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SpinelektronikChapter 12

Spin Transfer Processes

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Winter 05/06 Spinelektronik

Half-metallic ferromagnets (HFM)

2

• HFM: gap in D↑(E) or D↓(E) around EF

• intermetallic compounds

• oxides

• perovskites

• double-perovskites


Classes of ferromagnets

3

• (a) weak ferromagnet

• (b) strong ferromagnet

• (c) half-metallic ferromagnet (gap in the minority spin bands)

• (d) half-metallic ferromagnet (gap in the majority spin bands)


Simple oxides

4

• CrO2: simple oxide

• ferromagnetic metal

• ferromagnetic superexchange + double exchange

• other simple oxides: Fe3O4

CrO2


Perovskites

5

• different types of half-metallicity

LSMO

Sr2FeMoO6


Heusler alloys

6

• original Heusler: ferromagnetism without ferromagnetic elements

• half-metallicity in the minority spin bands

half HeuslerNiMnSb

full HeuslerCo2MnSi


Slater-Pauling curve for full-Heusler

7

• full-Heusler alloys follow a Slater-Pauling dependence (magnetic moment varies with number of valence electrons)

• large variety of compounds

• many have low ordering temperatures

Full Heusler Alloys: Slater-Pauling Curvetotal moment Mt versus total valence charge Zt: Mt=Zt-24

20 21 22 23 24 25 26 27 28 29 30 31 32

Number of valence electrons: Zt

−3

−2

−1

0

1

2

3

4

5

6

7

To

tal

spin

mo

men

t: M

t (µΒ)

Mn2VAl

Fe2VAl

Fe2CrAl

Co2VAl

Fe2MnAl

Rh2MnGe

Co2FeAl

Co2MnSi

Co2MnGe

Co2MnAl

Co2MnGa

Rh2MnAl

Rh2MnGa

Ru2MnSb

Co2CrAl

Fe2MnSi

Ru2MnSi

Ru2MnGe

Ru2MnSn

Co2TiAl

Ni2MnAl

Co2MnAs

Co2FeSi

Rh2MnTl

Rh2MnSn

Rh2MnPb

Mt=Z t

−24

Rh2MnIn

Co2TiSn

Mn2VGe

Co2MnSn

Co2MnSb


Full-Heusler alloy

8

• characteristic feature is a gap in the minority band structures half-metallic behavior

• similar electronic structure for all 4 systems

• holds for bulk crystals with perfect chemical order


Full-Heusler alloys: surface properties

9

• surface termination is important for the surface-electronic structure

• formation of gap states half-metallic behavior is destroyed


Half-metallic spin-valve

10

• Use zinc-blende compounds separated by semiconductors for decoupling

• No interface states at EF

• Tune FM-AF coupling by choice of spacer material & thickness

AP: DOS at EF

P (17 meV)(Conducting)

AP(Insulating)

Mn

Cr

Cr

Mn

Cd

Te

Te

Te

Mn

Cr

Cr

Mn

Te

Te

Te

Te

Te

P: DOS


Rashba effect

11

• electric field in the quantum well transforms into magnetic field acting on the spin in the rest frame of the electron

• precession of electrons along their path

Rashba Hamiltonian

€

⇓

Hso =αr σ ×

r k [ ]r e z

z


Spin transfer effects

12

• 1996 Theoretically predicted by Slonczewski and Berger

• 1999 First experimental observation of CIMS at Cornell

• 2003 Current-driven microwave oscillations

• originates from the interaction of spin-polarized electrons with the magnetization

• transfer of spin angular momentum to the magnetization of the ferromagnet

• induces the motion of domain walls

• may initiate entire magnetization reversal process

• applications in MRAM and magnetic logics

“History”


Current-induced magnetization switching

13

electron flux

ø 10

0 nm

Consider a FM / NM / FM structure with FM layers of different thickness:

