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Sensitive Measurement of a Fermi Surface

Sensitive Measurement of a Fermi Surface. Alexander S. Graffeo 2002 REU Program. Goal. To design and implement measuring equipment, which will increase the sensitivity of measurements in high magnetic fields, at a low cost. Fermi Energy. Imagine there are several electrons in a box at T=0.

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Sensitive Measurement of a Fermi Surface

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  1. Sensitive Measurement of a Fermi Surface Alexander S. Graffeo 2002 REU Program

  2. Goal • To design and implement measuring equipment, which will increase the sensitivity of measurements in high magnetic fields, at a low cost.

  3. Fermi Energy • Imagine there are several electrons in a box at T=0. • In accordance with the Pauli Exclusion Principle, a maximum of two electrons may occupy each energy level. Ef E2 E1 • The energy of the last filled level at T=0 is called the Fermi Energy Ef.

  4. What is a Fermi surface ? • These electrons exhibit wave-like properties. • Their motion is described by a wave vector K, consisting of Kx, Ky, and Kz components. • By connecting the points in k-space where energy of a wave vector equals the Fermi energy, contours may be formed. Kz Kx Ky

  5. The de Haas – Van Alphen Effect • While measuring Magnetization of Bismuth as a function of magnetic field at 14.2K, oscillations in M/H were observed. • A magnetized sample experiences a torque proportional to it’s magnetic moment T = m x B (all vector quantities) Where: T = torque m = magnetic dipole moment B = magnetic flux density Magnetization = m volume

  6. Measuring a Fermi Surface We can use the torque to measure oscillations in angular position of a sample as magnetic field strength and magnetization vary. A Wheatstone bridge circuit is used to measure small changes in resistance.

  7. Our Measurement Method – Micropiezolevers • When the micropiezolever is subjected to a magnetic field, the force causes the lever to bend. • This bending causes the resistance to change. F Sample ΔR

  8. The sample is placed on micropiezolever circuit. • The micropiezolevers may increase sensitivity to 10-11 emu, and only cost about $100.

  9. The micropiezolevers are placed on a probe and connected to a Wheatstone bridge

  10. Wheatstone Bridge • In most cases, is more accurate than an ohmmeter. • Measures resistance values over a wide range. • R3 = (R1/R2)Rx

  11. The Original Bridge • The wiring of the original box left something to be desired!

  12. Bridge #2 • A streamlined new look! • 25-Turn trimmer potentiometers.

  13. Bridge #3 • 25-turn, 100Ω trimmer potentiometers in series with 12-turn, 500Ω potentiometers.

  14. MgB2

  15. Sr2RuO4 Probe and Mounting

  16. The Fermi Surface of Sr2RuO4

  17. In Closing… • Mounting the sample proved possible with the use of micro-manipulators. • Despite being fragile, the micropiezolever has had the strength to support the sample. • Electronic bridge circuit has functioned properly as a bridge when tested on the lock-in. • It is expected from similar experiments that the goal of low cost, increased sensitivity will be met.

  18. ThisThanksSnake’sfor You! • Luis Balicas • Donovan Hall • Phil Meesan • REU Staff • Numerous employees at the NHMFL whom I constantly hounded for parts, equipment, and information.

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