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Magnetic measurements:

basic aspects

G. Hilscher TU Vienna





Introduction

Magnetic units

Force methods

Induction methods

SQUID Magnetometer





1

Magnetic Characterisation





e









0



Tc   T



gB JHeff 0 e T

C



M T M S B J

H,

 k BT

NgB J C  eff g J 

J 1

2

Low Temperatures & High Fields





B H0

M T M S B 1

H,

 2 k BT

NB



µBH/kBT 1B in 1T  0. 7 K





.H 

Moment of 1B in 0





k B .T



40T @ 300K 0.09

40T @ 1. 5K 18

17T @ 10mK 1200 3

Magnets



Electromagnets 1.5 -2.5 T SC Magnets 9 – 22 T

5cm









Nb3Sn

filaments 4

Pulsed Fields 40 – 60 T





15 mF







440 kJ 10 kV









10 -20 ms

pulse duration

5

access to the mains 10 MW 1 s

1.5 K Pot





3He liquid 300mK





6

3He/ 4He Fridge









1.5 K





99% 3He









3He





<3He/ 4He

7

Magnetic Units



SI System:   

B 0   

H M

Magnetisation defined as Moment / Volume

 Am2

M 

 V



m3

 A

m e

  M

H

 A m

m A 1





Solid State Physics: M as Moment/Mass



 Am2

M  m 

   kg

 J

T.kg



Am2 m m3 m3

e

 M

H

 kg A

 kg

or mol

8

Frequently used unit in magnetism: emu/g









g

9

CGS System:   4 M

B H   B M  H 

   G;   Oe



Magnetisation defined as Moment / Volume



 Gcm3

M 

 V



cm3

 emu

cm3

G e

  M

H

 Oe 1

G







Moment/Mass  Gcm3

M  m 

   g  emu

g



Gcm3 cm3

e

 M

H

 Oe g

 g  emu

g







Am 2 Gcm 3

M: 1 kg

1 g  emu

g



m3 cm 3

e: kg

 1000

4

 g  emu

g

10

Force Methods



 



E m  B    



F   B





Fz z dB

dz



Faraday-Balance Pendulm-Balance









11

Sensitivity:



g balance 1g 10  N

8 dB 10T/m

dz





Fz z dz

dB







z 10  Am 2

9

or 10  emu

6









moment: 1nA enclosing an area of 1m 2



12

Force or Torque Measurement with a cantilever







dHz /dz

sample









13

Torque Magnetometer









piezorestistive cantilever









14

Induction Methods

d

U (t )  

dt

B(H)

B = µ0 (H+M)







M(H)









15

d •N...number of windings

U (t )   N •A...winding area

dt •C...coupling factor





d

M   U (t )dt  N  dt  N . A.C  dB

dt



 

 

 N . A.Cµ0   dH   dM 



 coil geometry

should be 0 

 



N1 A1 – N2 A2  10-3 16

Extraction magnetometer

H



T,H

t





Sensitivity: 10-3 – 10-4 emu

Movement: 3cm with 0.5 - 1Hz

He Sample mass 0.1 -10g

Field 0 - 15T

Measurement @ H = const.

Temperature 2K - 300K





C  U (t ) dt  M



M (T,H)

17

Vibrating Sample Magnetometer,

Foner Magnetometer

Sensitivity 10-4 - 10-8 emu

Laudspeaker Field 0- 17T

82Hz Vibration Sample movement 1mm, 82Hz

Temperature 2 - 400K (800 K)

Sample mass: 0.05 - 0.5g



82 Hz

Oscillator





Lock-In

Amplifier M









Lock-In: links the 82Hz sample

movement with the

P.U. coil signal (82Hz),





18

 

tM0 cos t 

M



tH0 cos 

H t









 

U ind  dM NA 0e sin t 

NA dt t H 0



M 0 cos  M 0 sin 

t e

e ecos   sin  with e 

0

 



t 

H0

, e 





H0

19

AC or initial susceptibility









Probe







PU-Spule 1



PU-Spule 2



PSD

Feldspule





Oscillator tH0 cos 

H t

tH0 cos 

H t 20

21

SQUID Magnetometer









SC







SC wire;



22

SQUID Magnetometer



Flux-Response









SC







SC wire; 2nd order

Gradiometer coil

23

Superconductivity

SQUID Superconducting Quantum Interference Device





2) Meissner - Ochsenfeld

effect : Field expulsion

Bintern = 0









n0

3) Flux quantisation:

 = BF = n  0

 0 = h/2e = 2,07.10-15 Vs

But only in multiply

connected SC!

24

Flux in the SC ring: 

 int = ext + LI S

External flux is compensated by the flux expulsion

LIS until IS = IC ; we set LIC =  0 / 2







int / 

0



IS









ext /  0





IS IC

 ext /  0

1 2

25

V

DC-SQUID: 2 weak links







V









I

I J  I 0 sin(1  2 )  I 0 cos( i / 0 ) Max. & Minima for i  n0









26

V

DC-SQUID: 2 weak links









n 2 

 1  0 B

V

V



n0



 ext /  0

I 0 1 2

Ibias



27

V

DC-SQUID: 2 weak links







n 2 

 1  0



V

V



n0



 ext /  0

0 1 2



Ibias = I1+I2 = Ic1 sin 1 + Ic2 sin 2

Simplification: Ic1 = Ic2 =Ic

and point contacts

n 0



28

DC SQUID with integrated flux transformer









29

Magnetic Signal Levels









30

RF und DC SQUID Elektronik

Flux Locked Mode:





Additional to the external flux,

Flux with opposite sign

is coupled via the modulation

Coil into the SQUID that the

total flux

is kept constant

The deviation is measured with

a PSD amplified with an

Integrator coupled back

to the system









31

Demagnetising factor



M i M a 

H H







Hext



Hintern - N.M







Hext





  

H i H a N M

 H M    1

B i  0 i  B a  0 N

M 32

Sphere N x  N y  N z 1/3 (Lorentz Feld)

Kugel:

  

H i H a  M

3



i B a 20 M

B 

3





M int  e H int ; e M int /H a

int gem



eg

e 

int

1 N eg



Or

Oder analog

M int e 1

e   int



gem

H int  M int

N 1 e

N int 1/e 

int N





e   (z.B. bei T c 

int wird e  1/N .

gem



Supraleiter: e  und N 1 dann e  .

int 1 gem 33

First Nb RF SQUID









Einkopplungsspule, RF Spule



Punktkontakt mit Nb Schrauben









34