NM

thickFM

thinFM

electron flux

NM

thickFM

thinFM

Current-induced magnetization switching (CIMS):• the alignment of the FM layers depends on the current direction• non-equilibrium effect requires high current densities: 108 A/cm2 or 10 mA per (100 nm)2

• depends on symmetry of the system• relates to GMR like “actio = reactio”


First observation of CIMS

14

• electric field in the quantum well transforms into magnetic field acting on the spin in the rest frame of the electron

• precession of electrons along their path

z

Si3N4 membrane with holes coveredfrom two sides with metallic films:

Hole diameter : 5 - 10 nm

2-4 nm Co / 4 nm Cu / 100 nm Co

Current density: ~ 109 A/cm2

CPP-GMR

E.B. Myers et al., Science 285, 867 (1999)


Observation of CIMS

15

dV/d

I (Ω

)

J.A. Katine et al., Phys. Rev. Lett. 84, 3149 (2000)


Spin-transfer-torque acts like interlayer coupling

16

•

Coercive fields:Co1: 400 OeCo2: 200 Oe

“AF-coupled”

“FM-coupled”

GMR at high current (±50 mA):

Sample area:200 x 600 nm2

Current density:4 x 107 A/cm2

GMR at low current (±50 µA):“decoupled”

J. Grollier et al., Appl. Phys. Lett. 78, 3663 (2001)


Switching by Oersted field ?

17

•

The current gives rise to a circular magnetic field, which favors a vortex-like magnetization state in the small magnetic elements: required current density: 107 - 108 A/cm2

the maximum field at the edge scales like (for spin-transfer )B ∝ Ir

[23 Å NiFeCo / 40 Å Cu / 12 Å NiFe / 40 Å Cu]5

with a pillar diameter of 0.3 µm

Ir2

K. Bussmann et al., Appl. Phys. Lett. 75, 2477 (1999)


Mechanism of spin transfer effects (I)

18

• electric field in the quantum well transforms into magn

after X. Waintal et al., Phys. Rev. B 62, 12317 (2000)


Quantum-mechanic spin filtering

19

ψ in =cosθ

2

sinθ2

⇒

ψ in σ x ψ in = sinθ

ψ in σ y ψ in = 0

ψ in σ z ψ in = cosθ

ψ in ψ in = 1ψ R =

0

sinθ2

⇒

ψ R σ x ψ R = 0

ψ R σ y ψ R = 0

ψ R σ z ψ R = − sin2 θ2

ψ R ψ R = sin2 θ2

ψ T =cosθ

20

⇒

ψ T σ x ψ T = 0

ψ T σ y ψ T = 0

ψ T σ z ψ T = cos2 θ2

ψ T ψ T = cos2 θ2

Spin transfer: ψ in σ→

ψ in − ψ R σ→

ψ R + ψ T σ→

ψ T

=

sinθ − (0 + 0)0 − (0 + 0_

cosθ − (− sin2 θ2+ cos2 θ

2)

=

sinθ00

x

z


Mechanism of spin transfer effects (II)

20

• after X. Waintal et al., Phys. Rev. B 62, 12317 (2000)


Influence of spacer thickness

21

•

Spin-flip scattering (spin relaxation length λs) in the spacer leads to an asymmetric thickness dependence of the critical currents for CIMS:

Jc+: P → APJc

- : AP → P

GMR: ΔR A ∝ exp(-d/λs) ⇒ λs = 190 ± 20 nm

AP → P: Jc- ∝ exp(d/λs) ⇒ λs = 170 ± 40 nm

P → AP: Jc- ∝ exp(2d/λs) ⇒ λs = 140 ± 30 nm (70 ± 20 nm without factor 2)

Reflected electron must cross the spacer layer twice!F.J. Albert et al., Phys. Rev. Lett. 89, 226802 (2002)


