Spin-droplet state of an interacting 2D electron system

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

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

3. Ferromagnetic Bloch Instability Decreasing density Long range ineraction Energy Hartree-Fockapproximation Unscreened interaction, no correlations: ~ 2

4. Phase diagram Attaccaliteet al. (2001) rs~26 First order transition at rs~20:Senatore et al. (2001)

5. Clean system • Very low density Wigner Crystal rs~37 B. Tanatar and D.C. Ceperley (1989) ferromagnetic

6. Clean system ferromagnetic antiferromagnetic • Very low density Wigner Crystal rs~37 B. Tanatar and D.C. Ceperley (1989) Very small energy difference!

7. Methods: Shubnikov - de Haas beatings 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)

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

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

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

11. Samples: Si Field effect transistors Russian samples, beginning of 80th, Holland samples, mid 80th Typical parameters =3.4 x104 cm2/Vs @1.7K Valley degeneracy 2 therefore ps 5 [mm]

12. The Principle of the Recharging Technique Small correction - geometrical capacitance Maxwell relation: magnetic moment per unit area Important: //, so the recharging method is distinct from magnetocapacitance.

13. Finite thickness contributions to at Diamagnetic contribution change Capacitance contribution

14. Modulated magnetic field B+dB Current Amplifier + Gate VG _ Out SiO2 Ohmic contact Si 2D electron gas Recharging Technique can be measured whenever is measurable i.e. recharging technique is applicable even in the insulator!

15. M m Interactions No interactions gmBB n mB No interactions n Interactions Expected behavior T=0, finite magnetic field Prus et al,2003 B>T

16. / at n=1.5 gmBB~2EF kT/4 / B (T)

17. Raw data, low fields Compare with single spins∂M/∂n=mBtanh(b), b=gmBB/2T

18. / at 1

19. / at

20. / at and The same characteristic magnetic field

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

22. d/dn(n), T=1.7-13K

23. d/dn(n), T=0.6-4K

24. vs. Temperature

25. vs. Temperature

26. / vs. Temperature and density Position of the maximum of goes to as

27. (n), T=1.7-13K Non-renormalized Pauli susceptibility at

28. Magnetic moment at B=2T

29. Comparison with Transport Measurements

30. Main observations • is nonlinear at surprisingly low characteristic magnetic • Field • Strong, faster than 1/ divergence • Density at which is maximal related to • the metal-insulator transition Possible scenario: few electron droplets • Being created as the density increases • Melted with density and temperature • Typical number spin of a droplet /

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

32. Conclusion: • In the Insulating state of the correlated 2D electron system:spontaneous formation of spin dropletswith a large spin S2. • The low field spin susceptibility is strongly temperature dependent (1/T2) even at high densities, • The spin droplets are detected up to densities well in metallic phase, coexisting with electron liquid • /changes sign as density or temperature increases. For T 0 this happens right at n=nc Problems : • temperature is unexpected • Spin droplets should lead to saturation of dephasing time • Role of valley degeneracy is unclear

33. 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!

34. Old results (Prus et al, 2003)

35. Field dependence of the magnetic moment

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

37. Raw data

38. Susceptibility in at B=2T

39. d/dn(n), Holland sample

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

41. Clean system ferromagnetic antiferromagnetic • Very low density Wigner Crystal rs~37 B. Tanatar and D.C. Ceperley (1989) Very small energy difference! • Higher densities – thermal potential singularities A. Finkelstein (1983), Castellani at al.,(1984) Shekhter, A. and Finkel'stein, A. M (2005)

42. Real system S=0 • Localized electrons Antiferromagnetic coupling Bhatt and Lee (1982)

43. Real system S=0 • Localized electrons Antiferromagnetic coupling Bhatt and Lee (1982)

44. Real system S=0 • Localized electrons Antiferromagnetic coupling Bhatt and Lee (1982) • Itinerant electrons • Disorder enhances exchange interactions spontaneous formation of finite spin droplets Andreev, A. V. & Kamenev, A. (1998) Kurland, I. L. and Aleiner, I. L. and Altshuler, B. L. (2000)