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

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

Ferromagnetic Bloch Instability Decreasing density Energy

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

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

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

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) rsrs

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

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

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

Samples: Si Field effect transistors Russian samples, beginning of 80 th, Holland samples, mid 80 th Typical parameters  3.4 x10 4 cm 2

The Principle of the Recharging Technique Maxwell relation: Small correction

Diamagnetic contribution Capacitance contribution

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

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

B (T) g  B B~2E F kT/4

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

1

The same characteristic magnetic field

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

d  /dn(n), T=1.7-13K

d  /dn(n), T=0.6-4K

vs. Temperature

 (n), T=1.7-13K

Magnetic moment at B=2T

Comparison with Transport Measurements

Main observations Possible scenario: few electron droplets

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)

Conclusion: Problems :

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!

Old results (Prus et al, 2003)

Field dependence of the magnetic moment

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

Raw data

Susceptibility in at B=2T

d  /dn(n), Holland sample

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)

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)

Real system S=0 Bhatt and Lee (1982)

Real system S=0 Bhatt and Lee (1982)

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)