A microscopic picture: Spin-transfer at interface

22

•

Consider perpendicular Fermi wave vectors for spin-up and spin-down: k↑,↓

k↑ = k↓ for a non-magnetic metal N k↑ ≠ k↓ for a magnetic metal F

An incident electron is in general a superposition of spin-up and spin-down. In N thephase angle ϕ is constant, but in F ϕ varies because of “different propagation speeds”

of spin-up and spin-down components:ϕ(ζ) = ϕ(0) + (k↑ - k↓) ζ

Different states on the Fermi surfacehave different k↑ - k↓

⇒ Loss of coherence within about 10 monolayers from interface

⇒ Transfer of spin momentum

after J.C. Slonczewski (1999)


Absorbed spin momentum is a torque

23

τ =α I IM

M × (M × MP )

αI describes the strength of the spin-transfer (must be determined from a microscopic picture that takes material properties into account)M is the magnetization of the free layerMP is the magnetization of the pinned layerI is the current density. Its sign depends on the current direction!

τ is the absorbed moment and thus a torque on M

The spin-transfer (absorbed momentum) can be written as


Magnetization dynamics and spin-transfer (I)

24

The equation of motion for a magnetization M is the Landau-Lifshitz-Gilbert (LLG) equation:

∂M∂t

= −γM × Heff

Hef

f

MxHe

ff

M

stable precession with frequency γHeff/(2π)γ: gyromagnetic ratio

∂M∂t

= −γM × Heff +αM(M ×

∂M∂t)

damped precession with frequency γHeff/(2π)

α: Gilbert damping coefficient


Magnetization dynamics and spin-transfer (II)

25

Spin-transfer fro the pinned layer with magnetization MP acts as a torque on the free layer (magnetization M) and gives rise to a further term in its LLG equation:∂M∂t

= −γM × Heff +αM(M ×

∂M∂t) + α I I

MM × (M × MP )

Depending on the sign of the current density I, the additional term acts as a positive damping or a negative damping. In the latter case, it can (over-) compensate the Gilbert damping and leads to a destabilized precession that eventually switches M.

At the compensation point M rapidly jumps (thermally excited) between AP and P alignment.

For larger fields the describes small or large angle oscillatory motions with typical frequencies of GHz.


Example of simulated oscillatory motion of M

26

• The opening angles of these motions are large compared to FMR precessions

Rashba Hamiltonian

z

Hext is applied along the x-axis

Z. Li and S. Zhang, Phys. Rev. B 68, 024404 (2003)


Microwave oscillations driven by spin-pol. currents

27

•S.I. Kiselev et al., Nature 425, 380 (2003)

The phase diagram and the types of motion can be understood by solutions of the LLG equation when the spin torque term is included:

0.5

kOe

field

step

s

LLG simulation experiment


Electron beam lithography for CPP-GMR and CIMS

28

For CPP: RA ≈ 10-4 - 10-3 Ω µm2 ⇒ sub-µm structures are required


Lithographic procedure in detail

29


Realization of nanocontacts at FZJ

30

200 nm

AFM

Optical microscopy


Inverted CIMS in Fe(Cr)/Cr/Fe(Cr) nanopillars

31

•M. AlHajDarwish et al., J. Appl. Phys. 95, 6771 (2004)

Py/Cu/Py:• Stronger minority scattering (β>0)

• Normal GMR• Normal CIMS

Fe(5% Cr)/Cr/Fe(5% Cr): • Stronger majority scattering (β<0)

• Normal GMR • Inverse CIMS

⇒ Spin scattering asymmetries determine CIMS

So far, all experiments are performed with Co, Co alloys, and Py. Other materials?


