physics 590 ruslan prozorov AC magnetic measurements etc
lock-in amplifier
lock-in summary with integrator integrate out phase-sensitive detector (PSD)
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) small Hall probe H ac superconducting sample
creep B J F L Activation energy behavior Φ c 0 FL = J 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 AC H ac Hall probe sample V ac to lock-in VHall = RH IDCHDC I dc DC H dc Hall probe V ac to lock-in sample VHall = RH IACHDC I ac
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 amplitude measure frequency time 10-7 sec zero-crossing detector 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 amplitude amplitude frequency frequency problems: phase noise and finite Q - factor 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 A tunnel diode or Esaki diode is named after Leo Esaki (Nobel Prize in Physics 1973). Heavily doped narrow (~100 Å wide) p-n junction. 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 18 November 2009 Physics 590 - AC Magnetic Measurements
self-resonating circuit 4.2 K 100 80 LT 0.02-1000 K I (µa) 60 40 20 R~1 kω 0 0 50 100 150 200 250 300 V (mv) 2π f = 1 LC 0 0 16 Tesla 1 LC
actual hardware new student breadboard toy research grade resonator TDR 3 He cryostat (0.3 K) dilution refrigerator (0.01 K)
measurements of dynamic magnetic susceptibility 2π f = 1/ LC f L V f f 2L 2V 3 fmax / 0 10 0 0 sample coil 4πχ 4 λ ( µ ) tanh R πχ µ R λ µ 1 ( ) z H y H x H direct spin contribution Superconducting gaps: 0.02<Δ<20 mev Corresponding frequencies: 1 GHz <Δ<10 THz Tunnel diode energy: E = 50 nev = 0.5 mk superconducting penetration depth λ R. Prozorov et al., PRB 62, 115 (2000); APL 77, 4202 (2000); PRL 85, 3700 (2000). 18 November 2009 Physics 590 - AC Magnetic Measurements
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