Magnetometry at the NHMFL A Practical Guide to AC Susceptometer, Torque Magnetometer,VSM

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Magnetometry at the NHMFLA Practical Guide to
AC Susceptometer, Torque Magnetometer,VSM

• Eun Sang Choi
• National High Magnetic Field Laboratory

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Outline

• Introduction
• What we measure. (B or M)
• How we measure. (susceptometers, magnetometers)
• Brief survey of techniques
• Magnetometry at DC field facilities
• Ac susceptometer
• Torque magnetometer
• Capacitative torque magnetometer
• Piezoresistive torque magnetometer
• Vibrating sample magnetometer (VSM)
• Summary

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What we measure B or M
SI B µH µ0 (HM) µ0 (1?)H cgs B H
4pM B Magnetic flux density, Magnetic
induction ? susceptometer H Magnetic field
strength ? experimentally controllable M
(Volume) Magnetization ? magnetometer
Usually H gtgt M ? B(T), µ0H(T)
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How we measure susceptometer, magnetometer

• (1) Susceptometer 1
• Induced voltage sensor
• measure flux of changing fields (vibrating
  (rotating) coil, oscillating field..)
• Galvanomagnetic sensor Hall effect, MR ..
• Ferromagnetic sensor
• fluxgate, ferromagnetic thin film
• Other methods SQUID (10-12 (rf) 10-15 T
  (dc)), NMR, ESR.

1Landolt-Börnstein New Series Units and
Fundamental Constants in Physics and Chemistry,
Springer (1992).
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(2) Magnetometer1
Force (torque) method Faraday balance (10-7
emu) Gouy balance (10-6 emu) Vibrating reed
magnetometer (10-7 emu) Cantilever torque
magnetometer (10-3 10-8 (metal film), 10-9
10-11 emu (piezoelectric)) Trampoline force
magnetometer (10-9 10-10 emu) Induction (flux)
method SQUID (10-11 emu) Vibration Sample
Magnetometer (VSM) (10-7 emu) AC susceptometer
(10-9 emu) Indirect Method Magneto-Optical Kerr
effect (10-9 10-10 emu) ESR, NMR, Mössbauer,
Flux gate
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Faraday balance
Gouy balance
Trampoline magnetometer3
Vibrating reed2
2Richter et al., RSI (Rev. Sci. Inst.), 59, 1388
(1988)
3Aksyuk et al., Nature, 280 728 (1998)
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AC susceptometer
ac current for primary coil
Background voltage (without sample)
Sample in coil 1
Sample in coil 2
N of turns S cross section area f filling
factor hac oscillating external field ?ac
complex susceptibility (?-i ?) ? in-phase
signal ? out of phase signal
calibration factor (sensitivity)
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Balancing (compensation) techniques4,5 (1)
matched counter-wound coils ? minimize VB (2)
sample translation between two pick-up coils (3)
subtraction of an ac waveform equal to that of
empty pick-up coil i) balance (minimize VB)
using external compensator without sample ii)
use differential amplifier for sample and balance
signal
Calibration Paramagnetic standard (Al, Pt, Pd,
Tuttons salt) Ferromagnets Superconducting
materials
Other issues Skin depth for metallic samples (use
smaller freq.) Eddy current effect (heating,
phase shift)
4Goldfarb, RSI 55, 761 (1984) 5Whitmore et al.,
RSI 49 1579 (1978)
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6Rillo et al., Magnetic susceptibility of
superconductors and other spin systems ed by
Hein et al., P 1 (1991).
Balancing (compensation) techniques
(3) subtraction of an ac waveform equal to that
of empty pick-up coil i) balance (minimize VB)
using external compensator without sample ii)
use differential amplifier for sample and balance
signal
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• Application7
• Phase transitions (FM, AFM)
• Spin glass, superparamagnetism (frequency
  dependence)
• Superconductors (transition, irreversibility)
• de Haas van Alphen oscillation (increased
  sensitivity with modulation coil)
• Can be used at extreme conditions low T, high
  pressure, high (low) field

8Leithe-Jasper et al., Phys. Rev. Lett. 91,
037208 (2003)
7www.qdusa.com/resources/pdf/1078-201.pdf
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Ref 11
Sc
10Hamlin et al., Phys. Rev. B 76, 012505 (2007)
9R. Movshovich, Phys. Rev. B 53, 5465 - 5471
(1996)
11Schilling, Magnetic susceptibility of
superconductors and other spin systems ed by
Hein et al., P107 (1991).
12
NHMFL high field ac susceptometer

