - + = - - - - - - - electron as seen by an electronician: - - - - - - - electronics = manipulation of electrons by using their charge for storage and processing of information the spin is (almost) completely neglected
principal electronic device: MOSFET source metallic gate oxide drain (SiO 2 ) application: logic gates random access memory inconvenients: volatility of the information energy consumption limited density of information semi-conductor (Si) + - metallic gate conducting channel (2D electron gas) transistor blocked electron as seen by a magnetician: - - - - - - - purpose of magnetism: develop materials in which the electron spins tend to align parallel to each (magnets) the charge of the electrons plays a secondary role
application: mass storage of information (magnetic disks and tapes) advantages: non-volatility high storage density no energy consumption inconvenients: mechanical access to information Purpose of spin-electronics: ``Teaching electrons new tricks combine electronics and magnetism in order to make new devices in which both the charge and the spin oftheelectronplayanactiverole new fundamental physical questions new phenomena new devices and applications
giant-magnetoresistance Giant magneto-resistance (GMR) Baibich et al., PRL 61, 2472 (1988) Binasch et al., PRB 39, 4828 (1989) ferromagnetic metal (Fe, Co,...) current in-plane (CIP) non-magnetic metal (Cu, Ru,...) current perpendicular to the plane (CPP)
definition conventions for the magnetoresistance ratio R RAP R A = P RP ``optimistic definition RAP R A = P RAP ``pessimistic definition H R A = AP RAP RP + RP reasonable definition interlayer exchange coupling Ni 80 Co 20 /Ru/Ni 80 Co 20 Parkin and Mauri, PRB 44, 7131 (1991)
Co / Ru / Co Parkin et al., PRL 64, 2304 (1990) GMR without interlayer exchange coupling Co / Au / Co / Au(111) T =80K T =130K Barnas et al., Vacuum 41, 1241 (1990)
Exchange biasing to an antiferromagnet FM NM FM AF interfacial exchange interaction FeNi Cu FeNi FeMn Diény et al., PRB 43, 1297 (1991)
Biasing by artificial antiferromagnet free FM layer pinned FM layer weak coupling artificial AF strong AF coupling Applications of GMR: reading head for magnetic disks
Evolution of magnetic storage density 1GBytedrive mechanism of GMR: spin-dependent scattering two-current model ferromagnetic (F) configuration R F < R AF antiferromagnetic (AF) configuration RAF R A F can be larger than 50% RAF + RF
spin-dependent scattering probability E E P > P P > P DOS DOS
Fe 1-x V x /Au/Co x=0 x=0.3 x = 0.18 x=0.3 Renard et al., PRB 51, 12821 (1995) tunneling-magnetoresistance
Tunneling magneto-resistance (TMR) Jullière, Phys. Lett. 54A, 225 (1975) Moodera et al., PRL 74, 3273 (1995) insulating barrier θ ferromagnetic electrodes Mechanism of tunneling magneto-resistance parallel (P) configuration G P > G AP antiparallel (AP) configuration
Applications of TMR: magnetic random access memories (M-RAM) "bit" lines tunnel barrier FM electrodes "word" lines hot-electron spin-transistor
hot-electron spin-transistor Monsma et al. PRL 74, 5260 (1995) Science 281, 407 (1998)
magnetization switching due to spin-injection Magnetization switching due to spin-injection
AF differential resistance F current density Myers et al., Science 285, 867 (1999) Katine et al., PRL 84, 3149 (2000) ab initio calculations of perpendicular current GMR
model considered: ideal lead M central region (disorder,...) ideal lead y x z M L current periodic repetition of the supercell in x and y directions Conductances within the Landauer-Büttiker formalism C = C + C (spin-colinear case) 0 1 N N+1 2 σ e 1 C = h N// σ T ( k//, εf ) k // transmittance for spin σ, wavevector k // and energy ε F : [ Γ + Γ 1 G N G ] σ T ( k //, εf ) = Tr 1, N N1 H + 0,1 G H 1, N N, N + 1 (0)+ G 0,0 (0) + G N+ 1N, + 1 (0) + (0) ( G G ) 0, 1 Γ 1 = i H1,0 0,0 0,0 H
