Microwave Dynamics and Phase Locking in Spin Transfer

Nanocontacts

W. H. Rippard, M. R. PufallS. Kaka*, S. E. Russek, T. J. Silva

National Institute of Standards and Technology,Boulder, CO

J. A. KatineHitachi Global Storage Technologies

San Jose, CASupported by: NIST Nanomagnetodynamics

DARPA SpinS programNIST OMP Office

* Now at Seagate Research Labs,Pittsburgh, PA

Outline

IntroductionSpin transfer effectsDevice geometry

Spin transfer induced dynamicsin plane fieldsout of plane fields

Phase locking of devices

Injection locking to source

Mutual synchronization of oscillators

Summary

0.1 0.2 0.3 0.4 0.5 0.6 0.7

-200

-100

0

100

200

V Osc

(µV)

Time (ns)

Idc= 7.85 mA

Idc= 7.8 mA

Idc= 7.6 mA

Idc= 7.4 mA

Magnetodynamics

Larmor term:precession

My

Mz

Mx

M

H

10 1 eff

dm m Hdt

µ γ= − ×r rr

Precession

H

Spin Torque

Damping

M

Spin Torque Term

Spin torque cancounteract damping

1 1 21

J( )

2inj

z s

m m mel Mε γ

+ × ×h r r v

1Larmor Damping SpinTransfer

dm T T Tdt

= + +r

M Initial

My

Mz

Mx

0 1 1( )effm m Hµ γα− × ×rr r

MFinal

H

Damping term:aligns M with HEFF

MInitial

Slonczewski 1996

TSpin Transfer ≅ TDampingJ ~ 107A/cm2

Device Schematic

V+

Au

Cu“Fixed” layer

“Free” layerInsulator

~50 nmV-

5 nm

20 nm

Measurement setup

Detection:40 GHz Spectrum

Analyzeror

Sampling scopeDC current in

Device

bias teehigh bwprobes

Spinwave radiation

Micromagnetics

Measured signal results from IDC and GMR effect

Nanocontact Dynamics Device Schematic

• Step DC current• Measure DC R, microwave

power output

5 6 7 8 924.8

25.0

25.2

25.4

Res

ista

nce

(Ω)

Current (mA)

9.6 9.7 9.8 9.9 10.0

0.0

0.1

0.2

0.3

0.4

6 mA

6.5 mA 7 mA

7.5 mA

8 mA

8.5 mA

9 mA

Pow

er (p

W)

Frequency (GHz)

Devices are nanoscale current controlled microwave oscillators

Au

Cu

~50 nmT = 300K

“Free” layer“Fixed” layer

In-Plane Applied Fields

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

Field (T)

26.2 ±0.5 GHz/T

Freq

uenc

y (G

Hz)

Small-angle FMR frequency7.5

6.9

7.2

7.8

5 6 7 8

-0.23 GHz/mA

Current (mA)

Freq

uenc

y (G

Hz)

Current Response Field Response

Consistent with large angle version of FMRQualitative behavior in accordance with

Slonczewski equation

φ ≈ 80˚H

M

Out of Plane Fields

Precession occurs about the applied field directionlarger tunablity with current

Low IDemag ≈ Ms

Heff=Happ-Hdemag

Demag ≈ 0 THigh I

0.5 0.6 0.7 0.8 0.9 1.0

20

25

30

35

40

Freq

uenc

y (G

Hz)

Field (T)

Tunability:20 GHz to >40 GHz

Field Response

Device Output

Integrated voltage output:

V = 850 µV

Maximum GMR response:

∆R = 250 mΩI = 10 mA

∆V = 2.5 mV

Lower bound: Impedance mismatch not accounted forBoth frequency and power indicate approaching ~80° precessional angles

θ ∼ 85˚H

13.10 13.15 13.20

0

2000

4000

6000

8000

Spec

tral D

ensi

ty (n

V2 /Hz)

Frequency (GHz)

f = 13.15 GHz∆f = 7.1 MHzIdc= 10 mA

Injection LockingSynchronized Fireflies

Huygens (1665)Coupled pendulum clocks

http://www.pojman.com/NLCD-movies/NLCD-movies.html

General characteristic of all nonlinear oscillators:

Circadian rhythms, Huygens’ clocks, power grid, Josephsonjunctions, fireflies…….

