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

1. Magnetometry at the NHMFLA Practical Guide to AC Susceptometer, Torque Magnetometer,VSM Eun Sang Choi National High Magnetic Field Laboratory

2. 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

3. What we measure: B or M SI : B = μH = μ0 (H+M) = μ0 (1+χ)H cgs : B = H + 4πM B = Magnetic flux density, Magnetic induction  susceptometer H = Magnetic field strength  experimentally controllable M = (Volume) Magnetization  magnetometer Usually H >> M  B(T), μ0H(T)

4. ω 2ω Ferromagnetic core 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).

5. (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

6. 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)

7. Primary coil coil 1 M1 secondary (pick-up) coil coil 2 sample M2 M1,2 : mutual inductance between primary and secondary 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 χac: complex susceptibility (χ’-i χ’’) χ’: in-phase signal χ’’: out of phase signal calibration factor (sensitivity)

8. 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, Tutton’s 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)

9. Signal compensator 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

10. Hopkinson maximum NaFe4Sb12 • 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

11. CePtPb antiferromagnet9 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. primary coil 34 AWG copper, 1000 turns secondary coils 50 AWG copper, 2700 turns each 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) 12b“Magnetic Oscillations in Metals”, D. Shoenberg, Cambridge Press (1984).

13. d H 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)

14.  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)  > 0 if|| <  (3)  < 0 if ||>  cf) Shape effect : torque for isotropic non-spherical sample ( ~ 2H)13 13Schmiedeshoff et al., PRB 48 16417 (1993)

15. (1) Metal film cantilever W: width, L: length Y: Young’s modulus I : Moment of inertia t : thickness 14Feynman et al., ” The Feynman Lectures on Physics” vol 2 (Reading, MA: Addison-Wesley) ch 38. 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)

16. Induced diamagnetic moment due to eddy current : depend on ramp rate, field direction for sweeping up field • 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

17. (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) 63–72.

18. 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)

19. Commercial AFM tip Seiko PRC 120 BeCu foil 12 ~ 75 μm thickness Interchangeable spacer G-10 or Brass (TMTSF)2ClO4 sample NHMFL high field torque magnetometer I+ compensation loop Silicon beam cantilever

20. Loud speaker VSM (Vibrating Sample Magnetometer) Vrms ~ mAω Vrms:VSM signal m : moment A : amplitude ω : 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)

21. driving head x-y adjustment z adjustment He3 can sample tube (filled with exchange gas) sample rod High field cryostat heaters Pick-up coils 46 AWG, 3000 turns cryostat positioner /isolator magnet BeCu 21Xu et al., RSI 67 3914 (1996) : pickup coil design NHMFL high field VSM (H < 35 T, T > 0.6 K) EG&G (Lakeshore) VSM system Vibrating freq. ~ 82 Hz Amplitude ~ 0.1 mm 10-3 ~ 10-5 emu sensitivity Pick-up coil designed for better stability

22. NHMFL high pressure VSM ( H < 9T, T > 1.4 K) • High Pressure Self-Locking Pressure Clamp • Material: High Purity (Co-free) BeCu • Sample size: ~ 1 mm3 • Sample mass: < 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).

23. 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 User’s Guide “, D. Hall (1999). (http://www.magnet.fsu.edu/usershub/scientificdivisions/dcfield/magnetometry/documents/cantilever.pdf) dHvA measurement : “Magnetic Oscillations in Metals”, D. Shoenberg, Cambridge Press (1984).