ac measurement of magnetic susceptibility
TRANSCRIPT
AC Measurement of Magnetic Susceptibility
Physics 401, Fall 2017
Eugene V. Colla
Outline
• Ferromagnetism
• Measurement of the magnetic properties of
the materials
• Lab experimental setup and experiments
• Some results
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Ferromagnetism. Definition.
Some materials below a certain temperature (Tc) give rise to the magnetic field in absence of an applied field.
This magnetization is called spontaneous, the phenomenon – ferromagnetism and materials exhibiting this feature – ferromagnetics.
The main parameter of the ferromagnetic phase transition is spontaneous magnetization
0.0 0.5 1.00.0
0.5
1.0
T/Tc
Ms(T
)/M
s(0
)
Typical behavior of spontaneous magnetization as function of temperature
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Ferromagnetic materials.
Aleksandr Stoletov(1839 –1896)
Material Curie temp. (K)
Co 1388
Fe 1043
Fe2O3* 948
FeOFe2O3* 858
NiOFe2O3* 858
MgOFe2O3* 713
MnBi 630
Ni 627
MnSb 587
MnOFe2O3* 573
Y3Fe5O12* 560
CrO2 386
MnAs 318
Gd 292
“Stoletov” curve
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Stoletov performed pioneer works in area of ferromagnetic materials but better known by his research in photoelectric effect.
dM
dH
Domains. Hysteresis loop.
M~Ms
M=0
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* Courtesy Wikipedia
Kerr Effect. Visualization of the Domains
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John Kerr17 Dec 1824 –15 Aug 1907
The Diagram of Typical Kerr Microscope
Courtesy of Radboud University, Nijmegen The Netherlands
Domains
Several grains of NdFeB with magnetic domainsmade visible via contrast with a Kerr microscope.
Courtesy of Wikipedia
Kerr microscopeCourtesy of University of Uppsala (Sweden)
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Domains
Courtesy of Wikipedia
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Moving domain walls in a grain of silicon steel caused by an increasing external magnetic field
Hysteresis Loops. Remagnetization loses
𝑾 = 𝑽න𝑯𝒅𝑩 𝑾𝒍𝒐𝒐𝒑 = 𝑽ׯ𝑯𝒅𝑩=V*Loop_area
Energy of the magnetic field
By cycling around the loop
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“Hard” materials. Application.RAM memory
Hard drives, floppy, magnetic tape
Permanent magnets
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“Soft” materials. Application.
Power transformers
Chokes, inductors
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Magnetic Field, Susceptibility etc.
0B H M
B – magnetic inductionM – magnetization, in general M(H)
M Hχ – magnetic susceptibility, in general χ(H)
0 01
rB H H H
0
0
1;
r r
dB dB
dH dH
1r
Modulation Spectroscopy
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( )B f H
0 1H = H + H sinωt
H0
0 1H = H + H sinωt
0 1
dfB = f(H ) + (H sinωt)+ ...
dH
B0Bw
( )B f H
H1=const
𝑩𝝎~𝒅𝑩
𝒅𝑯
Measuring the magnetic permeability
0
0 0 0
,
( , ) (1 ( , ))H
dBH H
dH w
w w
By applying a small modulation of the H
field we can measure the derivative of the
B-H hysteresis loop or dependence of the
magnetic permeability on H field
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Setup #1. Investigation of the hysteresis loops.
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Setup #1. Investigation of the hysteresis loops.
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0 1 cosH H H tw
𝑯 =𝑵𝒑𝑰𝒑
𝟐𝝅𝒓
Major/minor loops. Demagnetization
B
H
saturation
80 160 240
-100
0
100
time
H(a
.u.)
Waveform of H-field
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Demagnetization
0
20
40
60- 2
- 1
0
1
2
-3.6
-1.8
0.0
1.8
3.6
B (
a.u
.)