Injection Locking Measurements

6.0 6.5 7.0 7.5 8.0

15.6

15.8

dV/d

I (Ω

)

10.7

10.8

10.9

11.0

f (G

Hz)

Current (mA)

No Modulation

15.6

15.8

dV/d

I (Ω

)

10.7

10.8

10.9

11.0

f (G

Hz)

6.0 6.5 7.0 7.5 8.0

-5

0

5

10

V rect (µ

V)

Idc

(mA)

Indirect evidence of phaselocking in frequency domain

Tsoi et al. 2001

locked

Modulation f = 10.86 GHz

nV2 /H

z

0

100

DC rect. voltage

Spectral Measurement of LockingSpectral measurement of locking

PS

D (n

W/H

z)

During locking the device takes on thenoise characteristics of the input signal

-oscillator linewidth approaches Hz

Time Domain MeasurementsSampling oscilloscope

Microwavesource

30 dB

Powersplitter Bias

tee

SMTdevice

DC Bias

0.1 0.2 0.3 0.4 0.5 0.6 0.7

-50

-25

0

25

50

V out (µ

V)

Time (ns)

f = 10.86 GHz

10.84 10.86 10.880

25

50

75

100

Am

plitu

de (n

V2/H

z)

Frequency (GHz)

f = 10.62 GHz

∆f = 7 MHzAmp = 44 µV

Spectral Measurement Time-domain Measurement

Electronic Phase Control of Oscillations

0.1 0.2 0.3 0.4 0.5 0.6 0.7

-200

-100

0

100

200

V Osc

(µV

)

Time (ns)

Idc= 7.4 mA

Idc= 7.6 mA

Idc= 7.8 mA

Idc= 7.85 mA

7.4 7.5 7.6 7.7 7.8

-100

-50

0

50

100

Rel

. Pha

se S

hift

(deg

rees

)

Idc (mA)

locked

Time-domain Measurements Relative Phase Change

Relative phase change over locking region is approximately 180 degreesDemonstrates electronic phase control of oscillators

Injection Locking of DevicesPhase relationship

General theory (Adler, 1973):

The Adler Equation

osc

injlinewidthlock V

Vff ∆=∆ Generally expect linear relationship

between locking range and oscillator-linewidth-injected signal

Injection Locking ResultsInject Vac at 14 GHz

No injection

27 28 29 30

13.8

14.0

14.2

14.4

Current (mA)

-2E-11

2.8E-10

27 28 29 30

13.8

14.0

14.2

14.4

Current (mA)

Freq

uenc

y (G

Hz)

0.00 0.15 0.300

100

200 Locking Range ∆f(Iac) = -27.4 + 685 Iac

Lock

ing

Ran

ge (M

Hz)

ac Injection Amplitude (mA)

Inject Vac at 12.7 GHz

21 22 23 24 25 26 27

12.4

12.6

12.8

Current (mA)

Freq

uenc

y (G

Hz)

22 24 26

12.4

12.6

12.8

Current (mA)

-2E-11

2E-10

0.00 0.15 0.300

100

200

Lock

ing

Ran

ge (M

Hz)

ac injection Amplitude (mA)

Locking Range ∆f(Iac) = -4.3 + 238 Iac

Lack quantitative understanding of locking range

Mutual Phase Locking

Measurement circuit:Device schematic:

500 nm Magneticinteraction

ac to power combiner

Ic2 Vac, c2

S.A.

ac to power combiner

Ic1

power combiner

Vac, c1

φ

Dual Contacts On Single Mesa

Insulator

Magnetic mesa

Leads to c1, c2

nanocontacts

500nm

Individual Device Outputs

8 9 10 1115.5

16.0

Current (mA)

Freq

uenc

y (G

Hz)

Contact 2

8 9 10 1115.5

16.0

Current (mA)

Freq

uenc

y (G

Hz)

Contact 1

Bias point

Swee

p C2

Bias contact 1 and sweep current through contact 2

15 16 170

5

2.5

Pow

er (n

W/H

z)

Frequency (GHz)

Contact 1

Contact 2

Output from Both DevicesCombined Output

Contact 1 = Constant biasContact 2 = Swept bias

8 9 10 1115

16

17

Current (mA)