recursive calculation of the Green s function + calculation of the surface Green s function: layer addition (or removal) invariance self-consistent (Dyson-like) equation Computational details: density functional theory (local density approximation) TB-LMTO method (Green s function) well adapted to surface problems imaginary energy for GF calculations: 10-7 Ry disordered systems: - 5 x 5 supercell averaged over 5 configurations, or 7 x 7 supercell averaged over 3 configurations - on-site potential parameters obtained from (layer dependent) CPA method k // -integration: 10 000 points in the full fcc(001) SBZ definition of GMR ratio: CF C GMR AF CAF
Cu / Co /Cu/Co / Cu GMR (%) 125 100 75 50 25 variable thickness 5ML 0 0 10 20 30 40 50 Magnetic layer thickness (MLs) Cu Co Co Conductances / atom (in units e 2 /h) 1.0 0.8 0.6 F 0.4 0.2 F AF 0.0 0 10 20 30 40 50 Magnetic layer thickness (MLs) 120 Cu /Co/Cu /Co/Cu GMR (%) 115 110 5ML variable thickness 0 10 20 30 40 50 60 70 80 90 100 Spacer layer thickness (MLs) Conductances / atom (in units e 2 /h) 0.25 F 0.24 0.23 AF 0.22 0 10 20 30 40 50 60 70 80 90 100 Spacer layer thickness (MLs)
Cu / (Co / Cu / Co / Cu) / Cu 5ML repeated N+1times GMR (%) Conductances / atom (in units e 2 /h) 200 175 15.0 125 100 0 2 4 6 8 10 12 14 16 18 20 Number of repetitions 1.0 0.8 F 0.6 0.4 F 0.2 AF 0.0 0 2 4 6 8 10 12 14 16 18 20 Number of repetitions 120 interfaces with 15% interdiffusion GMR (%) 90 60 ideal interdiffused Cu /Co/Cu /Co/Cu 30 0 2 4 6 8 10 Spacer layer thickness (MLs) 5ML variable thickness Conductances / atom (in units e 2 /h) 1.0 0.8 F (ideal) 0.6 F (interdiffused) AF (interdiffused) 0.4 F (interdiffused) 0.2 F (ideal) AF (ideal) 0.0 0 2 4 6 8 10 Spacer layer thickness (MLs)
Cu /Co/Cu (1-x) Pd x /Co/Cu GMR (%) 120 x= 0 (ideal) 90 x= 15% 60 x= 50% 30 0 2 4 6 8 10 Spacer layer thickness (MLs) 5ML variable thickness Conductances / atom (in units e 2 /h) 1.0 0.8 F (ideal) 0.6 F (x=15%) 0.4 AF (x=15%) F (ideal) 0.2 F (x=15%) AF (ideal) 0.0 0 2 4 6 8 10 Spacer layer thickness (MLs) 120 GMR (%) 90 60 Co Co 85 Ni 15 Cu /Co (1-x) Ni x / Cu /Co (1-x) Ni x / Cu 30 0 2 4 6 8 10 Spacer layer thickness (MLs) 5ML variable thickness Conductances / atom (in units e 2 /h) 1.0 0.8 F (Co 85 Ni 15 ) 0.6 F (Co) 0.4 F (Co 85 Ni 15 ) AF (Co 85 Ni 15 ) 0.2 F (Co) AF (Co) 0.0 0 2 4 6 8 10 Spacer layer thickness (MLs)
GMR (%) 120 90 60 30 Co Co 85 Cr 15 Cu /Co (1-x) Cr x / Cu /Co (1-x) Cr x / Cu 0 2 4 6 8 10 Spacer layer thickness (MLs) 5ML variable thickness Conductances / atom (in units e 2 /h) 1.0 0.8 F (Co) 0.6 F (Co 85 Cr 15 ) F (Co 85 Cr 15 ) 0.4 AF (Co 85 Cr 15 ) 0.2 F (Co) AF (Co) 0.0 0 2 4 6 8 10 Spacer layer thickness (MLs) domain wall magnetoresistance
w Bloch wall w A K easy axis Néel wall w A 2 2π M Co / Co / Co magnetic wall of variable thickness (linear rotation of magnetization) GMR (%) 250 200 150 100 50 0 0 10 20 Domain-wall thickness (MLs) Conductances / atom (in units e 2 /h) 3.0 F (no wall) 2.5 2.0 AF (wall) 1.5 1.0 0.5 0.0 0 10 20 Domain-wall thickness (MLs)
Giant magnetoresistance of ferromagnetic atomic point contacts atomic point contact FM configuration ferromagnetic wire electric current AF configuration explaination requires: narrow magnetic wall in an atomic point contact large resistance due to a narrow wall geometrical constriction new kind of magnetic wall: structure (almost) entirely determined by the constriction geometry energy = (almost) pure exchange energy width determined by the characteristic size of the constriction wall can be extremely narrow in an atomic point contact 1.0 0.5 M z / M s 0.0 unconstrained wall -0.5 constrained wall -1.0-1.0-0.5 0.0 0.5 1.0 P. Bruno, PRL 83, 2425 (1999) x / w 0
20 nm X 20 nm theory of tunneling magnetoresistance
simple approach: Jullière model θ assumptions: + = G G G ) ( ) ( 2 1 F F G ε ρ ε ρ σ σ σ P 1 P 2 G G G G A P AP P AP = + ) ( ) ( ) ( ) ( F F F F P ε ρ ε ρ ε ρ ε ρ + DOS E with measurement of the spin-polarization by spin-injection into a superconductor
Soulen et al., Science 282, 85 (1998) ab initio calculation of tunnel conductance Ni / vacuum / Ni(001) J. Henk (MPI Halle)
Fe / MgO / Fe(001) MgO Fe J. Henk (MPI Halle)