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unit: mm Cell 12 Magnet 35.1 T, 32 mm bore Available cryostats: He3 (0.3 – 60 K) or VTI (1.4 – 300 K) Magnet/Power supply status monitoring computer Data Acquisition computer Data acquisition program Magnet control

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System D Rotator Probe Sample holder : side A Sample holder mounted on the probe Side A Side B Before mounting top view Sr 2 RuO 4 Magnetic torque Capacitance between the two parallel plates side view

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1.5 mm SrMnBi 2 Electrical transport Resistance (Rxx) Hall sensor (THS 118: GaAs based) Hall Resistance (Rxy) Ba 2 Fe 2 As 2 Surface conductivity TDO (Tunnel Diode Oscillator) resonance freq. shift PdCoO 2 Magnetic torque Resistance change of piezo-resistive device 0.25 mm Sample holder : side B 11.4 mm

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C. Bergemann et al., Physica B 294, 371 (2001) Torque: Capacitance signal, T= 30 mK Sr 2 RuO 4 Triplet superconductor (Tc = 1.4 K)

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BaFe 2 As 2 D. E. Graf et al., PRB 85, 134503 (2012) J. G. Analytis et al., PRB 80, 064507 (2009) TDO frequency shift 30 mK 350 mK Parent compound of 122 pnictide superconductors

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SrMnBi 2 K. Wang et al., PRB 85 041101(R) (2012) J. Park et al., PRL 107 126402 (2011) CaMnBi 2 SrMnBi 2 Dirac Fermion compound

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PdCoO 2 Metallic triangular lattice compound C. W. Hicks et al., PRL 109 116401 (2012) Torque signal (piezo-cantilever) T=0.7 K

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Measurement techniques Resistance measurements by instrumentation (Rxx, Rxy, piezo-cantilever) principle: apply current (current source) and measure voltage (voltmeter) Conventional lock-in amplifier technique Oscillating current applied, phase sensitive detection of corresponding voltage DC resistance measurement technique DC current with switching polarities to remove offset AC resistance bridge Resistance determined by nulling or measuring unbalanced signal Q: what is advantage/disadvantage of the lock-in technique compared to the DC technique? Capacitance measurement for magnetic torque AH capacitance bridge: automatic balancing GR capacitance bridge: manual balancing Q: what other physical properties can be measured by the capacitance measurement device? TDO resonance frequency measurement Typical capacitance bridge

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Exercises 1: Resistance measurement on the standard resistor Lock-in technique configure resistance measurement setup with 1 lock-in amplifier (SR 830) Change parameters (current, frequency, time constant,..) and check the voltage readings DC technique Configure measurement setup with 1 DC current source (Keithley 6221) and 1 DC nanovoltmeter (Keithly 2182) Apply constant DC current ( < 10 mA) and monitor the voltage Setup the Delta mode and test with different parameters (current, delay time,..) Exercises 2: Capacitance measurement on the standard capacitor (1)AH bridge : hook up coax cables to the decade capacitor box and press buttons (2) GR bridge configure GR bridge and 1 lockin-amplifer for capacitance measurement balance the GR bridge to find the capacitance value (should be similar to obtained from (1) find the conversion factor between lock-in signal and capacitance (hints given in the appendix)

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Exercises 3: Balancing the piezo-cantilever Demonstration 1: TDO measurement Exercises 4: Setting up instruments for the real samples inside cryostat Build a measurement circuit with a given bridge circuit box Balance the bridge (1)Setup instruments for the Hall sensor (DC resistance delta mode) and piezo- cantilever (lock-in technique). Refer to the breakout box diagram in the next page. NOTE: Do not apply currents until further notice. (2) Instructor will setup AC resistance bridge for the transport measurement (3) Connect cables to the AH bridge for the capacitance measurement (4) Using the data acquisition program, collect the data at zero field as a function of time

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Exercise/Demonstration: Data analysis Exercises 5: Data acquisition (1)Collect data while sweeping magnetic field under different instrumentation setup (2)Collect data at different temperatures (3)Collect data at different angles (1)Plot the data using data analysis program Q1) Plot the temperature vs. magnetic field. Why does temperature reading change with field? Any way to circumvent the problem? Q2) What is the oscillation frequency of the quantum oscillations? Q3) Capacitance torque signal from Sr2RuO4 sample look different from the text book (saw- tooth not sinusoidal). Why? (2) Perform FFT with different settings (field range, different background, FFT windows, …) NHMFL breakout box variable resistor can be used as pseudo-current source setup when combined with lock-in oscillator (answer given in the appendix)

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Configure Delta (picture above) : set I-high, I-low, Delay.,,,, Press Delta to arm Press TRIG to start delta mode operation Oscillator out to the current terminals with a large resistor connected in series Connect voltage terminals to voltage input (A-B mode) DC resistance measurement (delta mode) osc. out voltage input sample Current limiting resistor (R) I = V/(Rsample+R) ~ V/R (if R >> Rsample) Resistance measurement (Lock-in technique) Appendix I

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Appendix II Torque interaction analysis in Sr 2 RuO 4 by Naoki Kikugawa Raw data (before de-torque) FFT: 28 – 34.5T De-torqued FFT: 28 – 34.5 T Sr 2 RuO 4 T = 1.4 K B // ~ c axis Data taken at Cell 12 (May 21, 2014) Remember: The oscillation is periodic in 1/B not in 1/H

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