• Instrumentation
• Sample position controlled by stepper motor
• AC current calibrator (e.g. Valhalla 2500) used
  for constant amp/phase ac current
• Lock-in technique for phase sensitive detection
• Ratio transformer for balancing12a
• Field modulation technique12b with modulation
  coil (1.81 mT/A) can be used for dHvA

12aBidinosti, RSI, 71 3816 (2000)
12bMagnetic Oscillations in Metals, D.
Shoenberg, Cambridge Press (1984).
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Torque magnetometer

F 0 for homogenous field (sample at field
center) Torque d (deflection of beam) metal
film cantilever ? capacitance (10-3 10-8
emu) piezoresistive cantilever ? resistance
(10-9 10-11 emu)
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single crystal sample placed in field center
When expressed in coordination of crystal axes
with cubic symmetry

(1) ? 0 if ? ?? (isotropic
magnetization) or if ?0 or 90, parallel to
in-plane or inter-plane. (2) ? gt 0 if ? lt ??
(3) ? lt 0 if ? gt ??
cf) Shape effect torque for isotropic
non-spherical sample (? ?2H)13
13Schmiedeshoff et al., PRB 48 16417 (1993)
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(1) Metal film cantilever
Dynamic range vs. sensitivity cantilever design
(thickness, length, ..) sample position choose
optimal angle for sensitivity or dynamic
range Material MP35N, Beryllium Copper alloy,
Phosphor Bronze (hard, non-magnetic) Consideration
of torsion (twisting)
Ref 15
15Brooks et al., RSI 58 117 (1987)
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• Instrumentation
• Capacitance measurement
• Eddy current effect
• Background due to gravitational force
• Mechanical noise (vibration isolation)

GR 1615 Bridge
Wein bridge
AH Bridge
0 15 V 50 20 kHz easy interface and
reading slow data acquisition
Use external oscillator and lock-in amp Fast data
acquisition Non-linear response Conversion
required
Coax cable with proper grounding required
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(2) Piezoresistive cantilever
Ref 16
Ref 17

• Piezoelectric AFM tip is used18
• Measure resistance change using a Wheatstone
  bridge type circuit
• Good for small mass/moment samples
• Low temperature heating of the piezoresistor
  (use less than 0.1 mA at 0.5 K)

16Tanaka et al., JACS 126 10518 (2004)
17E. Ohmichi et al., RSI, 73 3022 (2002)
18H. Takahashi, Ultramicroscopy 91 (2002) 6372.
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• Application
• Fermiology (dHvA)
• Magnetic Phase transitions
• magnetization anisotropy
• Superconductors (vortex, anisotropy..)

metamagnetic transition
HoNi2B2C
19Rathnayaka et al., Phys. Rev. B 76, 24526 (2007)
15Brooks et al., RSI 58 117 (1987)
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NHMFL high field torque magnetometer
I
compensation loop
Silicon beam cantilever
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VSM (Vibrating Sample Magnetometer)
Vrms mA?
VrmsVSM signal m moment A amplitude ?
frequency
1st VSM,

• Absolute magnetic moment can be measured
• Driving mechanism
• motor, pneumatic, piezo-actuator
• Feedback and phase-sensitive detection
• capacitative detection
• eddy current sensor
• servomotor

20Foner, RSI 30 548 (1959)
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NHMFL high field VSM (H lt 35 T, T gt 0.6 K)
EGG (Lakeshore) VSM system Vibrating freq. 82
Hz Amplitude 0.1 mm 10-3 10-5 emu
sensitivity Pick-up coil designed for better
stability
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NHMFL high pressure VSM ( H lt 9T, T gt 1.4 K)

• High Pressure Self-Locking Pressure Clamp
• Material High Purity (Co-free) BeCu
• Sample size 1 mm3
• Sample mass lt 10-2 gm
• Clamp mass 13 gm

Symmetrical design made of high purity BeCu1
22Guertin et al., Phys. Rev. B 65, 184413 (2002)
23R. P. Guertin et al., J. Appl. Phys. 103,
07B705 (2008).
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Summary
Useful references Ac susceptometer Magnetic
Susceptibility of Superconductors and Other Spin
Systems, Ed. By R. A. Hein, D. H.
Liebenberg Torque Magnetic Measurements with
Metal Film Cantilevers A Users Guide , D. Hall
(1999). (http//www.magnet.fsu.edu/usershub/scient
ificdivisions/dcfield/magnetometry/documents/canti
lever.pdf) dHvA measurement Magnetic
Oscillations in Metals, D. Shoenberg, Cambridge
Press (1984).