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Sasha Kuntsevich Nimrod Teneh Vladimir Pudalov Spin-droplet state of an interacting 2D electron system M. Reznikov Magnetic order in clean low- density systems Methods of magnetization measurements Recharging Technique Experimental results Implications Technion

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Electron gas with interactions Short range repulsive interaction 2nd order phase transition into ferromagnetic ordered state For a single-valley system Stoner (1947) Stoner instability

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Ferromagnetic Bloch Instability Decreasing density Energy

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Phase diagram Attaccalite et al. (2001) First order transition at r s ~20: Senatore et al. (2001) r s ~26

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Clean system B. Tanatar and D.C. Ceperley (1989) ferromagnetic

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Clean system Very small energy difference! antiferromagnetic ferromagnetic B. Tanatar and D.C. Ceperley (1989)

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Methods: Shubnikov - de Haas beatings F. Fang and P. Stiles (1968), T. Okamoto at al., (1999), S. Vitkalov at al. (2000), V. Pudalov at.al., (2001) 2 4 6 7 rsrs

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

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

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In-plane magnetoresistance A. Shashkin et al. PLR, 2001 Possible FM transition ??

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Samples: Si Field effect transistors Russian samples, beginning of 80 th, Holland samples, mid 80 th Typical parameters 3.4 x10 4 cm 2 /Vs @1.7K

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The Principle of the Recharging Technique Maxwell relation: Small correction

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Diamagnetic contribution Capacitance contribution

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Recharging Technique _ + VGVG Out Modulated magnetic field B+ Current Amplifier Ohmic contact Gate SiO 2 Si 2D electron gas

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Expected behavior T=0, finite magnetic field gg Interactions M n No interactions n Interactions Prus et al,2003 B>T

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B (T) g B B~2E F kT/4

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Raw data, low fields Compare with single spins M/n= B tanh(b), b=g B B/2T

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1

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The same characteristic magnetic field

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Interactions n n No interactions Interactions d /dn(n), expectations

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d /dn(n), T=1.7-13K

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d /dn(n), T=0.6-4K

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vs. Temperature

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(n), T=1.7-13K

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Magnetic moment at B=2T

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Comparison with Transport Measurements

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Main observations Possible scenario: few electron droplets

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Droplet scenario vs theory Fermi-liquid expectations: Spontaneous large spin droplets in disordered metal Diffusion enhanced interactions in quantum dots Mean Field treatment: Andreev, Kamenev (1998) Numerics: Shepelyansky (2001) Narozhny, B. N. and Aleiner, I. L. and Larkin, A. I. (2000)

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Conclusion: Problems :

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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!

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Old results (Prus et al, 2003)

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Field dependence of the magnetic moment

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In-plane magnetoresistance A. Shashkin et al. PLR, 2001Fleury, Weintal, 2010.

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Raw data

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Susceptibility in at B=2T

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d /dn(n), Holland sample

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Stoner Ferromagnetic Instability Stoner (1947) Finkelstein (1983) For a short range repulsive interaction Diffusion enhanced interactions in quantum dots Mean Field treatment: Andreev, Kamenev (1998) Numerics: Shepelyansky (2001)

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Clean system Very small energy difference! antiferromagnetic ferromagnetic A. Finkelstein (1983), Castellani at al.,(1984) Shekhter, A. and Finkel'stein, A. M (2005) B. Tanatar and D.C. Ceperley (1989)

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Real system S=0 Bhatt and Lee (1982)

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Real system S=0 Bhatt and Lee (1982)

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Real system S=0 Bhatt and Lee (1982) Andreev, A. V. & Kamenev, A. (1998) Kurland, I. L. and Aleiner, I. L. and Altshuler, B. L. (2000)

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