GMR in CPP Geometry

32

• Easy axis / hard axis behavior confirms epitaxy of nanopillar

Fe (001) easy axis: Fe (011) hard axis:

I- V-

I+ V+

variable B

small I


Spin-Torque Induced Switching

33

• W-shaped background due to contamination layer in pillar

• Hysteretic switching of free layer with γFe/Ag > 0 as expected

variable I

fixed B

Fe (001) easy axis: Fe (011) hard axis: 50 K


Current-Induced Microwave Emission

34

• Quality factor f/Δf of up to 90

• Microwave power per line is estimated to be of the order of 1 nW

fixed I

variable B

50 K

DC

curre

nt


R-I Loops vs. Microwave Excitations

35

• Microwave excitations appear close to switching processes and go along with peaks and dips in R-I curves


Interfacial dependence of CIMS

36

• Spin torque transfer depends on the electronic matching

M


Precession of transmitted spins

37

• Calculation of a single spin response

• transmitted electron precesses around the magnetization in the ferromagnet

• precession amplitude decays into the ferromagnet

• spin torque decays too

M

M.D. Stiles et al., Phys. Rev. B 66, 014407 (2002)


Explanation for inverse CIMS

38

Consider spin scattering asymmetries (similar to the case of the inverse GMR).Slater-Pauling curve gives an idea about volume and interface scattering

asymmetries as transition metal alloys XY and their interfaces X/Y

⇒ Py,Co, CoFe: stronger scattering of minority electrons (β > 0)⇒ BUT FeCr and Fe/Cr: stronger scattering of majority electrons (β < 0)


Mechanism of inverse CIMS (I)

39

New discussion for stronger scattering of the majority electrons:

β > 0β < 0

⇒ Polarization properties of a FM layer change with β


Mechanism of inverse CIMS (II)

40

both β > 0

both β < 0

antiparallel alignment

parallel alignment

⇒ CIMS is inverse when β of the thick (polarizer) layer or both β change sign⇒ Note: GMR is only inverse when βL βR < 0


Beyond the macrospin picture

41

• micromagnetic structures during the CIMS process

• very “chaotic” magnetization distribution during switching

• excitation of spin-wave modes


Current-driven domain wall motion

42

•A. Yamaguchi et al., Phys. Rev. Lett, 92, 077205 (2004)

Arrows indicate “technical” current.

The spin of the conduction electrons follow adiabatically the local magnetization, which varies slowly across the domain wall. Each conduction electron thus transfers a momentum to the domain wall.

Envisaged application:Switching of magnetic elements by reversibly pushing a domain wall across the elements

⇒ MRAM?

h


Application of CIMS in GMR-MRAM cells

43

•J.-G. Zhu et al., J. Appl. Phys. 87, 6668 (2000)

CIMS would simplify the chip layout because the paired word lines are not needed

VMRAM Memory cell:


CIMS in tunnel junctions

44

•Y. Huai, P.P. Nguyen, F. Albert, Grandis Inc., MMM/Intermag 2004

Low resistive TMR junctions: PtMn/CoFe/Al2O3/CoFe/NiFe • 0,5 - 10 Ωµm2

• 1 - 20 % TMR • 0,1 x 0,2 µm2

• critical current depends on external field • switching at low current densities of 1x107 A/cm2

• low current densities due to “hot spots”?

75.5

74 .5

73 .5

72 .5

71 .5-2.5 -1.5 -0.5 0.5 1.5 2.5

R (Ω

)

Current (mA)

75.5

74 .5

73 .5

72 .5

71 .5

-120 -70 -2 0 3 0 80 13 0 1 8 0

Field (Oe)

R (Ω

)

Field sweep: Current sweep:

Potential application: Simplified write-procedure of MRAM cells with less wiring!


Switching limitations

45

• Oersted field switching inefficient at small structures

• alternative: spin-transfer switching

0 200 400 600 800 1000

20

40

60

80

100

120

140

0 200 400 600 800 10000

2

4

6

8

10

12

14

16

18

20

22

Switc

hing

Fie

ld (O

e)

Lateral Dimension (nm)

Magnetic Dot Aspect Ratio = 2.0

Field Assist Switching

Sw

itchi

ng C

urre

nt (

mA

)

Lateral Dimension (nm)

Current Induced Switching

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