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Magnetic measurements:
basic aspects
Introduction
Magnetic units
Force methods
Induction methods
SQUID Magnetometer
G. Hilscher TU Vienna
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TcT
e
eC
T
C eff g JJ1
Magnetic Characterisation
MH,T
NgBJ
MS BJgBJHeff
kBT
0
0
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Low Temperatures & High Fields
Moment of 1 B in.H
kB.T
40T @ 300K 0.09
40T @ 1.5K 18
17T @ 10mK 1200
1B in 1T 0.7 KµBH/kBT
MH,T
NB
MS B 1
2
BH
kBT
0
0
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Magnets
Electromagnets 1.5 -2.5 T SC Magnets 9 – 22 T
5cm
Nb3Sn
filaments
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Pulsed Fields 40 – 60 T
15 mF
440 kJ 10 kV
access to the mains 10 MW 1 s
10 -20 ms
pulse duration
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1.5 K Pot
3He liquid 300mK
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3He/ 4He Fridge
3He
<3He/ 4He
99% 3He
1.5 K
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Magnetic Units
SI System:
M
V
Am2
m3
Am e
MH
Am
m
A1
Solid State Physics: M as Moment/Mass
Magnetisation defined as Moment / Volume
M
m Am2
kg
J
T.kg
eMH
Am2
kg
m
A
m3
kgor m3
mol
B 0HM
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Frequently used unit in magnetism: emu/g
g
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CGS System: BMG; HOe
Magnetisation defined as Moment / Volume
M
V
Gcm3
cm3
emu
cm3G e
MH
G
Oe1
eMH
Gcm3
Oe g
cm3
g emug
Moment/MassM
m Gcm3
g emu
g
M: 1 Am2
kg1 Gcm3
g emu
g
e: m3
kg
1000
4
cm3
g emu
g
B H4M
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Pendulm-BalanceFaraday-Balance
Force Methods
Em B FB
Fz zdB
dz
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Sensitivity:
g balance 1g 108N dBdz10T/m
Fz zdB
dz
z 109Am2 or 106 emu
moment: 1nA enclosing an area of 1m2
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sampledHz /dz
Force or Torque Measurement with a cantilever
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piezorestistive cantilever
Torque Magnetometer
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Induction Methods
dt
dtU )(
M(H)
B(H)
B = µ0 (H+M)
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dt
dNtU )(
•N...number of windings•A...winding area
•C...coupling factor
dMdHCµAN
dBCANdt
ddtNdttUM
geometrycoil
beshould 0
0..
..)(
N1 A1 – N2 A2 10-3
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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
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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
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HtH0 cost
MtM0 cost
Uind NAdMt
dtNAH0e0 sint
e0 ecostesint with e
M0 cos
H0, e
M0 sin
H0
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P robe
P U -S pule 1
P U -S pule 2
Fe ldspu lePSD
HtH0 cost
AC or initial susceptibility
Oscillator HtH0 cost
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SC wire;
SQUID Magnetometer
SC
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Flux-Response
SC wire; 2nd order
Gradiometer coil
SQUID Magnetometer
SC
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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
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Flux in the SC ring: int = ext + LI SExternal 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
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DC-SQUID: 2 weak links
V
I
000210&.)/cos()sin( nforMinimaMaxIII
iiJ
V
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DC-SQUID: 2 weak links
V
V
ext / 0
0 1 2
V
n120
n0
IIbias
B
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DC-SQUID: 2 weak links
Ibias = I1+I2 = Ic1 sin 1 + Ic2 sin 2
Simplification: Ic1 = Ic2 =Icand point contacts
V
V
ext / 0
0 1 2
V
n 0
n120
n0
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DC SQUID with integrated flux transformer
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Magnetic Signal Levels
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RF und DC SQUID Elektronik
Flux Locked Mode: Zusätzlich zum externen
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
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MHiMHa
Hext
Hext
Hintern - N.M
Hi Ha NM
Bi 0Hi MBa 01NM
Demagnetising factor
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Kugel: N x N y N z 1/3 (Lorentz Feld)
Hi Ha M
3
Bi Ba 20M
3
Mint eintH int; egem Mint/Ha
eint eg
1Neg
Oder analog
egem Mint
H int NMint
eint
1Neint
11/eint N
eint (z.B. bei Tcwirdegem 1/N .
Supraleiter:eint 1 und N 1 dannegem .
Sphere
Or
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First Nb RF SQUID
Einkopplungsspule, RF Spule
Punktkontakt mit Nb Schrauben