Idc (A)
time (m
in)
0 20 40 60
-2
-1
0
1
2
I DC (
A)
time (min)
Demagnetization of 4C65 toroid from Ferroxcube
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Hysteresis Loops
Fig. A family of AC hysteresis loops for grain-oriented electrical steel (BR denotes
remanence andHC is the coercivity). Courtesy Zureks (Wikipedia)
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Measuring the magnetic permeability
-200 -100 0 100 2000
2
4
6
8
10
12
14
'/1
000
H (A/m)
max
~12700
-10 0 10
8
10
12
H (A/m)
0 500 1000-4
-2
0
2
4
I DC (
A)
time (s)
DC current profile and magneticpermeability of MagneticsZW44715TC
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From permeability to B-H hysteresis loop
Step#1. Performing one fast IDC scan the based on the result preparing the “smart” IDC profile
ECE storeroom unknown material Sample #5
0 200 400 600 800
-1
0
1
I DC (A
)
time (s)
Step#2. Performing precise scan the. Plotting raw data based
-1.0 -0.5 0.0 0.5 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Y (
mV
)
IDC (A)
Voltage units measured by SR830
Current in primary coil in A
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From permeability to B-H hysteresis loop
Step#3. What we are measuring? Calibration.
Lock-in measures emf on the pickup coil
;lock in
dV B S
dt
Here Ip is ac current in primary coil L3; 𝑰𝒑 =𝑽𝟎𝐬𝐢𝐧(𝝎𝒕)
𝑹𝟐
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From permeability to B-H hysteresis loop
Step#3. What we are measuring? Calibration.
Primary coil of Np turns supplied by current Ip creates magnetic field H and flux dΦ
For toroid: 𝑯 =𝑵𝒑𝑰𝒑
𝟐𝝅𝒓R2 <r < R1
2
1
2
1
ln
2 2
R
R
RI N t dr I N td H da
r R
da=dr*t
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From permeability to B-H hysteresis loop
Step#3. What we are measuring? Calibration.
2
1
ln2
pickup p p
pickup
N N I t RN d
R
Total flux detected by pickup coil:
Inductance of the toroid:
0 0; ( )
rL L L i L
I
0 20
1
ln2
pickup pN N t RL
R
Np and Ip number of turns of AC primary coil and AC rms current
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From permeability to B-H hysteresis loop
-1.0 -0.5 0.0 0.5 1.00.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Y (
mV
)
IDC (A)
𝑯𝟎 =𝑵𝒑𝑰𝑫𝑪
𝟐𝝅𝒓
0
p
lock in r
dIV L
dt
-400 -200 0 200 4000
1000
2000
3000
4000
5000
6000
'
H (A/m)
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0
2
cos( )pdI V
tdt R
w w
w
~ w !
From permeability to B-H hysteresis loop
0 0 0 0( ) ( )
r
dBH H H
dH
Step#4. From r(H) to B-H
After integrating →
-400 -200 0 200 4000
1000
2000
3000
4000
5000
6000
'
H (A/m)
-400 -200 0 200 400
-0.2
0.0
0.2
B(T
)
H (A/m)
0( ) ( )
rB H H dH
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Software issue
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Icon on the desktop
1st week experiment
2nd week experiment
Demagnetization
B-H measurement
Preparation of the profile of the experiment
Software issueMeasuring profile preparation. Using profile template
Open a new file
Create a new file
Save prepared file for future use
Software issueMeasuring profile preparation. Using profile template.
Software issue
Measuring profile preparation
Example of simple protocol
Advanced profile
-400 -200 0 200 4000
1000
2000
3000
4000
5000
6000
'
H (A/m)
Software issueMeasurement Window
Lock-in amplifier response
The profile of the appliedDC current
Structure of the data file (B-H experiment)
Data analysis using Origin
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To calculate the permeability better to use the template :
\\engr-file-03\phyinst\APL Courses\PHYCS401\Common\Origin templates\AC magnetic Lab\MU_CALCULATION.otw
Raw dataParameters Calculated results
It does not contain the equations – you have to write them
Data analysis using Origin. Integrating.
0( ) ( )
rB H H dH
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Data analysis using Origin. Integrating.
0( ) ( )
rB H H dH offset
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Ms
-Ms
References
• Information about magnetic materials can be found in :
\\engr-file-03\phyinst\APL
Courses\PHYCS401\Experiments\AC_Magnetization\Magnetic
Materials
• SR830 manual: \\engr-file-03\phyinst\APL
Courses\PHYCS401\Common\EquipmentManuals\SR830m.pdf
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