Damped expectations for the second generationeinstein.drexel.edu/~bob/70Birthday/KeithGilmore.pdf · Albert Fert Peter Grünberg Cu Co Cu Co Cu. Background Currents control magnetic

Damped expectations for the second generation:

controlling the chaos

Theorist

Theorist Experimentalist

or

Wow, you’re working on your report already? It’s not due until Thursday!

Yeah, I know … Mom says the pills I’m taking are starting to work.

I thought we could go outside and play … it’s snowing … Calvin?

What? Oh, sorry, I wasn’t listening.

I really have to finish this.

total magnetization

macroscopic picture microscopic picture

microscopic picture

total magnetization

macroscopic picture

Background Field driven magnetodynamics

G H

HMdtdM /mgddtdL /

M

LL ˆ

precession

damping MM ˆ

precession

damping

L

d

Background Equation of Motion (damped-driven oscillator)

MMHM-M ˆ

precession

damping

}

{

Background

H

V+ V- e-

50 mm

After current Before current

Current-driven magnetodynamics

Background Current driven magnetodynamics

Wide domain wall

Electron flow

If spins follow magnetization direction

Reaction torque on magnetization

Domain wall translates

s

Bs

eM

jPmv

Adiabatic spin-transfer torque

Background Equation of Motion

)M(vM)M(vMMHM-M ss ˆˆ

precession

damping

}

{

adiabatic spin torque

non-adiabatic spin torque

{ }

Field (H) driven terms Current (vs) driven terms

Background

Background

Background Magnetic state affects current

Mfixed

Mfree q

2.04

2.00

R(W)

H (T) -0.2 0.2 0

Giant Magnetoresistance

Albert Fert Peter Grünberg

Cu

Co

Cu

Co

Cu

Background Magnetic state affects current

Mfixed

Mfree q

2.04

2.00

R(W)

H (T) -0.2 0.2 0


Nobel prize

2007 Albert Fert Peter Grünberg

Cu

Co

Cu

Co

Cu

Background Currents control magnetic state

Mfixed

Mfree q

2.04

2.00

R(W)

H (T) -0.2 0.2 0


J. Z. Sun et al. JAP (2003)

Spin-Transfer Torque

I (mA) -20 20 0

2.05

2.00

R(W) Antiparallel

Cu

Co

Cu

Co

Cu

Spin currents can switch magnetization!

Background Current-induced switching dynamics

Low current damped motion

High current switching

High current, high field stable precession

M

Heff Damping torque

Spin transfer torque

Better MRAM

Current-tunable microwave oscillators

Background Complex phase diagram

-0.5 1.5

J (108 A/cm2)

0.16

0 0.0

0.2

0.08

0.5

Parallel

Antiparallel

Precession

DR

(W

)

Fie

ld (

T)

Mfixed

Mfree q

Cu

Co

Cu

Co

Cu



precession

damping

}

{



{ }

Field (H) driven terms Current (vs) driven terms

well understood, conservative


less well understood, dissipative




precession

damping

}

{



{ }





We want to understand the origin of these parameters


precession

damping

}

{



MMHM-M ˆ

Model Motivating data

Ni

Co Fe

Temperature (K)

Dam

pin

g,

Ferromagnetic resonance

measurements

MMH-MM ˆ

Coupling to the environment

uniform precession

magnons electronic excitations

phonons

eddy currents

electron-hole pairs

Stoner excitations

electron-lattice scattering

scattering to degenerate modes

magneto-striction

magnon-phonon scattering

Extrinsic effects

Intrinsic effects

Model Effective Field Model

eff

0

M

1H =

M

Em

nk nk

nk

E f

eff

0

M M

1H =

M

nk nknk nk

nk

ff

m

reversible

magnetocrystalline anisotropy

dM M

H0

conductivity-like

resistivity-like

Temp.

Dam

pin

g

irreversible

Fermi Surfaces

Real Fermi Surfaces Representative Fermi Surfaces

kx

ky kz

Up Spin Down Spin

Iro

n

Co

bal

t N

icke

l

Band Structure

H nk = nk nk

Breathing Fermi Surface : Hso(t) = -x l s(t)

kx

ky kz

kx

ky kz

kx

ky kz

t

t Energy pumped from Zeeman to spin-orbit type producing electron-hole pairs

Scattering of excited electrons into holes reestablishes equilibrium

kx

ky kz

t

t

Continued pumping and scattering damp the precession

M

M

M

M

dM

dM

.