Freq

uenc

y (G

Hz)

Mutual Phase Locking

Locking range

20

0

Log

(pow

er)

Contact 1

Contact 2

0.0

0.2

0.4

0.6

Pow

er (n

W/H

z)

0

10

20

Pow

er (n

W/H

z)

15 16 170.0

0.5

1.0

Pow

er (n

W/H

z)

Frequency (GHz)

Mutual Phase Locking: Power & Phase

8.0 8.5 9.0 9.5 10.0 10.5 11.00

20

40

60

80

100

120

140

160

180

Pc1 Pc2

8.0 8.5 9.0 9.5 10.0 10.5 11.00

20

40

60

80

100

120

140

160

180

Pc1 Pc2 Pc1 + Pc2

8.0 8.5 9.0 9.5 10.0 10.5 11.00

20

40

60

80

100

120

140

160

180

Pc1 Pc2 Pc1 + Pc2 Pboth measure

21 ccout PPP +=

Pow

er (p

W)

Current (mA)

Incoherent sum:

8.0 8.5 9.0 9.5 10.0 10.5 11.00

20

40

60

80

100

120

140

160

180

Pc1 Pc2 Pc1 + Pc2 Pboth measure PCoherent sum

( )φcos2 2121 ccccout PPPPP ++=

Coherent sum:

Rel. Phase φ during lock ≈ 0o

…Phase locking a route to higher powers (n2), phased arrays

Mutual Phase Locking

8.5 9.0 9.5 10.0 10.5 11.0106

107

108

Line

wid

th (H

z)Current (mA)

Linewidth

8.5 9.0 9.5 10.0 10.5 11.015.5

16.0

16.5

17.0

Freq

uenc

y (G

Hz)

Current (mA)

Frequency

Contact 1

Contact 2

Linewidth decreases below individual oscillators when lockedNo clear master/slave relationship between devices

-stabilization against thermal effects?

Possible Locking Mechanisms Contact 1 Contact 2

• AC Dipole fieldsEstimate coupling field on theorder of several Oe

Possible mechanism

• Mode OverlapSimulations do not support such largearea of precession

Improbable mechanism

Contact 1 Contact 2

• Spin wave radiation between contactsSimulations support spinwave coupling between devices

Possbile mechanism

FIB cutting of magnetic mesa:

Cut Mesa

FIB cut

nanocontact

Cut between two contacts:Look for change in interaction

5 6 7 8 9 109.5

10.0

10.5

11.0

11.5

(log scale)

Current (mA)

Freq

uenc

y (G

Hz)

Phase locking Pre-FIB

5 6 7 8 9 109.5

10.0

10.5

11.0

11.5 mc2s310c10b

Current (mA)

Freq

uenc

y (G

Hz)

Bias point

Contact 1 Contact 2

5 6 7 8 9 10 119.5

10.0

10.5

11.0

11.5 mc2sc1m8b

Current (mA)

Freq

uenc

y (G

Hz)

Locking range

Combined output

5 6 7 8 9 109.5

10.0

10.5

11.0

11.5

(log scale)

Current (mA)

Freq

uenc

y (G

Hz)

Post FIB Loss of Phase Locking

5 6 7 8 9 109.5

10.0

10.5

11.0

11.5

(log scale)

Current (mA)

Freq

uenc

y (G

Hz)

Bias point

5 6 7 8 9 10 119.5

10.0

10.5

11.0

11.5

(log scale)

Current (mA)

Freq

uenc

y (G

Hz)

No phase locking

Indicates spinwaveradiation responsiblefor synchronizationat large distances

Combined output

Contact 1 Contact 2

SummaryObserve coherent microwave dynamics resulting from spin

torque effect

Qualitative behavior consistent with Slonczewski equation

Oscillators can be injection locked to:Injected AC currentApplied AC fields Proximate devices through spinwave interactions

(possibly through dipole fields at very close spacings)Qualitative behavior consistent with non-linear oscillator analysis

Remaining questions:

What determines locking range:How do we quantify the strength of the spinwave interaction.

What determines linewidth and phase relation of synchronized devices:No clear master/slave relationship.

Quantitative agreement with current/field dependence:Not given by Slonczewski equation.

Likely all point to understanding of the mode structure