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

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

Vac to lock-in

sample

Vac to lock-in

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

10-7 sec

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

problems: phase noise and finite Q - factor

frequency

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

12 fL C

π = 1LC

0 50 100 150 200 250 3000

I (µA

V (mV)

R~1 kΩ

actual hardware

3He cryostat (0.3 K)

dilution refrigerator (0.01 K)

new studentbreadboardtoy

researchgraderesonator

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

Vf LC ff Lf

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

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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