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physics 590
ruslan prozorov
AC magnetic measurements etc
18 November 2009 Physics 590 - AC Magnetic Measurements
lock-in amplifier
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
lock-in summary
with integrator
phase-sensitive detector (PSD)
integrate out
18 November 2009 Physics 590 - AC Magnetic Measurements
AC magnetic susceptibility
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
typical AC susceptometer
18 November 2009 Physics 590 - AC Magnetic Measurements
AC measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
solenoid in external fields
18 November 2009 Physics 590 - AC Magnetic Measurements
now we place it in field
18 November 2009 Physics 590 - AC Magnetic Measurements
resulting current
18 November 2009 Physics 590 - AC Magnetic Measurements
collective behavior (spin glass, vortices, superparamagnetic particles)
18 November 2009 Physics 590 - AC Magnetic Measurements
superconductors – Tc, weak links, irreversibility line etc
18 November 2009 Physics 590 - AC Magnetic Measurements
local AC response
18 November 2009 Physics 590 - AC Magnetic Measurements
even simpler device – measure B(x)
superconducting sampleHac
small Hall probe
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
creep
B
J
FL
Jc
F 0L
Φ=
Activation energy behavior
Pinning
• Vacancies, voids, inhomogeneities, where superconductivity is weak
• Pinning decreases energy losses caused by flux creep
18 November 2009 Physics 590 - AC Magnetic Measurements
influence of vortex creep
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
local vs. global AC susceptibility
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
AC susceptometers
• A true AC susceptometer must have an AC component of the applied field• The use of lock-in amplifier does not guarantee that the device is an AC
susceptometer
sample
Hac
Idc
Vac to lock-in
sample
Hdc
Iac
Vac to lock-in
AC
DC
Hall probe
Hall probe
Hall H DC DCV R I H=
Hall H AC DCV R I H=
18 November 2009 Physics 590 - AC Magnetic Measurements
classifications
• Local – measure magnetic induction B(t)– MO, Hall-probe, GMR
• Global – measure total magnetic moment– SQUID based, VSM, torque, Faraday balance
• Amplitude – measure the amplitude• Frequency – measure frequency shift
– MW cavity perturbation, TDR, resonant (see below)
• Resonant – taps to a resonance in the SAMPLE– NMR, FMR, EPR
• Non-resonant – measure non-resonant response (may still use resonant circuit)
• Microscopic– scattering– Mossbauer– phase contrast etc
18 November 2009 Physics 590 - AC Magnetic Measurements
different types and designs – the amplitude domain
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
QD AC coil set for PPMS
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
Analog vs frequency-domain measurements
zero-crossing detector
time
ampl
itude
10-7 sec
time
ampl
itude
time
ampl
itude measure frequency
advantages of the frequency domain• arbitrary wave form • bandpass filtering• mixing• aggressive amplification• extremely stable standards
resonant techniques
18 November 2009 Physics 590 - AC Magnetic Measurements
measure resonant frequency SHIFT!
18 November 2009 Physics 590 - AC Magnetic Measurements
driven vs. self-resonating circuit
frequency
ampl
itude
frequency
ampl
itude
problems: phase noise and finite Q - factor
frequency
ampl
itude
self-resonating circuit is equivalent to an infinite - Q resonator. phase noise is the only issue (can be dealt with with ultra-high stability clocks)
mw cavity set-up
18 November 2009 Physics 590 - AC Magnetic Measurements
microwave cavity-perturbation technique
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
what is measured and the calibration
18 November 2009 Physics 590 - AC Magnetic Measurements
tunnel-diode: negative differential resistance
18 November 2009
A tunnel diode or Esaki diode is named after Leo Esaki (Nobel Prize in Physics 1973).
Doping results in a conduction band on the electronic n-side to overlap with the (hole states) valence band on the p-side.
Tunneling current decreases with bias, because band overlap decreases
Heavily doped narrow (~100 Å wide) p-n junction.
Physics 590 - AC Magnetic Measurements
self-resonating circuit
0.02 - 1000 K
16 Tesla
0 0
12 fL C
π = 1LC
≠
0 50 100 150 200 250 3000
20
40
60
80
100
I (µA
)
V (mV)
R~1 kΩ
LT
4.2 K
18 November 2009 Physics 590 - AC Magnetic Measurements
actual hardware
18 November 2009 Physics 590 - AC Magnetic Measurements
3He cryostat (0.3 K)
dilution refrigerator (0.01 K)
new studentbreadboardtoy
researchgraderesonator
TDR
measurements of dynamic magnetic susceptibility
18 November 2009
R. Prozorov et al., PRB 62, 115 (2000); APL 77, 4202 (2000); PRL 85, 3700 (2000).
Physics 590 - AC Magnetic Measurements
30 0max 0
2 1/ 42 2/ 10
sample
coil
Vf LC ff Lf
LVf
π πχ−
= ∆⇒ − ≈ −∆ ≤
∆
( )( )
4 tanh 1RR
λ µπχ µ
λ µ−
direct spin contributionsuperconducting penetration depth
Superconducting gaps: 0.02<Δ<20 meVCorresponding frequencies: 1 GHz <Δ<10 THzTunnel diode energy: E = 50 neV = 0.5 mK
Hz
HxHy
λ
AC measurements - conclusions
• very useful when frequency is important (collective behavior, resonances, hysteresis etc)
• sensitivity is enhanced due to use of lock-in amplifiers or frequency-domain measurements
• disadvantage – perturbs the sample, usually significantly• variety of possible artifacts, stringent requirements for electronics etc
18 November 2009 Physics 590 - AC Magnetic Measurements
18 November 2009 Physics 590 - AC Magnetic Measurements
comparison with conventional techniques
technique standard best real lab
induction (extraction) coil 10-4 10-5 10-4
torque (torsion) /H-dependent/ 10-7 10-9 10-7
VSM 10-6 10-7 10-5
Faraday balance 10-6 10-7 10-5
SQUID magnetometer 10-7 10-8 10-6
two-coil AC susceptibility 10-7 10-8 10-6
microwave cavity perturb. 10-8 10-11 10-10
Tunnel-diode resonator 10-11 10-12 5x10-12
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