Current research in current-driven magnetization dynamics

S. Zhang, University of Missouri-Columbia

Beijing, Feb. 14, 2006

Outlines

Magentoelectronics started from discovery of giant magnetoresistive (GMR) effect

Spin-dependent transport in magnetic metal based nanostructures

Spin angular momemtum transfer: physics and potential technology

Perspectives and conclusions

M.N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988).

400

110

H (kOe)-40 H // [ 0 11]

What is giant magnetoresistance?

R

Origin of GMR—two current model

e e e e

EF

A ferromagnet Different numbers ofup and down electrons

R R

Up and down resistances

Low resistance High resistance

GMR Reading head

Bit width

Bit length

Conductorlead

JM Spin

valve

Spin valve

OR MNMM

AF

“0”“1”

Concert efforts: theorists, experiments and technologists on GMR Theorists: predict, explain, model and design GMR

effects and devices

Experimentalists: design, fabricate, characterize, and measure GMR devices

Technologists: produce, evaluate, pattern, integrate, and deliver GMR devices

It would be otherwise impossible to push the information storage so rapidly

History of magentic tapes and hard disks

Now: 80Gbits/in2

5 years: 1 Terabits/in2

In 1988, giant Magnetoresistance (GMR) was discovered;in 1996, GMR reading heads were commercialized Since 2000: Virtually all writing heads are GMR heads

GND

Magnetoelectronics: Magnetic Tunnel Junctions

High tunneling probabilityLow resistance

Low tunneling probabilityHigh resistance

Al-O barrier

Cu (30)

IrMn

Co-Fe-B(4)

Ta (5)

IrMn (12)

Al-O (0.8)

Cu (20)

Ta (5)

Py (5)

Ta (5)

Co-Fe-B(4)

-1500 -1000 -500 0 500

0

20

40

60

80

100

0

10

20

30

40

50

60

T=4.2 KRp=23.4 RS=4.68 km2

TMR=95.4%

TM

R (

%)

H (Oe)

(b)

TMR curves measured at RT (a) and 4.2 K (b) for the Co-Fe-B/Al

2O

3/Co-Fe-B junction after annealing.

Annealed at 265 0CT=300 K

S=10 x 20 m2

Rp=22.3 RS=4.46 km2

TMR=58.5%

T

MR

(%

)

(a)

VSource: Dr. Xiufeng Han

Brief History of TMJ

1974, M. Julliere (a graduate student) published an experiment article which claimed 14% TMR in Fe/Ge/Fe trilayers. A simple model was proposed (the paper became a sleeping giant).

1982, IBM reported 2% TMR on Ni/AlO/Ni. 1995, Moodera (MIT) and Miyazaki (Japan) reported

10% TMR for Co/AlO/Co. 1998, DARPA launched MRAM solicitation 1999, Motorola’s 128kB MRAM demo 2003, IBM, Motolora, 4Mb MRAM chip demo More than 10 startup MRAM companies formed. MRAM becomes internationally recognized future

technology

Emerging non-volatile memory technologies

Flow

Spin

Quantity FRAM

PCRAM

MRAM

PFRAM SiC Bipolar

PMC

Molecular

Polymer Perovskite

NanoX’tal

3DROM

Current-driven spin torques

GMR/TMR: magnetization states control spin transport (low-high resistance).

Adverse effect: spin transport (spin current) affects magnetization states?

Every action will have reaction—spin transfer

T

spin angular momentum transfer? Momentum transfer—electromigration

Angular momentum transfer—magnetization dynamics

An impurity atom receives a force by absorbing a net momentum of electrons:electromigration is one of the major failure mechanisms in semiconductor devices.F

The atom receives a torque by absorbinga net spin angular momentum of electrons:the spin torque can be used for spintronics

Interaction between spin polarized current and magnetization (J. Slonczewski, IBM)

m mout in

m e Bout

m e Bin P

dMJ J

dt

J PJ Me

J PJ Me

MpM

Spin torque on the magnetic layer M

( )

/

J P

eJ B

dMa M M M

dt

a PJ e

0, 0

t t

Current torque on DW

(Magnetic field pressure on DW, )

0, 0t t

Massless motion!!

From Sadamichi Maekawa

Current induced Domain wall motion

Magnetization dynamics: LLG equation (micromagnetics)

1;| | | | 1; 1

( )

( )

( )

J P

J J

eff

eff

p

eff

b

a m m m

m mm m c m

x x

dm dmm H m

dt dtdm dm

m H mdt dt

m m V

E mH

m

LLG+spin torque

Where

Spin valve

Domain wall

Novelty of spin transfer torques

Manipulation of magnetization states by currents

Self-sustained steady state magnetization dynamics

Unusual thermal effects

Interesting domain wall dynamics

Dynamic phases: synchronization, modification and chaos

First observation of current induced magnetic switching by Spin torques

Co1=2.5nmCo2=6.0nm

Katine et. al., PRL (2000).

Self-sustained steady-states precession

2| | ( ) ( )eff J p p eff

dEm H a M m M m H

dt

The first term is always negative (damping), the second termcould be positive or negative (it even changes sign at different times).

