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Spin Susceptibility of a 2D Electron Gas

Spin Susceptibility of a 2D Electron Gas. M. Reznikov. Sasha Kuntsevich, Nimrod Teneh, V ladimir. Pudalov, Teun Klapwijk Aknowl eg ments: A. Finkelstein. Metal-Insulator Transition in a Silicon Inversion Layer. V. Pudalov at al., 2001. Motivation.

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Spin Susceptibility of a 2D Electron Gas

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  1. Spin Susceptibility of a 2D Electron Gas M. Reznikov Sasha Kuntsevich, Nimrod Teneh, Vladimir. Pudalov, Teun Klapwijk Aknowlegments: A. Finkelstein

  2. Metal-Insulator Transition in a Silicon Inversion Layer V. Pudalov at al., 2001

  3. Motivation • Theory: interaction and disorder enhanced susceptibility • A. Finkelstein (1983), Castellani at al.,(1984) • Temperature-dependent correction to Pauli Susceptibility due to electron-electron interaction (A. Finkelstein, A. Shekhter, 2006) A. Chubukov, D. Maslov,2009

  4. Shubnikov - de Haas measurements of the Spin Polarization 2 6 7 4 rs F. Fang and P. Stiles, (1968), T. Okamoto at al., (1999) S. Vitkalov at al. (2000), V. Pudalov at.al., (2001) Advantages Disadvantages • Straightforward separation between • orbital (diamagnetic) and spin contributions • Requires low temperatures and finite • magnetic fields (B B>kBT) • Problematic in the vicinity of the MIT

  5. Analysis of the in-plane magnetoresistance A. Shashkin et al. PLR, 2001, S. Vitkalov et al. PRL 2001 • Advantages: • Does not require high magnetic field • Critical density is accessible • Disadvantages: • Heavily interpretation-dependent: • a) Saturation of the in-plane magnetoresistance • full polarization • incorrect atlow B (e.g E. Tutuc at al.) • b) The saturation field may be recovered on the basis of the low field magnetoresistance

  6. In-plane magnetoresistance A. Shashkin et al. PLR, 2001, S. Vitkalov et al. PRL 2001

  7. Samples Si Field effect transistors Russian samples, beginning of 80th, Holland samples, mid 80th, ¼3.4 x104 cm2/Vs @1.7K Typical energy scales p¼ 3 ps¼~/(kB¢ 2K)

  8. ef W2D m WAl eVG e0 The Principle of the Measurements Maxwell relation:

  9. Modulated magnetic field B+dB Current Amplifier + Gate VG _ Out SiO2 Ohmic contact Si 2D electron gas Experimental setup Advantages Disadvantages • Measures thermodynamic magnetization • Accessibility of the “Insulating phase” • Does not require low temperatures • Measures thermodynamic magnetization • Measures , which is unknown • at small n; Requires assumptions for the • integration

  10. dm/dn, expectations for degenerate caseno interactions m gmBB Polarization field B

  11. dm/dn, expectations for a single spin

  12. Raw data, low fields

  13. Raw data

  14. d/dn(n), T=1.7¥13K, Russian sample

  15. d/dn(n), Holland sample

  16. Problem O. Prus, Y. Yaish, M. Reznikov, U. Sivan, and V. Pudalov, PRB 2003: Assumption: at large density the susceptibility is the renormalized Pauli one This assumption happened to be wrong!

  17. (n), T=1.7¥ 13K

  18. (n), T=1.7¥ 13K, offset 0.7V offset 0.7V offset 0.5V

  19. Old results (Prus et al, 2003)

  20. Susceptibility vs. Temperature

  21. Field dependence of the magnetic moment

  22. Susceptibility in at B=2T

  23. Maximal magnetization @ 1.7K

  24. Raw data

  25. -dM/dn at 1.5 1011 cm-2 B

  26. Comparison with Transport Measurements

  27. Conclusions • Low-field susceptibility is many times the Pauli one • Susceptibility is strongly temperature dependent • even at high densities (most surprising) • Low temperature susceptibility is strongly nonlinear • The field scale for the nonlinearity is Bc¼ kBT/6B

  28. ТД измерения: ранние результаты. A. Shashkin et al., PRL 96 036403 (2006). Порядок величины! (n=0.3 Гц) Образец закрывается при малых n ВЫВОД О ФМ НЕУСТОЙЧИВОСТИ; (B>1.5 Т, Т<0.6К) НЕТ ЗАВИСИМОСТИ ВОСПРИИМЧИВОСТИ ОТ Т.

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