AC Measurement of Magnetic Susceptibility

Physics 401, Spring 2019

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

0 500 1000-4

-2

0

2

4

I DC (

A)

time (s)

DC current profile and magneticpermeability of MagneticsZW44715TC

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-250 -200 -150 -100 -50 0 50 100 150 200 2500

2000

4000

6000

8000

10000

12000

14000

H (A/m)

r'

H (A/m)

r_max

~12700

-8 -6 -4 -2 0 2 4 6 89000

10000

11000

12000

13000

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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