1. 1
Magnetic measurements:
basic aspects
Introduction
Magnetic units
Force methods
Induction methods
SQUID Magnetometer
G. Hilscher TU Vienna

2. 2
Tc
T
e
e C
T

C  eff g JJ 1
Magnetic Characterisation
MH,T
NgBJ

MS BJ
gBJHeff
kBT
0
0

3. 3
Low Temperatures & High Fields
Moment of 1 B in .H
kB.T
40T @ 300K 0.09
40T @ 1.5K 18
17T @ 10mK 1200
1B in 1T  0.7 KµBH/kBT
MH,T
NB

MS B 1
2
BH
kBT
0
0

4. 4
Magnets
Electromagnets 1.5 -2.5 T SC Magnets 9 – 22 T
5cm
Nb3Sn
filaments

5. 5
Pulsed Fields 40 – 60 T
15 mF
440 kJ 10 kV
access to the mains 10 MW 1 s
10 -20 ms
pulse duration

6. 6
1.5 K Pot
3He liquid 300mK

7. 7
3He/ 4He Fridge
3He
<3He/ 4He
99% 3He
1.5 K

8. 8
Magnetic Units
SI System:
M 
V
 Am2
m3
 A
m  e M
H
 A
m
m
A
1
Solid State Physics: M as Moment/Mass
Magnetisation defined as Moment / Volume
M

m  Am2
kg
 J
T.kg
e M
H
 Am2
kg
m
A
 m3
kg
or m3
mol
B 0H M

9. 9
Frequently used unit in magnetism: emu/g
g

10. 10
CGS System: BM G; H Oe
Magnetisation defined as Moment / Volume
M

V
 Gcm3
cm3
 emu
cm3
G  e M
H
 G
Oe
1
e M
H
 Gcm3
Oe g
 cm3
g  emu
g
Moment/Mass
M

m  Gcm3
g  emu
g
M: 1 Am2
kg
1 Gcm3
g  emu
g
e: m3
kg
 1000
4
 cm3
g  emu
g
B H 4M

11. 11
Pendulm-BalanceFaraday-Balance
Force Methods
Em B  F B
Fz z
dB
dz

12. 12
Sensitivity:
g balance 1g 108
N dB
dz
10T/m
Fz z
dB
dz
z 109
Am2
or 106
emu
moment: 1nA enclosing an area of 1m2

13. 13
sample
dHz /dz
Force or Torque Measurement with a cantilever

14. 14
piezorestistive cantilever
Torque Magnetometer

15. 15
Induction Methods
dt
d
tU )(
M(H)
B(H)
B = µ0 (H+M)

16. 16
dt
d
NtU )(
•N...number of windings
•A...winding area
•C...coupling factor
 dMdHCµAN
dBCAN
dt
d
dtNdttUM
geometrycoil
beshould 0
0
..
..)(
N1 A1 – N2 A2 10-3

17. 17
MdttUC )(
T,H
He
M (T,H)
Extraction magnetometer
H
t
Sensitivity: 10-3 – 10-4 emu
Movement: 3cm with 0.5 - 1Hz
Sample mass 0.1 -10g
Field 0 - 15T
Measurement @ H = const.
Temperature 2K - 300K

18. 18
Vibrating Sample Magnetometer,
Foner Magnetometer
Lock-In
Amplifier
82 Hz
Oscillator
Laudspeaker
82Hz Vibration
Lock-In: links the 82Hz sample
movement with the
P.U. coil signal (82Hz),
M
Sensitivity 10-4 - 10-8 emu
Field 0- 17T
Sample movement 1mm, 82Hz
Temperature 2 - 400K (800 K)
Sample mass: 0.05 - 0.5g

19. 19
HtH0 cost
MtM0 cost 
Uind NA dMt
dt
NAH0e0 sint 
e0 e
cost e
sint with e

M0 cos 
H0
, e

M0 sin
H0

20. 20
P robe
P U -S pule 1
P U -S pule 2
Feldspule
PSD
HtH0 cost
AC or initial susceptibility
Oscillator HtH0 cost

21. 21

22. 22
SC wire;
SQUID Magnetometer
SC

23. 23
Flux-Response
SC wire; 2nd order
Gradiometer coil
SQUID Magnetometer
SC

24. 24
Superconductivity
SQUID Superconducting Quantum Interference Device
2) Meissner - Ochsenfeld
effect : Field expulsion
Bintern = 0
3) Flux quantisation:
= BF = n 0
0 = h/2e = 2,07.10-15 Vs
But only in multiply
connected SC!
n 0

25. 25
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
ext / 0
int /
0
IS

ext / 0
IS
1 2
IC

26. 26
DC-SQUID: 2 weak links
V
I
000210
&.)/cos()sin( nforMinimaMaxIII iiJ
V

27. 27
DC-SQUID: 2 weak links
V
V
ext / 0
0 1 2
V
n 1
2
0
n0
I
Ibias
B

28. 28
DC-SQUID: 2 weak links
Ibias = I1+I2 = Ic1 sin 1 + Ic2 sin 2
Simplification: Ic1 = Ic2 =Ic
and point contacts
V
V
ext / 0
0 1 2
V
n 0
n 1
2
0
n0

29. 29
DC SQUID with integrated flux transformer

30. 30
Magnetic Signal Levels

31. 31
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

32. 32
MHiMHa
Hext
Hext
Hintern - N.M
Hi Ha NM
Bi 0Hi MBa 01 NM
Demagnetising factor

33. 33
Kugel: Nx Ny Nz 1/3 (Lorentz Feld)
Hi Ha M
3
Bi Ba 
20M
3
Mint eintHint; egem Mint/Ha
eint 
eg
1 Neg
Oder analog
egem 
Mint
Hint NMint

eint
1 Neint
 1
1/eint N
eint  (z.B. bei Tcwird egem  1/N.
Supraleiter: eint 1 und N 1 dann egem  .
Sphere
Or

34. 34
First Nb RF SQUID
Einkopplungsspule, RF Spule
Punktkontakt mit Nb Schrauben