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AC Measurement of Magnetic Susceptibility
Physics 401, Spring 2014
Eugene V. Colla
Outline
• Ferromagnetism
• Measurement of the magnetic properties of
the materials
• Lab experimental setup and experiments
• Some results
4/14/2014 2
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
4/14/2014 5
* Courtesy Wikipedia
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)
4/14/2014 6
Domains
Courtesy of Wikipedia
4/14/2014 7
Moving domain walls in a grain of silicon steel caused by an increasing external magnetic field
Hysteresis Loops. Remagnetization loses
𝑾 = 𝑽 𝑯𝒅𝑩 𝑾𝒍𝒐𝒐𝒑 = 𝑽 𝑯𝒅𝑩=V*Loop_area
Energy of the magnetic field
By cycling around the loop
4/14/2014 8
“Hard” materials. Application.RAM memory
Hard drives, floppy, magnetic tape
Permanent magnets
4/14/2014 9
“Soft” materials. Application.
Power transformers
Chokes, inductors
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4/14/2014 11
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
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
4/14/2014 13
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)
4/14/2014 18
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
4/14/2014 19
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
4/14/2014 20
From permeability to B-H hysteresis loop
Step#3. What we are measuring? Calibration.
Lock-in measures emf on the pickup coil
0p p
lock in r
dI dIdV L L
dt dt dt
Here Ip is ac current in primary coil L3; 𝑰𝒑 =𝑽𝟎𝐬𝐢𝐧(𝝎𝒕)
𝑹𝟐
4/14/2014 21
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
4/14/2014 22
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
4/14/2014 23
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)
4/14/2014 24
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
4/14/2014 25
Software issue
4/14/2014 26
Icon on the desktop
1st week experiment
2nd week experiment
Demagnetization
B-H measurement
Preparation of the profile of the experiment
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
4/14/2014 29
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
4/14/2014 30
Data analysis using Origin. Integrating.
0( ) ( )
rB H H dH offset
4/14/2014 31
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
4/14/2014 32