mse 7025 magnetic materials (and spintronics)cfpai/mse7025/mse7025_lecture11_fmr.pdf · 3 march 9...

MSE 7025 Magnetic Materials

(and Spintronics)

Chi-Feng Pai [email protected]

Lecture 11: Characterization Techniques Episode II: FMR

(Magnetic dynamics and damping)

mailto:[email protected]

Course Outline • Time Table

Week Date Lecture

1 Feb 24 Introduction

2 March 2 Magnetic units and basic E&M

3 March 9 Magnetization: From classical to quantum

4 March 16 No class (APS March Meeting, Baltimore)

5 March 23 Category of magnetism

6 March 30 From atom to atoms: Interactions I (oxides)

7 April 6 From atom to atoms: Interactions II (metals)

8 April 13 Magnetic anisotropy

9 April 20 Mid-term exam

10 April 27 Domain and domain walls

Course Outline • Time Table

Week Date Lecture

11 May 4 Magnetization process (SW or Kondorsky)

12 May 11 Characterization: VSM, MOKE

13 May 18 Characterization: FMR

14 May 25 Transport measurements in materials I: Hall effect

15 June 1 Transport measurements in materials II: MR

16 June 8 MRAM: TMR and spin transfer torque

17 June 15 Guest lecture (TBA)

18 June 22 Final exam

Dynamics of magnetization

• Low frequency (~Hz)

• High frequency (~GHz)

Dynamics of magnetization: RF regime

• Larmor frequency

• Electron-spin resonance (ESR)

– Electron “paramagentic” resonance

• If an RF power is being injected

– Hdc along z-axis

– Hrf along x-axis

– Absorption of RF power

rf 0 cosxH H H t

When L


• Electron spin energy level – Studying unpaired electrons

2B z z L

e

eE g B g B

m


• Dynamics equation re-visit

• Free precession

• With magnetic damping

eff 0 efft

MM B M H

0 eff eff

st M

MM H M M H

Damping term

0

Dynamics of magnetization: LLG equation

• Landau-Lifshitz equation

• Gilbert damping term

• Landau-Lifschitz-Gilbert equation (LLG eqn.)

0 eff

st M t

M MM H M

0 eff eff

st M

MM H M M H

sM t

MM

Gilbert damping constant

Dynamics of magnetization: LLG equation

• Landau-Lifschitz-Gilbert equation (LLG eqn.)

• Normalized LLG equation

• Effective field

0 eff

st M t

M MM H M

0 eff

ˆ ˆˆ ˆ

t t

m mm H m

eff ext demag ...an H H H H

Damping mechanisms

• Correlated precession of moments

– Spinwaves or magnons

– Transverse relaxation

– Longitudinal relaxation

0k

1 11~ ~10 sB

0 0k k

~ 0.2TB

Ferromagnetic resonance (FMR)

• RF dynamics in a real ferromagnetic material

– Internal field related to demag effect

• Kittel formula

in ext i iH H N M

y

x

z

2 2

0 0x z s y z sB N N M B N N M

0, 1y z xN N N ?

0in ext i iB B N M

0x

y y z s

MM B N N M

t

0

y

x x z s

MM B N N M

t

z sM MextB


• Real data

YIG

Difference in damping!

f = 3.33GHz

f = 8GHz

0

2 fH

Linewidth


• So what can we get from FMR measurements?

• 1. (Effective) demagnetization field

• 2. Damping constant


• So what can we get from FMR measurements?

• 1. (Effective) demagnetization field

• 2. Damping constant

0

2 fH B

02 2

H Bf f


• FMR setup – RF microwave cavity

– RF signal generator

– Transmission lines

– Electromagnet


• FMR setup – RF microwave cavity

– RF signal generator


• FMR setup – Coplanar waveguide (CPW)

– Vector network analyzer (VNA)


– Electromagnet


• FMR setup – Coplanar waveguide (CPW)

– Vector network analyzer (VNA)


– Electromagnet

SMA (SubMiniature version A) connectors (50 Ohm) Pass band: Typically 0–18 GHz, some up to 26.5 GHz


• FMR setup


• Probe station for (spin-torque) FMR

GSG-150um

RF Probe Head

Attached Hall Probe

Magnets (-2000 Oe to 2000 Oe)



Adjustable field angle up to ~ 40 deg



Coplanar waveguide (CPW) form



• Real data

-2000 -1000 0 1000 2000-10

-8

-6

-4

-2

0

2

4

6

8

10

Vm

ix (V

)

In-plane Field (Oe)

6.0 GHz

7.0 GHz

8.0 GHz

9.0 GHz

-2000 -1000 0 1000 2000

-16

-12

-8

-4

0

4

8

12

16

Vm

ix (V

)

In-plane Field (Oe)

5.36 GHz

6 GHz

7 GHz

8 GHz

9 GHz

10 GHz

Pt/CoFeB/MgO Pt/CoFeB/MgO



• Real data

-2000 -1000 0 1000 2000-6

-4

-2

0

2

4

6

Vm

ix (V

)

In-plane Field (Oe)

6.0 GHz

7.0 GHz

8.0 GHz

9.0 GHz

0 40 80 120 160-20

-10

0

10

f = 9 GHz

CoFeB (3 nm)/ Pt (6 nm)

Vm

ix (V)

Bext

(mT)

Pt/CoFeB/MgO



• Real data

400 800 1200 1600 20002

3

4

5

6

7

8

9

10

11

4Meff

=4450 70 Oe

Fre

quency (

GH

z)

H0 (Oe)

0 0 eff42

f H H M

0 1 2 3 4 5 6 7 8 90

100

200

300

400

500

600

(

Oe)

Frequency (GHz)

= 0.13 0.01

eff2 f

B

(cgs)

mse 7025 magnetic materials (and spintronics)cfpai/mse7025/mse7025_lecture11_fmr.pdf · 3 march 9...

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