Ecole Franco-Roumaine Magnétisme des systèmes nanoscopiques et structures hybrides Brasov, septembre 2003 Spin tunnel and Spin Polarisation Laurent Ranno Laboratoire Louis Néel, Grenoble Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Summary I- Introduction to Tunnel Effect II-Magnetic Tunnel Effect III-Bias Voltage and Temp Dependence IV-Spin Polarisation V- Half Metals Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
I- Introduction to Tunnel Effect Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Tunnel Effect has a Quantum Mechanics Origin w ∆ E E 0 E A classical electron with energy E<E 0 cannot enter the barrier zone However a quantum electron obeys the Schrödinger equation ! (1D model) d 2 2 � − ψ + ψ = ψ V x E ( ) m dx 2 2 Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
� d 2 2 � − ψ = ψ E Off the barrier m dx 2 2 Plane waves mE − ω ψ = i kr t 2 e ( ) = ± k and 2 � d 2 − � − E 0 < ψ = − ψ E E E 0 ( ) In the barrier and m dx 0 2 2 Evanescent waves − ω ψ = qr i t ∆ m E e 2 = ± q and b 2 Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
� ∆ m E 2 = ± q 2 � ∆ = E eV 1 1 = = m free electron nm 0 . 2 q Tunnel barriers must be very thin insulating layers Width = w < 10 nm Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
For a more general barrier shape V(x) w ∆ E E x d 2 2 � − ψ + ψ = ψ V x E ( ) m dx 2 2 d m 2 2 ψ = � − ψ = ψ V x E k x 2 ( ( ) ) ( ) dx 2 2 x ± k u du ( ) � ψ = x e ( ) 0 W. K. B. Approximation Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
x ± k u du What is neglected ? ( ) � ψ = x e ( ) 0 ψ d x ( ) = ± ψ k x x ( ) ( ) dx ψ ψ d x dk x d x 2 ( ) ( ) ( ) = ± ψ ± x k x ( ) ( ) dx dx dx 2 dk x ( ) = ± ψ + ψ x k x x 2 ( ) ( ) ( ) dx m 2 = − k x V x E ( ) ( ( ) ) The barrier potential should vary smoothly 2 � Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
We are dealing with transport. What about the current ? To pass a current, we must apply a bias voltage across the barrier. eV the barrier has a transmission coefficient T Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
� Simmons The probability to find the electron (energy E) on the other side of the barrier is : w − m V u E 2 ( ( ) ) − du 2 � 2 = ψ ψ = ψ = P E e 2 ( ) 0 V x dt Electrons coming from the left to the right ∞ = dN V n V P E dV dt ( ) ( ) � x x x x 0 ∞ E π dN m 2 4 = P E dE f E dE ( ) ( ) � x x � dt h // 3 0 0 Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
w 1 2 ∆ E E No bias voltage E 0 Current 1 2 = Current 2 1 J(V=0)=0 Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
w Bias voltage eV<<E 0 E E 0 eV ∞ E π dN dN e m 2 4 = − = − + J e P E dE f E f E eV dE 1 2 ( ) ( ) [ ( ) ( )] � x x � dt dt h // 3 0 0 V − S E = J E e 1 . 02 10 3 . 16 10 0 Simmons (1963) has calculated approximate recipes 0 S Linear J(V) at low bias Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
w Bias voltage 0<eV<E 0 E E 0 eV = α + β J V V 3 ( ) dJ = α + β V 2 ( 1 3 ) Simmons ’ parabolic fit dV β contains the barrier height and the barrier width Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
dJ Why ? dV From the experimental point of view : = + ω v << V t V v t V ( ) cos( ) Using a voltage source : 0 0 dJ = + ω = + ω J V J V v t J V v t V ( ) ( cos( )) ( ) cos( ) ( ) dV 0 0 0 Measuring the ω component of the signal with a lock-in amplifier gives directly the differential conductance Filter all the constant voltage and non- ω noise Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Reduced effective w Bias voltage eV>E 0 E E 0 eV J increases rapidly but in fact such a bias voltage corresponds to the electrical breakdown regime Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
dJ/dV J V V Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