Energy damping and pumping:

Limit cycle: the energy change is zero in an orbit

[ ( ) ( )] 0eff J pE

E dm m H a m m

Calculated limit cycles2 2 2sin cos 2 sin cosE K H

Kiselev et al., Nature (2003)

Experimental identification of limit cycles

Unusual Thermal effects

Eb

PAP

Neel-Brown relaxation:

( , )exp( / )b Bf T E E k T

( , )f T Mwhere is algebraic dependent on T, E

Question: in the presence of the spin torque, how do we formulatethe relaxation time?

Thermal activation

Difficulty: the spin torque is not conservative: ( )J p ma m m F m

LLG equation at finite temperatures

( ) ( ) ( )

0

( , ) ( ', ') 2 ( ') ( ')

eff J P

i jij

dm dmm H h m a m m m

dt dth

h r t h r t D r r t t

random field

( )

( )

eff m

eff

J p m

M

H E m

m H

a m m F m

Dm P

The magnetization receives following fields

Precessional conservative field

Non-conservative damping field

Non-conservative spin torque field

Diffusion field

Solution of Fokker-Planck equation

( ) [ ( ) ( )] ( ) 0eff J p ME E

B

P E dm m H a m m dm D P m

D k T

is diffusion constant (dissipation-fluctuation relation)

The probability energy density is:

'

'

( ) exp

( )

' ' ( ')( )

eff

B

J pE

effE Eeff

E

EP E A

k T

a dm m m

E E dE E dE C Edm m H

where

Experimental data interpretation

Telegraph noise

P

AP

P AP

P AP

H

P AP

J

P AP

J P AP

H+

J

R

Field alone Current alone

P AP

H

H-I phase boundary of equal dwell times.

Comparison with experiments

Equal dwell timesfor P and AP states

P AP

By simultaneously changingH and J, one can always have

( )(1 )bc

IE H Const

I

Synchronization, modification and chaos

Limit cycle

+ 1. Another oscillator2. AC external field3. AC external current

Linear oscillator

Calculated limit cycles2 2 2sin cos 2 sin cosE K H

Observation of synchronization by an AC current

Rippard et al, PRL (2005)

Observation of mutual synchronization

Kaka et al., Nature (2005); Mancoff et al, Nature (2005)

Observation of mutual synchronization

Narrower spectrum width at synchronization

Dynamic phases due to AC currents

M

M

M

M

20( )

0.02

200( )

0

aca Oe

H Oe

K

Synchronization spectrax1

Modification spectra (beating)

x2

Synchronization and modification agree well with experiments

Chaos spectrax3

Theories of spin torques in ferromagnets

Me Berger, domain drag force, based an intuitive physics picture

Bazaliy, et al,

Waintal and Viret, a global pressure and a periodic torque

Tatara and Kohno, spin transfer torque and momentum transfer torque.

Zhang and Li, adiabatic torque and non-adiabatic torques

Barnas and Maekawa, non-adiabatic torque relates to the damping of the adiabatic torque

within a ballistic transport model for half-metallic materials

MM M

x

Spin torques in a domain wall

1

ex s sf

m mJ m M

t M

�

Equation of motion for conduction electrons

( )e J Jff bM M

M H MM M

M M c Mx xt t

/ 0.01exJ J

sf

c b

where

Interaction between conduction electrons and magnetization:

ex

H m M

( , , )xm m x v t y z / /xm t v m x

If the wall is in steady motion, the current driven wall velocity is independent wall structure and pinning potentials

extJ

x

WHcv

ext ext xH H e

Steady state wall motion

Steady state wall velocity is thus

xss ejj

eff J J

m m m mm H m b m m c m

t t x x

Wall velocity for different materials in a perfect wire

Ms (A/m) P Wall velocity (m/s)

Co 14.46x105 0.35 1.41

Permalloy 8x105 0.7 5.1

Fe2O3 4.14x105 1.0 14.0

CrO2 3.98x105 1.0 14.6

27 /101 cmAjs

Observed Domain wall motion in a nanowire

Yamagushi et al., PRL (2004)

Observed Wall velocity

8 2

3 /

1.2 10 /

v m s

j A cm

for

Vortex domain wall motion driven by current

05.0,01.0

/108 28

cmAje

Wall transition: from vortex all to transverse wall

xv

yv

Magnetic tunnel Junction

1 0

Goal: using a reasonable current to switch magnetization, ideally less than 106 A/cm2

Conductorlead

J

Oscillation of M (GHz) by a DC current

Application 2: local AC magnetic field oscillators (generators)

Local AC field (1000 Oe) with spatial resolution 10nm!

Application IV: concerns of CPP reading heads

Bit width

Bit length

Conductorlead

JM Spin

valve

“0”“1”

The large current density in CPPreading heads may produce unwanted switching!

Goal: eliminates current-inducedswitching for current densitylarger than 107A/cm2

Acknowledgement

Students: Dr. Yu-nong Qi, Mr. Zhao-yang Yang, Mr. Jie-xuan He

Postdoctoral: Dr. Z. Li (Postdoctoral)

Collaborators: P. M. Levy (NYU)

A. Fert (Orsay-Paris) Funded by: NSF-DMR, NSF-ECS, DARPA, NSFC