Upload
others
View
20
Download
0
Embed Size (px)
Citation preview
MSE 7025 Magnetic Materials
(and Spintronics)
Chi-Feng Pai [email protected]
Lecture 11: Characterization Techniques Episode II: FMR
(Magnetic dynamics and damping)
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
Dynamics of magnetization: RF regime
• Electron spin energy level – Studying unpaired electrons
2B z z L
e
eE g B g B
m
Dynamics of magnetization: RF regime
• 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
Ferromagnetic resonance (FMR)
• Real data
YIG
Difference in damping!
f = 3.33GHz
f = 8GHz
0
2 fH
Linewidth
Ferromagnetic resonance (FMR)
• So what can we get from FMR measurements?
• 1. (Effective) demagnetization field
• 2. Damping constant
Ferromagnetic resonance (FMR)
• So what can we get from FMR measurements?
• 1. (Effective) demagnetization field
• 2. Damping constant
0
2 fH B
02 2
H Bf f
Ferromagnetic resonance (FMR)
• FMR setup – RF microwave cavity
– RF signal generator
– Transmission lines
– Electromagnet
Ferromagnetic resonance (FMR)
• FMR setup – RF microwave cavity
– RF signal generator
– Transmission lines
– Electromagnet
Ferromagnetic resonance (FMR)
• FMR setup – RF microwave cavity
– RF signal generator
Ferromagnetic resonance (FMR)
• FMR setup – RF microwave cavity
– RF signal generator
Ferromagnetic resonance (FMR)
• FMR setup – Coplanar waveguide (CPW)
– Vector network analyzer (VNA)
– Transmission lines
– Electromagnet
Ferromagnetic resonance (FMR)
• FMR setup – Coplanar waveguide (CPW)
– Vector network analyzer (VNA)
– Transmission lines
– Electromagnet
Ferromagnetic resonance (FMR)
• FMR setup – Coplanar waveguide (CPW)
– Vector network analyzer (VNA)
– Transmission lines
– Electromagnet
SMA (SubMiniature version A) connectors (50 Ohm) Pass band: Typically 0–18 GHz, some up to 26.5 GHz
Ferromagnetic resonance (FMR)
• FMR setup
Ferromagnetic resonance (FMR)
• FMR setup
Ferromagnetic resonance (FMR)
• FMR setup
Ferromagnetic resonance (FMR)
• Probe station for (spin-torque) FMR
GSG-150um
RF Probe Head
Attached Hall Probe
Magnets (-2000 Oe to 2000 Oe)
Ferromagnetic resonance (FMR)
• Probe station for (spin-torque) FMR
Adjustable field angle up to ~ 40 deg
Ferromagnetic resonance (FMR)
• Probe station for (spin-torque) FMR
Coplanar waveguide (CPW) form
Ferromagnetic resonance (FMR)
• Probe station for (spin-torque) FMR
Ferromagnetic resonance (FMR)
• Probe station for (spin-torque) FMR
Ferromagnetic resonance (FMR)
• Probe station for (spin-torque) FMR
• 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
Ferromagnetic resonance (FMR)
• Probe station for (spin-torque) FMR
• 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
Ferromagnetic resonance (FMR)
• Probe station for (spin-torque) FMR
• 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)