I-V non linear curves (ferromagnetic/insulator/ferromagnetic) courbe I(V) à 2 K et 52 K 0.32 V (2 K) 0.24 V (52 K) 0.16 0.08 0 -0.08 -0.16 -0.24 -0.24 -0.16 -0.08 0 0.08 0.16 V (Volt) No temperature dependence of tunnel effect (1 st order) Thèse E. Favre-Nicolin (Grenoble 2003) Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
II-Magnetic Tunnel Effect Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
In 1972 Gittleman et al. measured the resistance and MR of Ni grains in a SiO 2 matrix Longitudinal MR is <0 contrary to the sign of the bulk Ni AMR ρ // > ρ perp R > R M J M J 50% Ni Gittleman et al. Phys. Rev. 5 (1972) 3609 Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Gittleman et al. 1972 : � ⋅ m m � σ = σ + σ T H T T 1 2 ( , ) ( ) ( ) 0 1 m 2 Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Development of film deposition techniques Trilayer : better characterisation of electrodes and control of magnetisation R changes by 14% at low temperature depending on the magnetic configuration Co Ge (10-15nm) +dry oxygen Fe Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
1995 200 µ m x 300 µ m 11.8% at 300 K 24% at 24 K φ =1.9 eV and t=1.6 nm V 50% =200mV And also Miyazaki, Tezuka JMMM 139 (1995) L231 Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Magnetic Tunnel Junction Ferro (free) Insulator Ferro (pinned) IBM 1997 Same technical solutions as GMR structures to get 2 different coercive fields i.e. well defined parallel and antiparallel states. Hard - Soft materials (Co - NiFe) Different shape anisotropies for both electrodes Pinning to AF layer (MnFe) or Artificial AF layer (Co/Ru/Co) Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Jullière ’s model (1975) − N E N E ( ) ( ) Not magnetisation = F F ↑ ↓ P + N E N E ( ) ( ) BUT Polarisation of electrodes is the parameter F F ↑ ↓ − N P + N P ( 1 ) ( 1 ) = N i i = N i i ↓ i ↑ i 2 2 Assume : No spin-flip transition across the barrier at low voltage 2 parallel channels (spin up and spin down) Conductance is the sum of spin up and down conductances Conductance is proportional to the density of state (d.o.s.) 1 and d.o.s. 2 = G G N E N E ( ) ( ) spin spin F spin F i 0 i electrode 1 i electrode 2 = + G G N E N E G N E N E ( ) ( ) ( ) ( ) F F F F ↑↑ ↑ ↑ ↓ ↓ 0 0 1 2 1 2 = + G G N E N E G N E N E ( ) ( ) ( ) ( ) F F F F ↑↓ ↑ ↓ ↓ ↑ 0 0 1 2 1 2 Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Jullière ’s model (M. Jullière, Phys. Lett. 54 A, 225 (1975)) TMR ratio : + = G G G N N ↑↓ ↑↑ 0 1 2 − = − = G G G N N P G N N P G N P N P ↑↑ ↑↓ ↑ ↓ 0 2 2 0 2 2 0 1 1 2 2 1 1 − − G G G G P P 2 = = ↑↑ ↑↓ ↑↑ ↑↓ P 1 P 1 2 or + + G G 2 G P P 1 ↑↑ ↑↓ ↑↑ 1 2 − R R − P P (pick your definition ) 2 = ↑↑ ↑↓ 1 2 − R P P 1 ↑↑ 1 2 Does depend on P i Does not depend on the barrier (height, width) because of assumption about G 0 i.e. no spin dependence of transmission Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
Exp : TMR=14% Fe/a-Ge/Co (Jullière) Theor : P Co 34% +P Fe 44% TMR 26% 69.1% at 4.2 K From Jullière ’s formula P CoFe =50.7% similar to expected CoFe TMR junction (Tohoku 2000) Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
� Slonczewski ’s model (1989) Ferromagnetic electrodes Barrier in the model k ↑ F ↓ m ↑ k ↓ F k 2 2 = 2 ± E E exch m Solve Schrödinger for both channels, calculate conductances − − q k k k k 2 = P ↑ ↓ ↑ ↓ F F F F + + q k k k k 2 ↑ ↓ ↑ ↓ F F F F Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
− − q k k k k 2 ∆ m E 2 = = ± P ↑ ↓ ↑ ↓ q F F F F + + 2 q k k k k 2 � ↑ ↓ ↑ ↓ F F F F − − k k k k q 2 = ⋅ = P ↑ ↓ ↑ ↓ F F F F High barrier + + q k k k k 2 ↑ ↓ ↑ ↓ F F F F m mk = = ∝ DOS E mE k ( ) 2 Free electrons π π 3 2 2 2 � � − N E N E ( ) ( ) = F F P ↑ ↓ Back to Jullière ’s formula + N E N E ( ) ( ) F F ↑ ↓ Spin Tunnel Course Brasov sept. 2003 Laurent Ranno (Lab. Louis Néel)
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