Model State energies change with precession

F

k

M

Generation of electron-hole pairs due to energy

changes – breathing Fermi surface

ground state excited state

Spin-orbit energy depends on spin

direction (s)

nk

nknkso mH )ˆ(sx

M M M

Representative spin:

lattice scattering

time axis

nk

nknkf

M

0M

1

m eff

H

Model

Conductivity-like term decreases as scattering rate increases

F

k Total

~ s(T)

Temperature

Dam

pin

g lattice

scattering

lattice scattering

short lifetime small damping

F

k

long lifetime large damping

The breathing Fermi surface contribution

Bubbling Fermi Surface : V(t) = Hso(t) - Hso

kx

ky kz

The effective perturbation generates electronic excitations over the Fermi surface, reducing the Zeeman energy.

M

M dM

V(0) = 0

V(t) = Hso(t) – Hso(0)

Electron-electron and electron-lattice scattering restores equilibrium.

kx

ky kz

Model State populations change with precession

M

Generation of electron-hole pairs due to

population changes – bubbling Fermi surface

Eigenstates depend on spin direction (s)

)ˆ()ˆ( zHmHV sososo

M M M

Representative spin:

time axis

F

k

nk

nknkf

mM

0M

1effH

Model

Resistivity-like term increases as scattering rate increases

F

k

DOS

F

The bubbling Fermi surface contribution

~r(T)

Temp.

Dam

pin

g

Total

Model Qualitative prediction

eff

0

s M M

1H =

M

nk nknk nk

nk

ff

m

conductivity-like ‘breathing’ terms

Resistivity-like ‘bubbling’ terms

eff

0 (1)

s M

1H =

M

nknk

nk

f

m

eff

0 (2)

s M

1H =

M

nknk

nk

fm

total damping

conductivity-like

resistivity-like Dam

pin

g,

Scattering rate (temperature)

Qualitative predication

MMH-MM ˆ

Model Qualitative match with experiment

total damping

conductivity-like

resistivity-like Dam

pin

g,


Qualitative predication

Ni

Co Fe

Temperature (K)

Dam

pin

g,

Ferromagnetic resonance measurements

MMH-MM ˆ

Background

Current (vs) driven terms Field (H) driven terms

Equation of Motion


precession

damping

}

{



{ }

Model Non-adiabatic STT as extension of damping

),,0(Im Eq

),,(Im 0Eq

)M(vM)M(vMMH-MM ss ˆˆ

precession

damping

}

{



{ }

Conservative torques

Dissipative torques


),,0(Im Eq

),,(Im 0Eq


precession

damping

}

{



{ }


Dissipative torques

precession on

current off

Rotation in time:


),,0(Im Eq

),,(Im 0Eq : all Fermi level electrons contribute nk

nk


precession

damping

}

{



{ }


Dissipative torques

precession on

current off

Rotation in time:


),,0(Im Eq

),,(Im 0Eq : all Fermi level electrons contribute nk

nk


precession

damping

}

{



{ }


Dissipative torques

precession off

current on

Rotation in space:


),,0(Im Eq

),,(Im 0Eq : all Fermi level electrons contribute

: Fermi level electron contributions are weighted by their velocity

nk

nk

nk

nknk

sv

v


precession

damping

}

{



{ }


Dissipative torques

precession off

current on

Rotation in space:


),,0(Im Eq

),,(Im 0Eq : all Fermi level electrons contribute

: Fermi level electron contributions are weighted by their velocity

nk

nk

nk

nknk

sv

v


precession

damping

}

{



{ }


Dissipative torques

rr

s

t

s

dt

sd ˆˆˆ

Model Qualitative Summary

total dissipation

changes in energy

changes in populations

o

r


nk

nknk

sv

v

rr

s

t

s

dt

sd ˆˆˆ

Dissipation occurs through the spin-orbit interaction and electron-lattice scattering

nk

nknkf

mM

0M

1effH

conductivity-like breathing terms

resistivity-like bubbling terms

: precession dissipation parameter : spin-transfer torque dissipation parameter

Model

Model

Model

Newton’s apple tree England

Descendant of Newton’s apple tree

NIST, Maryland

HAPPY BIRTHDAY!

Thanks for the chaotic upbringing

END

Damped expectations for the second generation

Documents

Damped expectations for the second generationeinstein.drexel.edu/~bob/70Birthday/KeithGilmore.pdf · Albert Fert Peter Grünberg Cu Co Cu Co Cu. Background Currents control magnetic