physics 590 ruslan prozorov ac magnetic...

physics 590

ruslan prozorov

AC magnetic measurements etc

18 November 2009 Physics 590 - AC Magnetic Measurements

lock-in amplifier


lock-in summary

with integrator

phase-sensitive detector (PSD)

integrate out


AC magnetic susceptibility


typical AC susceptometer


AC measurements


solenoid in external fields


now we place it in field


resulting current


collective behavior (spin glass, vortices, superparamagnetic particles)


superconductors – Tc, weak links, irreversibility line etc


local AC response


even simpler device – measure B(x)

superconducting sampleHac

small Hall probe


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


influence of vortex creep


local vs. global AC susceptibility


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=


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


different types and designs – the amplitude domain


QD AC coil set for PPMS



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


measure resonant frequency SHIFT!


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


microwave cavity-perturbation technique


what is measured and the calibration


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


actual hardware


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



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

physics 590 ruslan prozorov ac magnetic...

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